        ммммммммммммм                            ммм           мммм
     мллллллллплпппппллм       ммппппмммм млм  мллллллллмммммлпп плл
    пллллллллллллллм  плл   млллмллммм   пллллм плллллллмллмммллн лп
        пппллллллллллм он  лллллллллллпплмоллл    лллллм    пплллоп
Mo.iMP  мллм  плллллллнл  оллллллллл    олллл     олллллн      плп
      мллллллл  ллллллллн оллллллллн     ллл       лллллл
     млллллллн  олллллллл олллллллл       п        оллллллм   мл
    млллллллн    лллллллл  ллллллллн               оолллллллллп
   млплллллл мм  ллллллллн ллолллллн               оллллллпп
  млпллллллмллллмолллллллл ол пллллл           м   лнллллл             м
 мл оллллллллллп  ллллллллл плм  плллмм    ммлллп ол олллн         ммлл
лл   ллллллллп    ллллллллллм плм  пплллллллллп мммп ллллмммммммлллллп
 плм   млллп       пллллллллллм  ппмм ппмллпп  пллм   ппплплллллллпп
    ппппп                ппллп      ппппп        ппппппппппппп
          ARRoGANT                CoURiERS      WiTH     ESSaYS

Grade Level:       Type of Work           Subject/Topic is on:
 [ ]6-8                 [ ]Class Notes    [Gambling and science    ]
 [ ]9-10                [ ]Cliff Notes    [together.               ]
 [x]11-12               [x]Essay/Report   [                        ]
 [ ]College             [ ]Misc           [                        ]

 Dizzed: 07/94  # of Words:16500 School:Public          State:NY   
ФФФФФФФФФ>ФФФФФФФФФ>ФФФФФФФФФ>Chop Here>ФФФФФФФФФ>ФФФФФФФФФ>ФФФФФФФФФ>ФФФФФФФФФ
To appear in Social Epistemology, 1992.  (version appeared: in Proc.
Eighth Intl. Conf. on Risk and Gambling, London, 7/90.)

          C O U L D   G A M B L I N G   S A V E   S C I E N C E?
                    Encouraging an Honest Consensus

                          by Robin Hanson
              Visiting Researcher, The Foresight Institute
                P.O. Box 61058, Palo Alto, CA 94306 USA
                hanson@charon.arc.nasa.gov 510-651-7483

    The pace of scientific progress may be hindered by the tendency of our
academic institutions to reward being popular, rather than being right. A
market-based alternative, where scientists can more formally "stake their
reputation", is presented here.  It offers clear incentives to be careful
and honest while contributing to a visible, self-consistent consensus on
controversial (or routine) scientific questions.  In addition, it allows
patrons to choose questions to be researched without choosing people or
methods.  The bulk of this paper is spent examining potential problems with
the proposed approach.  After this examination, the idea still seems
plausible and worth further study.

INTRODUCTION

    After reviewing the discrepancy between what we want from academic
institutions and what we get from current institutions, a market-based
alternative called "idea futures" is suggested.  It is described through
both a set of specific scenarios and a set of detailed procedures.  Over
thirty possible problems and objections are examined in detail. Finally, a
development strategy is outlined and the possible advantages are
summarized.

THE PROBLEM

    THE SCIENTIFIC REVOLUTION Four centuries ago, some Europeans complained
that the existing academic institutions were biased against them. Insiders,
it was said, were "inflated by letters" and shunned anyone who dared
"speculate on anything out of the common way" [De]. Outsiders --
astrologers, chemists, and people like Bacon and Galileo -- argued that
they and their theories should be judged by how well they agreed with
observations, and not by how they agreed with the authorities of the day
[Gal].  This was the age of utopias [Whi], as these rebels debated possible
academic reforms and imagined whole new social institutions, for both
academia in particular and society in general.

    Within a century or so, the intellectual descendants of these outsiders
became the new insiders in a process now called the "Scientific
Revolution".  They introduced a new respect for observations along with new
social institutions, such as the Royal Society of London, inspired by those
utopian ideals.  Since then science has made impressive progress.  Most
controversial issues of four centuries ago seem long settled by now, and
continued research may well settle most of today's controversies.  Academia
can claim some credit for this, and academic institutions have continued to
evolve in response to perceived problems, formalizing publication in
journals, credit in citations, and evaluation in anonymous peer review.

    PROBLEMS WITH ACADEMIA Yet little has really changed.  Academia is
still largely a medieval guild, with a few powerful elites, many slave-like
apprentices, and members who hold a monopoly on the research patronage of
princes and the teaching of their sons.  Outsiders still complain about
bias, saying their evidence is ignored, and many observers
[Gh,Red,SmP,Syk,Tr,Tul] have noted some long-standing problems with the
research component of academia. {footnote: Teaching reform is beyond the
scope of this paper.  I am content to observe that there are no obvious
reasons why the changes I will propose should make teaching worse.}

    As currently practiced {footnote: Early peer reviewer consisted more of
personally observing experiments and trying to reproduce analyses.} peer
review is just another popularity contest, inducing familiar political
games; savvy players criticize outsiders, praise insiders, follow the
fashions insiders indicate, and avoid subjects between or outside the
familiar subjects.  It can take surprisingly long for outright lying by
insiders to be exposed [Red].  There are too few incentives to correct for
cognitive [Kah] and social [My] biases, such as wishful thinking,
overconfidence, anchoring [He], and preferring people with a background
similar to your own.

    Publication quantity is often the major measure of success, encouraging
redundant publication of "smallest publishable units" by many co-authors.
The need to have one's research appear original gives too little incentive
to see if it has already been done elsewhere, as is often the case, and
neglects efforts to integrate previous research.  A preoccupation with
"genius" and ideological wars over "true" scientific method [Gh] needlessly
detract from just trying to be useful.

    Perhaps the core problem is that academics are rewarded mainly for
telling a good story, rather than for being right. (By "right" I include
not only being literally correct, but also being on the right track, or
enabling work on the right track.)  Publications, grants, and tenure are
based what other insiders think today, independent of whether one's ideas
and results are proved correct or valuable later.  Even for researchers
with a good track record, grant proposals must usually describe in some
detail exactly what will be discovered and how; true exploratory work is
done on the sly.  This emphasis on story-telling rewards the eloquent, who
know how to persuade by ignoring evidence that goes against their view, and
by other standard tricks [Cia].

    Admittedly, someone who has published an unusual idea that has proven
right is thought of more highly, all else being equal.  But all else is
usually not equal.  Outsiders find it hard to get an unusual idea
published, and being able to say "I told you so" is of little help to
academics who have failed to gain tenure.  The powerful often get credit
for the successes of those under them [Re].  Only in the most experimental
fields, where feedback is direct and frequent, can we expect people who are
disliked -- but usually right -- to be rewarded through informal
reputations.

    Perhaps our biggest problem is the distortion evident when a science
question becomes relevant for public policy, as in the recent debates over
"Star Wars" or the greenhouse effect.  The popular media tend to focus on
those scientists prone to hyperbole.  An honest consensus of relevant
experts is often lost from public view, as advocates on each side accuse
the other of bias and self-interest.  Public policy can suffer dramatically
as a result, a consequence that becomes more serious as the pace of
technological change quickens.

    On the whole, current academic institutions seem less than ideal, with
incentives that reward being popular, fashionable, and eloquent, instead of
being right.

    INCENTIVES MATTER Are these complaints just sour grapes?  Those who do
well by an existing system tend to believe problems are minor. But even if
the best ideas eventually win, we should worry if the people who advocate
those ideas don't win.  Good intentions and culture can only go so far in
countering bad incentives; if you must publish or perish, you will do what
it takes to publish (or perish).

    The social organization of any human effort can have a tremendous
effect on its efficiency.   Consider that different past societies with
different ways of organizing science have had very different rates of
scientific progress; compare Europe with China over the last five
centuries.  Our rate of progress may be less than 2% of what it could be
[Be].

    Are we wasting precious resources?  Imagine what would happen if we
used academic peer review to decide what products to manufacture. Proposals
for new products would be reviewed anonymously by powerful people who
produce similar products.  These reviewers would pass judgement without
taking any personal risk, and those judged favorably would win regardless
of how useful their product turned out to be.

    I much prefer our current business system, with all of its problems,
where investors must take a personal risk when they endorse a product.
Institutions like the stock market are comparatively egalitarian and
flexible, allowing most anyone to participate in the ongoing debate about
the profit potential of any public business or the relative potential of
various industries, management styles, etc.  Why can't we have academic
research institutions more like this?

    ACADEMIC REFORMS Most efforts to improve academic institutions focus on
incremental reform within the existing peer review framework. Should
reviewers be anonymous?  Should submissions be anonymous?  How many people
should review each proposal?

    Occasionally someone proposes a more radical reform within the current
framework.  The surprising lack of agreement among reviewers [Cic] has lead
some [Gi] to suggest we fund equally or randomly among "qualified"
applicants, and let everything be published.  Conversely, the fact that a
small fraction of scientists receive most citations [Co] has lead some [By]
to suggest that we simple give $1M a year, no strings attached, to the top
thousand scientists, chosen by an iterated popularity poll. Some have
suggested universities and private labs be funded in proportion to their
publication [Ro] or citation [Ts] count.  And some [Tu] advocate prizes,
once a central method for funding research [He]. Still others suggest
scrapping the whole thing, abolishing tenure [SmP] or government funding
[Fe,Wa] in favor of some existing alternative like private patrons, popular
media, patents, or research tax credits.

    Once in a while a whole new social institution is proposed. Science
courts [Kan] (also called "scientific adversary procedures") were invented
to blunt hyperbole on science controversies by using court-like proceedings
to encourage cross-examination and to document areas of agreement.
Hypertext publishing [Dr,Han88] imagines an electronic publishing medium
where any critic could directly link a criticism to any published item, and
where readers could decide what is worth reading by have software
automatically combine the direct evaluations of previous readers they
respect.

    In this paper I propose a new academic institution, tentatively called
"idea futures", intended to overcome some of the limitations of existing
alternatives.  It is utopian in the sense of describing a coherent vision
of how things might be rather different, but hopefully practical in the
sense of considering what could go wrong and how to start small.

    WHAT WE WANT Before considering specific mechanisms, let us reflect a
moment on what we want from academic incentives.  We want to encourage
honesty and fair play; the game should be open to anyone to prove
him/herself.  Patrons who fund research, either private foundations or
governments, presumably want research to be directed toward the academic
subjects and questions of interest to those funders.  (Patrons also include
the researchers themselves, to the extent that reduced salaries are
understood to be in exchange for some research autonomy.)  On controversial
questions, we want a clear measure of the current opinion of relevant
experts, a measure which political advocates could not easily distort.  And
those who contribute to such a measure should have clear incentives to be
careful and honest.

    Presumably we want as much progress as possible per effort invested, at
least in situations where the following notion of "progress" makes sense.
Consider a well-posed question, such as "Is the Earth basically
spherical?", with a handful of possible answers (such as "No, it's flat").
Experience indicates that, with enough study and evidence, one of the
answers will eventually stand out as best to most anyone who considers the
question carefully.  At least this seems to happen for most questions that
have been traditionally labeled "scientific"; questions about the morality
of abortion or the nature of God may not fare as well.  Where there is such
a limiting "right" answer, "progress" can mean the rate at which general
scientific opinion converges to that answer.  {footnote: This definition of
progress is more objective than citation counts [Co], and hopefully avoids
debates about whether more knowledge is good, or whether there is really an
ultimate truth.}

    Translating these goals to an individual level, we want our
institutions to reward academics for pushing scientific opinion toward the
"right" answer, presumably by somehow increasing their reputation,
influence, or resources.  Let us imagine an academic who, after some
reflection or observation, comes to a tentative conclusion which he/she
would like others to consider.  If most everyone already agrees with this
conclusion, even without seeing the new supporting evidence or analysis,
the academic should receive little credit for just making an "obvious"
claim.

    However, credit should be possible if the claim is surprising, i.e., if
people who have not yet seen the evidence are not yet willing to agree. If,
upon reviewing the evidence, most everyone now agrees with the surprising
claim, then the academic should certainly receive some credit.  And, in
fact, peer review can handle this case.  But what if there is not uniform
agreement?  It still seems that the academic should be rewarded, if this
surprising claim is eventually born out. And others who supported this
claim in the face of disagreement should also gain credit [Led], since they
helped push the general opinion in the right direction.

    Why shouldn't savvy academics now win credit by supporting as many
claims as possible, or by multiplying controversies?  Clearly they should
risk losing credit when they are wrong, so that credit is in some ways
conserved.  The ratio of possible loss to gain should depend on how unusual
one's position is.  Siding with the majority and being right should gain
one less than siding with a minority and being right. The total amount
gained or lost should depend on how much of their reputation each academic
has chosen to stake on this issue, as well as on how interesting the issue
is to the ultimate research funders.

    In summary, part of what we want from academic incentives is a fair
game for staking our reputation, so that on questions of interest to
funders, we converge as fast as possible to the "right" answer.

THE PROPOSAL

    Surprising as it may seem, such a social institution exists.  It is
relatively simple, cheap, decentralized, and egalitarian.  It could create
a consensus on disputed science questions that would be clear, expert,
honest, and self-consistent across a wide range of issues.  This consensus
should respond quickly to new information, and predict at least as well as
any other co-existing consensus mechanism.  It is well-grounded in our best
theories of decision and incentives.

    And it is ancient.  We need only revive and embellish a suggestion made
back during the utopian scientific revolution.  Chemical physicians,
excluded by the standard physicians from teaching in the British schools,
repeatedly offered challenges like the following (circa 1651):

    Oh ye Schooles. ... Let us take out of the hospitals, out of the Camps,
or  from elsewhere, 200, or 500 poor People, that have Fevers, Pleurisies,
etc.   Let us divide them into halfes, let us cast lots, that one halfe of
them may  fall to my share, and the other to yours; ... we shall see how
many Funerals  both of us shall have: But let the reward of the contention
or wager, be 300 Florens, deposited on both sides: Here your business is
decided. [De]

    They proposed to bet on their medical therapies, apparently believing
bets to be a useful augmentation of the existing academic incentives! Bets
are a long-established and robust reputation mechanism, widely seen as a
cure for excessive verbal wrangling; you "put your money where your mouth
is".  In science and elsewhere, phrases like "you bet" are standard ways to
express confidence.  Offers to make token bets are particularly compelling,
and scientists of equal stature often make and publicize such bets, with
recent bets on resource depletion, computer chess, black holes [Hal], solar
neutrinos, nuclear weapon yields [Ev], and cold fusion [Gar,Lew,WSJ].

    Nor is gambling foreign to science funding.  King Charles II, founding
patron of the Royal Society of London, was fond of laying wagers on the
outcome of the Society's experiments [ShS].  Until 1830, public lotteries
funded Colombia, Harvard, and Yale [Gei].  In 1872 Leland Stanford, founder
of Stanford University, hired Eadweard Muybridge to help win his bet that a
trotting horse has all four legs off the ground at some point; in the
process Eadweard invented moving pictures [Jac].

    Consider the example of Piers Corbyn, a London astrophysicist who has
been unable to get academic meteorologists interested in his unusual theory
of long-term weather cycles [NS].  Since June 1988 he has been making bets
to gain publicity, betting against the bookmaker William Hill, who uses
odds posted by the British Metrological Service. And he has been winning.
Over the last 26 months (4/89-5/91), Corbyn has made at least 9 bets a
month (and averaged over 20 bets a month) and has won 80% of these bets,
gaining an average rate of return of over 25% per bet.  (Depending on what
independence you assume between bets in a given month, the chance of this
happening randomly is between one in 400 and one in 1050.)  Yet the Service
still refuses to take Piers seriously, or make even token bets against him.
Which doesn't seem quite fair; hasn't Pier earned the right to be
considered?  William Hill has taken on the bets for the publicity, but is
tired of losing, and has adjusted their odds accordingly.  Why shouldn't
these be the odds used for official British agricultural policy, instead of
the Service's predictions?

    Or consider Julian Simon, a population and natural resource optimist,
who found he could not compete for either popular or academic attention
with best-selling doomsayers like Paul Ehrlich.  So in 1980 Simon
challenged Ehrlich to bet on whether the price of five basic metals,
corrected for inflation, would rise or fall over the next decade. Ehrlich
accepted, and Simon won, as would most anyone who bet that way in the last
two centuries.  This win brought Simon publicity [Ti], but mostly in the
form of high-profile editorials saying "Yeah he won this one, but I
challenge him to bet on a more meaningful indicator such as ..."  In fact,
however, not only won't Ehrlich bet again, though his predictions remain
unchanged, but none of these editorial writers will actually put their
money where there mouths are!  And the papers that published these
editorials won't publish letters from Simon accepting their challenges
[Si].  Shouldn't Simon's open challenges count as much as best-sellers in
setting environmental policy?    -

    If the primary way that academics are now rewarded for being right,
rather than popular, is an informal process for staking their reputation,
which has various biases because of its informality, and if we want a
better reputation game, why not literally make bets and formalize the
process?

    Imagine a betting pool or market on most disputed science questions,
with the going odds available to the popular media, and treated socially as
the current academic consensus.  Imagine that academics are expected to
"put up or shut up" and accompany claims with at least token bets, and that
statistics are collected on how well people do.  Imagine that funding
agencies subsidize pools on questions of interest to them, and that
research labs pay for much of their research with winnings from previous
pools.  And imagine that anyone could play, either to take a stand on an
important issue, or to insure against technological risk.

    This would be an "idea futures" market, which I offer as an alternative
to existing academic social institutions.  Somewhat like a corn futures
market, where one can bet on the future price of corn, here one bets on the
future settlement of a present scientific controversy.  This is admittedly
an unusual (though not entirely original [Bru,Ho81,Ho84,Lea,So])
suggestion; but consider what might happen.

SCENARIOS

    CONTINENTAL DRIFT In 1915 German meteorologist Alfred Wegener published
his theory of continental drift, for which he had collected extensive
evidence.  But contemporaries considered his theory to be "impossible", and
Wegener died an intellectual outcast in 1930 [Mar]. Yet in the 1960's his
theory began to be taken seriously, and is now the established view.
Wegener eventually gained fame, but overall academia seems to discourage
activity like his.  Some of Wegener's peers, for example, probably found
his thesis plausible, but decided that to say so publicly would be a poor
career move.

    With idea futures, Wegener could have opened a market for people to bet
on his theory, perhaps to be judged by some official body of geologists in
a century.  He could have then offered to bet a token amount at, say, 1-4
odds, in effect saying there was at least at 20% chance his claim would be
vindicated.  His opponents would have had to accept this estimate, and its
implications about the importance of Wegener's research, or they would have
to bet enough to drive the market odds down to something a little closer to
"impossible".  They could not suppress Wegener merely by silence or
ridicule.

    As Wegener increased his stake, buying more bets to move the price back
up, his opponents would hopefully think just a little more carefully before
betting even more to move the price back down.  Others might find it in
their interest to support Wegener; anyone who thought the consensus odds
were wrong would expect to make money by betting, and would thereby move
the consensus toward what they believe. Everyone would have a clear
incentive to be careful and honest.

    The market would encourage more research related to continental drift,
as one could make money by being the first to trade on new relevant
information. Eventually the evidence would more clearly tip in Wegener's
favor, and the price of his bets would rise.  Wegener, or his children,
could then sell those bets and reap some rewards.  While those rewards
would not make up for years of neglect, at least he would get something.

    As the controversy became settled, and opinions converged, people would
gradually sell and leave the market.  Few people, if any, need be left for
the final judging, which could usually be avoided (using mechanisms to be
described below).

    COLD FUSION A more recent controversy began in March 1989, when Pons
and Fleishman announced "fusion in a jar" at a dramatic press conference.
In the months that followed, media aftershocks of confirmation attempts
were tracked by thousands of scientists and others, who argued with each
other about the chances of cold fusion being real.  Proposals to bet came
up often, even in the public debates. Critics, uncomfortable with airing
scientific disputes in public, complained that Pons and Fleishman broke the
rules by going to the popular media instead of through normal peer review
channels, unfairly gaining extra attention and funding. Supporters
countered that popular media spread information quickly to other
scientists; cold fusion, if right, was too important to wait for normal
channels.

    In the journal Science, Robert Pool speculated that a market in cold
fusion might have gone something like Figure 1 [Poo].  If there really had
been a betting market, then there really would have been a market price
that journalists like Pool could publish as news.  A table of going prices
might appear on the science page in the newspaper, much like the stock page
in the business section, conveying current scientific opinion better than
the current "balanced" interviews with extremists on all sides.  It's been
suggested [Ze] that the added information in betting market prices might
have helped resolve the debate more quickly.

                      FUSION CONFIDENCE INDEX
                      
                Georgia confirms  Russia heat    Stanford 
                               |  neutrons       confirms
   Announce fusion    TexaxAM  |  |              |            
   in bottle          confirms |  |   U.Wash     *             
      |         Hungarian  |   |  *   tritium    ***           
      | BYU     neutrons   |   *** *   |         *  *          
      | confirms     |     |  *    *   *        *    **        
       \    |        |      * *     * **        *      *****   
        \   *        |     * *       *  *       *              
         ** **       *     *            *      *               
        *  *  *     * *   *   Georgia    *     *               
       *       *    * ** *    reverses---*     *              
     **        **  *    *                 *   *             
               * * *    |        TexaxAM  *   *              
                  *  MIT sees    hedges----*  *              
                     nothing                **                

       Mar23      Apr3     Apr10     Apr14     Apr18         

  Figure 1  A Hypothetical Market in Cold Fusion (Science 28Apr89)

    There needn't be a conflict between going through slow proper channels
and getting the word out, if a fast market were a proper channel. The
effect of staged media events might be reduced as it might not be news if
the price didn't change; advocates would have to convince, not the average
listener, but those people willing to make bets. Remaining biases, such as
the overconfidence evident in figure 1, would be reduced by technical
traders and other trading specialists.

    Cold fusion businesses would have been less risky to start.  As it was,
a new fusion business had to bet both that cold fusion was real, and that
they were the best group to develop and market it in that case. With idea
futures they could, by both starting a business and betting against cold
fusion (essentially taking out insurance), really only be betting on their
ability to develop cold fusion if it were real.

    Insights from a great many people whose opinions on the cold fusion
controversy were ignored, such as inarticulate folks without Ph.Ds, could
have been integrated in a decentralized manner.  Popular play would end up
subsidizing professional efforts on questions of popular interest, offering
more "direct democracy" in setting research priorities.

    NEUTRINO MASS Betting markets could also function in the absence of
overt controversy, as in the following (hypothetical) story.

    Once upon a time the Great Science Foundation decided it would be a
"good thing" to know the mass of the electron neutrino.  Instead of trying
to figure out who would be a good person to work on this, or what a good
research strategy would be, they decided simply to subsidize betting
markets on the neutrino mass.  They spent millions.

    Soon the market odds were about 5% that the mass was above 0.1eV, and
Gung Ho Labs became intrigued by the profits to be made.  They estimated
that for about $300K spent on two researchers over 3 years, they could make
a high confidence measurement of whether the mass was above 0.1eV. So they
went ahead with the project, and later got their result, which they kept
very secret.  While the market now estimated the chance of a mass over
0.1eV at 4%, their experiment said the chance was at most 0.1%.

    So they quietly bought bets against a high mass, moving the price down
to 2.5% in the process.  They then revealed their results to the world, and
tried their best to convince people that their experiment was solid. After
a few months they mostly succeeded, and when the price had dropped to 0.7%
they began to sell the bets they had made.  They made $500K off of the
information they had created, which more than covered their expenses to get
that information.

    If Gung Ho Labs had failed to convince the world of their results, they
would have faced the difficult choice of quitting at a loss, or holding out
for the long-term.  A careful internal review would probably be conducted
before making such a decision.

    Internally, Gung Ho would be free to use whatever organizational
structures it found effective; even peer review, tenure, and fixed
salaries.  The two researchers need not risk their life savings to be paid
for their efforts.  But the discipline of the external market should keep
these internal institutions from degenerating into mere popularity
contests.

    KILLER PEANUT BUTTER Once upon another time, Munchem Biolabs found
compelling evidence that peanut butter was more deadly than most
pesticides, a conclusion that Lunch Industries Exclusive (LIE) wanted
desperately to suppress.  LIE's usual procedure was to fund a bunch of
competing studies to come to opposite conclusions, which usually kept the
waters muddy enough that legislators and customers would ignore it all.
But this time they had to deal with an idea futures market on the question,
and the public was beginning to take the odds in such markets seriously.

    Munchem had moved the market odds of deadly peanut butter up rather
high.  LIE now had two choices; either they could use overwhelming cash to
move the odds back down, or use competing studies, advertising, etc. to
persuade others to bet on their side.

    If they bet alone, they would know they were throwing their money away
with no obvious limit on future spending.  Not only might Munchem find
allies, but LIE employees who knew they were bluffing might be tempted to
pick up a little free money with some anonymous bets.  If word of Lunch's
bluff got out, as insider information often does, investors would flock in
and wipe out the effect of LIE's bets.

    If LIE tried to throw away other people's money through a persuasion
campaign, they would face a market dominated, as most liquid markets are,
by battle-hardened speculators.  These investors, not easily persuaded by
clever jingles, would quickly hook up with research insiders, who generally
know which labs tend to find whatever results their customers want.

    So in the end, Lunch Industries accepted the market odds, and began
research on non-toxic peanut butter.

PROCEDURES

    Rather than just present an abstract utopian vision of market-based
academic incentives, this paper aims to consider in some detail what
problems might arise and possible approaches for dealing with them.  The
following is a core set of procedures tentatively selected to deal best
with known problems, a core that will be expanded upon later in this paper.
No doubt, experience with real idea futures markets will show many of these
suggestions to have been naive.  I offer them primarily to make plausible
the idea that betting markets could be applied to a much wider range of
scientific questions than is presently considered feasible.  (This section
is somewhat dense, and may be profitably skimmed on a first reading.)

    ASSETS Imagine that John bets Mary $5, at even odds, that it will rain
next Monday. Since they don't entirely trust each other, John and Mary put
the bet in writing and each give $5 to Frank, a trusted third party. John
has essentially paid $5 for an I.O.U. that says "Worth $10 If Rain Monday",
since if he wins he gets $5 from Mary and his own $5 back. Mary's I.O.U.
says "Worth $10 If Not Rain Monday".  On Tuesday one of them can cash in
their I.O.U. for $10 from Frank.

    This standard betting scenario can be improved by breaking it into
different transactions; first create the I.O.U.s and then sell them.
Replace Frank with a stable financial institution, let's call it a "bank",
which will sell a pair of "$10 if rain", "$10 if not rain" coupons to
anyone for a price of $10.  The bank takes no risk, since exactly one of
the coupons will be worth $10 in the end.  And since the bank holds the $10
in the meantime, it can afford to offer interest on the $10, and perhaps
pay a local meteorologist to be an impartial judge. Now Mary can first buy
a coupon pair from the bank for $10 and then offer to sell her "$10 if
rain" coupon to John or anyone for $5, retaining the "$10 if not rain" for
herself.

    A central clearinghouse for such offers, which matched compatible
offers and insured that traders made good on their offers, would always
hold a best current offer to sell and to buy.  If the transaction costs of
processing an offer through the clearinghouse were small, as current
technology allows, then the "spread" between these offers could be quite
small, leaving a going "market price".  A going price of $3.20 for "$10 if
rain Monday" would represent a temporary consensus of a 32% chance of rain
Monday.

    In general, these markets trade assets of the form "X if A" (often
called "contingent assets"), where X is some pre-existing "base" asset and
A is one of a set of mutually exclusive claims that some judging
organization agrees, eventually, to choose from.  The base X can be any
stock, bond, currency, commodity, or even another compatible contingent
asset.  The set of claims constitutes a "question", and each claim is one
possible answer to the question.  To enable trading on a question, we
require an agreement between several parties - an author, a judge, and one
or more banks, registries, clearinghouses, and randomness checkers.

    An author carefully words a set of claims, and a judging organization
agrees if necessary, to offer a verdict in favor of one of these claims at
some, perhaps indirectly specified, date.  Registries hold records of
public, i.e. not anonymous, trades made at clearinghouses. (Clearinghouses
may be required to hold additional private records of all trades, available
to be subpoenaed by criminal investigators.)

    Consider a question with possible answers {A,B,...}.  Any bank
authorized in the agreement on that question can "split" any allowed base X
(usually anything) into the assets {"X if A", "X if B", ...}, or "join"
those assets back into X.  In the example above, $10 was split into "$10 if
rain" and "$10 if not rain".  The bank is trusted to report the net effect
of these transactions to a central agent, who keeps track of the net
"market capital" that has been split along this question.

    On the specified date, and a short wait after a public announcement,
the judges are given an agreed-upon judging-fee in order to study the
question and render their verdict.  Verdicts assign a percentage of
validity to each of the possible question answers.  If the verdict is 98%
in favor of A, then banks are authorized to let people exchange their "X if
A" assets for 98% of X.

    The judging-fee is obtained from the banks, who devalue the current
assets contingent on that question by some percentage, a percentage which
can be no more than a pre-specified max-judging-percentage. This
devaluation creates an incentive for traders to "settle out of court" and
sell before the judging date.

    What if there is too little capital in the market to support the
required judging fee?  John and Mary's market only has $10 in it, and with
a 10% max-judging-fee, only $1 is available for judging, short of the $5 a
meteorologist judge might require.  In this case we can hold an "audit
lottery" [Pol]. {footnote: This name is suggested by the way an auditor
might randomly select expense reports for more careful scrutiny.} The
current market capital, $10, is gambled with whomever offers the best
price, among those approved by the randomness checker. If the gamble is
won, every asset contingent on this question increases in value, resulting
in enough market capital for judging to proceed, in this case $50.  If the
gamble is lost, all such assets become worthless and judging is not needed.
{footnote: Investors can insure against the added risk audit lotteries
impose by putting money into an pot to be gambled in the same lottery, but
on the other side.}

    Judges can be given more flexibility to deal better with uncertainties
regarding when a question will be judgeable and how much that will cost.
For example, the max-judging-percentage could be spent in discrete units,
each with a specific percentage-unit and fee-unit.  After spending each
percentage-unit, the judges would have the choice to postpone judging to a
later date and/or raise the next fee-unit. If necessary, an audit lottery
would be held before each new unit.

    If desired, judges can also be given a direct financial incentive to be
careful and honest.  "Appeals" markets can be created on the same question,
but judged by an independent group much later and/or with a much higher
judging-fee.  For a limited period after a verdict is announced, an amount,
up to a fixed fraction of the original judging-fee, would be spent trying
to move the price in the appeals market toward the verdict specified.
Judges would end up with some contingent assets saying their verdict would
be upheld in the appeals market, assets they could sell immediately, at a
loss, if they so chose.

    Idea futures markets need no central management.  Anyone could author a
claim on any subject of interest to them, contract with different judging
groups to judge that claim on different dates, and allow different banks to
deal in each question.  And anyone should be able to open a clearinghouse
to sell any asset.  All of these groups could compete openly for the
attention and respect of investors.

    INVESTORS Investors could be as diverse as they are in current markets,
each focusing on some specialty while avoiding risk from other areas. For
example, if the market odds are "incoherent", i.e., deviate from the
standard axioms of probability, a trader who corrects that deviation can
make better than the average rate of return without significant risk.
Therefore coherence specialists should keep the market consensus roughly
consistent over a wide range of subjects.  Similarly, technical traders
would keep the pattern of price changes close to the ideal random walk
[Mal].  The market odds should also quickly reflect information contained
in any co-existing consensus measures, such as opinion polls or reports of
elite committees, as traders could make easy money if alternative measures
were reliably better predictors than the market.

    A contingent asset, like "X if F", that is split again creates
conjunctive contingent assets like "X if F and A".  Conjuncts which combine
many claims may be popular, since they offer investors the greatest
expected return.  Conjunctive assets also allow one to bet the conditional
probability of A given F and remain insensitive to the verdict on F.  In
this way diverse traders, each of whom has only local knowledge, could
manage a large network of dependencies such as the currently popular "Bayes
net" models [Pe].

    SOCIAL ATTITUDES Some new social attitudes toward these new markets are
important elements of the envisioned approach.  As with current financial
markets, the market odds should be treated as the current social consensus
on a question by popular media and policy makers. While one may of course
disagree with this consensus in conversation, it is not impolite for others
to inquire whether one who so disagrees has made investments commensurate
with their wealth and the fuss they are making.  People who do so invest
should receive the same sort of social credit now granted to "do-gooder"
advocates who devote personal resources to changing current opinion on some
important issue. Like Phileas Fogg, the hero of Vernes Around the World in
Eighty Days, "a man who rather laid wagers for honor's sake than for the
stake proposed" [Ve], these investors should not be treated as mere
risk-loving gamblers.

    Social credit should also go to philanthropists who choose to subsidize
a market on some important question.  By funding an automatic
inventory-based [St] market-maker, which always offers to buy or sell at
prices determined solely by its current inventory, one gives away money
only to those who move the market price in the direction of its final
verdict.

    Reputation scores could be computed from each person's public trades,
recorded at registries.  A trade is considered "public" if the trader
committed at trading time to a date at which the trade would be publicly
revealed, and that date has passed.  One simple reputation score would be
the ratio of the current market value of assets held to their value when
purchased, corrected for a few distortions.  People with high reputation
scores should be respected for having been right against the crowd, and
such scores might even compete with G.P.A.s or number of papers published
as an evaluation measure.

OBJECTIONS

    The main difference between "blue sky" fantasies and serious but
radical suggestions is in how well they handle the details.  If you are
like most readers, you will by now have thought of one or more problems
with or objections to idea futures.  If so, you are encouraged to scan this
section and go directly to the issues of concern to you.  (Most of these
issues have been raised by at least three independent commentators in
previous discussions.)

    ISN'T GAMBLING ILLEGAL?  Yes, betting markets on science questions
appear to be only legal in Great Britain, where they are highly regulated.
Even Nevada, which allows sports betting, prohibits general betting to
avoid scandals that might "taint" the gambling industry. Which is a shame
because most of the arguments against betting, discussed below, do not
apply well to science betting.  We allow scattered markets that give us
rather good consensus estimates on horse races and football teams, yet not
on important science and technology questions!  In the long term perhaps we
can persuade legislators to allow science bets because of their extra
benefits and reduced problems. Science betting certainly seems easier to
justify than the currently popular regressive taxation through state
lotteries.

    ISN'T BETTING A USELESS ZERO-SUM GAME?   A standard argument for making
betting illegal is to keep people from wasting their energies in
unproductive activities.  The only obvious value in betting on dice throws
is entertainment, but laws to prohibit this usually also prohibit much
more.  Life insurance, joint stock companies [Bre], and commodity futures
markets [Ros] were all prohibited by anti-gambling laws until advocates
managed to obtain exemptions.

    Being monetarily zero sum does not make betting useless.  Betting
markets allow traders to reduce risk, and create informative prices.  In
liquid markets most of the trading, liquidity, and price rationalization
comes from speculators, for whom the market is basically a betting game.
Buying any particular stock in the stock market, for example, is basically
a bet in a zero-sum game when compared to investing in the standard
"market" combination of all assets in the same tax and risk category.
(While, if the prices are irrational, such bets may help the economy as a
whole, this "externality" also benefits people not betting on that
question.)

    In fact, a standard way to analyze financial portfolios is to break
them into contingent assets, each of which has value in only one possible
world [ShW].  A "complete" market, where one can bet on anything, is best,
allowing investors to minimize risk and maximize expected return [La].

    Science bets would not only allow corporations to more easily insure
against technological risk, but they would create prices embodying the sort
of valuable information that governments now fund research to obtain.  When
the betting stakes are invested in stocks, the money is hopefully being put
into productive use by those companies. Therefore, ignoring transaction
costs and judging fees, the average rate of return of contingent assets
split from stocks would be the same as the return on those stocks.

    DOES ANYBODY EVER BET THIS WAY?  Liquid markets in contingent assets
are a somewhat different betting mechanism from the usual bookies or
pari-mutuels.  But they are not untried.  Such markets are widely used to
teach MBA students about how markets work [Fo], and are usually done on
elections.  Financial traders sometimes use them to bet on sports. And I
have developed a board game where players use such a market to bet on a
murder mystery as it unfolds.  Most ordinary people learn the mechanism
very quickly.

    WHAT ABOUT COMPULSIVE GAMBLING?  About 2% of the population seems
unable to resist the temptation to risk more than they can afford to lose
[APA] in casinos, racetracks, and high risk financial markets.  Lost in the
thrill of "action" and the hope that all of their financial worries will
soon be over, they often regret their excess later, and resort to desperate
measures, like theft, to pay debts.

    Compulsive gambling is encouraged by advertising and easy access to
games with a quick and possibly large payoff.  British law reduces this
problem by requiring casino players to apply 48 hours in advance, by
allowing them to sign up on lists of people to be excluded from all
casinos, and by forbidding youth and on-site alcohol, entertainment, and
credit [Ke].  Margin limits in financial markets serve some similar
functions.

    Governments may impose similar rules to discourage compulsive gambling
in idea futures, though it is important that any advertising restrictions
not prevent the wide dissemination of current consensus odds on important
issues.  More importantly, unless options (or investments on margin) are
offered, science questions are generally too long term to be a problem,
offering no more "action" than long-term stock investments.  Traders who
regret their purchase a few days later can sell and get most of their money
back.  And, given that many other options markets exist, it is not clear
that allowing science options would increase opportunities for compulsive
risky investing.

    IS THERE ENOUGH INTEREST IN SCIENCE QUESTIONS?  A recent science
fiction [Bre] novel imagined wide-spread betting on science and technology
questions, supplanting horse racing in popularity.  And it is possible that
having a direct, if small, influence and personal stake in science would
heighten the public's interest.  At present, though, fewer people probably
follow science than football.

    We don't need to interest everyone, however, just enough to pay for the
modest overheads involved.  Few people have interest and opinions about the
future price of corn, yet corn futures markets thrive.  A great many people
are now involved in scientific research, many more follow scientific
journals, and even more follow science in the popular media. Many of these
people have strong opinions on various science controversies and feel they
have insufficient opportunity to express them.  Idea futures would thrive
if it tapped only a small fraction of current interest and effort.

    Having a fraction of science funding channeled through betting markets
would certainly accomplish this.  So might basic attitude changes toward
seeing markets as a legitimate place to "take a stand" on important issues,
trading scores as indicators of who is right more often, and the market
price as a valid consensus measure.  Idea futures does not need large sums
of money to be successful; even when there is only $100 bet on a question,
the market still offers the social benefit of a visible consensus and
incentives for honesty.

    WILL THESE MARKETS BE TOO THIN?  In a market with low "liquidity",
there are so few traders that you have to wait a while to find someone
willing to trade with you.  Automated market-makers [Hak], always ready to
trade at prices determined by their current inventory, can increase
liquidity and maintain a small "spread" between their buy and sell price
offers. And they can be very cheap if the basic transaction costs are low,
which they could be if thousands of markets shared the same computerized
market place.

    But the market might remain "thin" in the sense that prices could
change quickly against a trader in response to each small amount traded, so
they would have to wait to get a "reasonable" price.  A lack of expected
market thickness can be a self-fulfilling prophecy, since traders prefer
thick markets [Ec].  This is a standard explanation for the limited number
of futures and options markets currently available.

    Funding channeled through market-makers would of course thicken the
markets, as would consistency arbitrage and conditional offers that connect
questions.  And improving computer technology, with lower transaction costs
and automated trading strategies, should make thinner markets more
tolerable.  Besides, two people making a bet is a very thin market, but it
happens all the time.  And just one person posting an offer to bet on a new
subject could be an important contribution to our social consensus.

    Thin markets are known for being good places to find overlooked
bargains, and are less prone to speculative bubbles (a single rational
person can squash one).  A thin idea futures market may actually seem
better to some people, as the cost to change the current market consensus
would be less.  But thicker markets are better in general.

    DOESN'T BETTING ONLY WORK FOR CLEAR CUT QUESTIONS LIKE HORSE RACES?
Most organized betting focuses on questions which, like sporting events,
will become very clearly resolved in a fixed time.  This minimizes disputed
verdicts and judging costs, and it makes sense for risk and
entertainment-seeking bettors to focus on such subjects.  But this does not
imply that, given a specific subject area, betting markets are not a
reasonable alternative to other consensus, reputation, and incentive
mechanisms.  Any incentive mechanism must pick some arbiter of quality, and
subjects that are difficult for bets are also difficult for other
approaches.  For example, peer review, which uses averages of anonymous
expert reviews as a quality measure, is widely believed to work better in
the "hard sciences" than elsewhere.

    Eventually most scientific controversies seem to get resolved enough to
settle a bet.  This resolvability is in fact central to popular notions of
what defines science.  Scientific claims are often defined as claims of
"fact" which future evidence could possibly disprove [Pop], or at least
alter our degree of confidence in.  And science is widely believed to be
"progressive", so that as evidence accumulates and relevant studies
continue, opinions gradually converge.  Beautiful theories killed by ugly
facts are left behind.  Or as Bacon said, "Truth is the daughter, not of
authority, but of time".

    Actually, most people believe that opinions on most questions of fact
usually convergence with time, evidence, and sincere study.  We hope that
history will prove us right.  We debate and discuss, essentially saying
"I'll bet if we talked it out, you'd see I'm right".  We take the advice of
experts, indicating that we think we would come to believe what the experts
believe, if only we were to study what the experts have studied.

    Even if we aren't sure whether opinions will converge, we think there
is a good chance they would converge if only a knowledgeable and detached
enough group would spend enough effort to study and debate the question.
And if that group is diverse and independent enough, we believe we would
probably agree with them.  If so, we should accept their verdict to settle
a bet.

    HOW OFTEN DO BELIEFS REALLY CONVERGE?  Just because people believe
their opinions converge, doesn't mean that they do. After all, there are
strong social reasons to want to believe in convergence.  Even if most
questions that are settled today were once controversial, this doesn't mean
that most old controversies are now settled.  Perhaps yesterday's questions
referred to concepts that are not even considered to make sense today.
Historical studies, examining random scientific questions and claims of
several centuries ago, should be done to shed light on these doubts.

    But there are reasons to be optimistic.  Standard decision theory,
though it does not adequately account for the computational costs of
deducing the implications of theories and evidence, is instructive and
indicates that rational agents should come to agree [Se]. Consider an ideal
decision theory agent who has a degree of belief in some particular claim A
and continues to observe new evidence. Asymptotically, either all new
evidence will be irrelevant and have no bearing on A, or the agent will
become certain about whether A is true or false.  Now imagine that the
claim A specifies a detailed possible world, i.e. says that the real world
is one particular world out of the many possible worlds.  If two ideal
agents start out with wildly different beliefs, but neither of them is
completely certain about A, and if they both observe the same not
asymptotically-irrelevant evidence, then they will asymptotically come to
agree about A.

    Studies indicate that people also have strong tendencies to conform and
agree when exposed to each others opinions [Li] and arguments [My]. In
fact, the rate at which they come to agree often seems faster that can be
rationally justified by decision theory.   Randomly selected legal juries
usually come to a unanimous verdict on complex legal questions.

    WHAT IF BELIEFS NEVER CONVERGE?  Even if beliefs usually converged,
idea futures might be unworkable if it dealt badly enough with situations
where beliefs don't converge.  One approach is to have mutually exclusive
claim sets include a "this question too vague to judge" claim which the
judges could choose if it seemed clear that no amount of study or time
would ever allow a choice between the rest.  Most people could then bet on
the question conditional on it being resolved.  This solution fails,
however, if sincere beliefs never converge and yet it never becomes clear
whether or not beliefs will converge.  A deadline by which a question must
be resolved could deal with this, but has other disadvantages.

    If investors can reasonably estimate the chances that a question will
be unresolvable in this manner, then the problem is manageable. High-risk
questions will only be traded if there is enough disagreement [Jaf] or
subsidies to justify it, and for low-risk questions the problem can be
ignored.  And, it seems, resolvability can be estimated. Questions about
religion and morals are more difficult, as are certain long-standing
riddles like the nature of consciousness.  On the other hand, a question
about a physical property of a substance, like a bond angle in some new
molecule, seems quite resolvable.  As a rule, one should prefer questions
closer to direct observations.  And general claims for which relevant
evidence will always be available should do better than claims like what
someone had for breakfast ten years ago.

    WHAT DO CONVERGENT BELIEFS HAVE TO DO WITH TRUTH?  The philosopher
Peirce claimed that "The opinion which is fated to be ultimately agreed to
by all who investigate, is what we mean by the truth" [Th]. However, the
question of whether the convergent opinion we might all come to with
unlimited evidence, study, and debate is the way the world "really" is, is
beyond the scope of the paper.  Even if it isn't "truth", we are all
interested in it, and it's hard to think of a better truth-estimate on
which to base academic incentives.

    WHAT ABOUT BADLY WORDED CLAIMS?  Even if an issue becomes settled, a
poorly worded claim on that issue may be unresolvable.  To avoid this, we
need techniques for avoiding ambiguity and incentives for players to use
them.

    Wording a claim so it is both relevant to some important issue and
minimally ambiguous is a skill that is routinely learned in many
professions.  Lawyers and philosophers obtain clarity through standardized
words and language, and experimental scientists are adept at finding
connections between abstract theories and specific observations.  Claims
should avoid slippery concepts and phrasing which allows many
interpretations.  Verbose annotations can also help by discussing
motivations, examples, intended word meanings, judging criteria, etc.

    If copyright laws are interpreted as applying to claim wordings, then
claim authors may be able to charge an extra royalty fee for each join.
Claim authors would then compete with each other for royalties from
investors, who would prefer authors with reputations for writing clear and
interesting claims. Added incentives come if authors bet against their
claim being judged too vague.

    To avoid excessive costs in forming a claim, a question could hold a
"clarification lottery".  After a certain time, or when the market capital
reached a certain amount, judges could be funded in the usual manner to
replace a hastily worded claim with a more considered one.

    Even when one cannot really word a good claim to bet on directly,
markets offer other ways to bet on a subject.  For example, if one believed
that when physicists disagree with chemists, the chemists are usually
right, one could invest in a "basket" or mutual fund which bets on the side
of chemists in as many controversies as possible.

    CAN'T WRONG IDEAS STILL BE USEFUL?  Absolutely.  If you think an idea
is probably wrong, but is probably more like the right answer than anything
else around, then bet on that.  If you just think that work on the idea is
likely to inspire something interesting, then bet on that. These questions
will be harder to judge though.

    WHAT IF THE FINE PRINT DIFFERS FROM THE SUMMARY?  Verbose claims would
probably be described by short summary sentences or phrases in price lists,
offers, etc.  As with contracts and political ballot initiatives, there are
problems when a deceptive title differs from the fine print. In extreme
cases people might sue for misrepresentation, but usually we can only
encourage the buyer to beware.

    WHAT ABOUT SUCKER BETS?  If a stranger offers to bet you on an oddball
subject, there is a good chance they are trying to trick you with a
deceptive claim.  Even if it looks like you couldn't lose, you are
well-advised to decline; the fact that they are making an offer gives you
information.

    In markets on pre-existing controversies where many traders have
already examined the claims, this is less likely, though still possible. In
general, traders should look claims over carefully and not bet unless they
honestly think they know better than than the other traders.

    DON'T SCIENCE QUESTIONS RESOLVE TOO SLOWLY?  The fundamental questions
that get people interested in science, such as whether the universe is
infinite, can take decades or even centuries to resolve.  But this does not
prevent markets in such questions. Most any newspaper will show that people
regularly buy bonds scheduled to mature in forty years. Fifty year-olds who
buy such bonds are not counting on living to be ninety; they know they can
sell the bonds in the market at any time.

    At present, you usually can't get a Ph.D. on whether the universe is
infinite; you focus instead on a smaller question that is hopefully
relevant for the bigger ones.  Idea futures investors will similarly prefer
shorter-term questions.  A question that takes ten years to resolve (say
starting at 50/50 and ending more than 90% certain 90% of the time) should
have the same sort of daily price fluctuations (around 1.5%) as stocks do,
and so support a similar mix of short-term speculators, and long-term
fundamentals-oriented investors.

    But for longer-term questions, investing in fundamentals is less
attractive.  Less information comes out per unit time in a long-term
market, so there is less money to be made for a given market thickness. And
if you must hold out for decades until other investors come to their
senses, the extra rate of return above the market average that you get for
your information may be very small, and so you may prefer to quit now if
you have better opportunities elsewhere.  To make things worse, this
creates an opportunity for strategic behavior.  Someone might move the
price in some direction and try to hold it there in the hope that other
traders will not be willing to hold out as long and therefore quit at a
loss.

    Finally, you may not trust the underlying financial institutions to
remain stable over a century or more.  Few people would probably bet that
"Nuclear war will destroy most of civilization", even though many people
would like to for insurance reasons.  And even if the banks don't go
bankrupt, uncertainties about the relative long-term value of different
base assets the betting stakes could be invested in may completely swamp
any added return from winning a bet.  This problem could be minimized if
the "market asset" [ShW], a maximally diversified world mutual fund, became
the standard base asset.

    Even with all these problems, there will probably be rather thick and
well subsidized markets on a few very basic science questions, as funding
agencies and amateurs seeking to influence important issues would focus on
them.  Such questions could be connected, through a network of conditional
offers, to related shorter-term questions which research could more
directly resolve, allowing researchers of simpler questions to obtain some
of the subsidies on the basic questions.

    In financial markets, the conventional wisdom is that longer-term price
movements are less rational, as there is less incentive to correct
irrational deviations.  But there is still some incentive, and so idea
futures may still offer an improvement over the existing situation.

    WHY SHOULD I TRUST THE JUDGES?  Even when sincere opinions would
converge, investors may worry about judges being biased by bribes or
various shared interests and associations.  Fortunately, investors get to
pick the assets they buy, and therefore the judges they bet on.  So they
can prefer long-lived judging organizations with reputations for fairness
and avoiding scandals, and which use various available means to discourage
foul play.

    Incentives for traders to settle out of court and avoid judging
altogether certainly help avoid judging foul play.  So do clear-cut claims
and judging criteria that leave little room for judging discretion.  If we
wait so long that the right verdict becomes "obvious" it would also be hard
for judges to cheat.  Also more trustworthy are juries of people who have
never had a stake in the question, randomly selected from a large
population, deliberating openly and offering to consider any relevant
evidence.

    The question of whether some proposed evidence is relevant for some
deliberation could even have its own betting market; juries could offer to
consider any evidence for which the market odds of relevance were above
some threshold.

    Incentives to detect foul play could come from both the ability to sue
cheating judges, and possibly from large bonds which judges might post
payable to anyone who uncovers such corruption.  Also, any persistent
difference in the market odds on the same claim with different judges would
constitute consensus about judging bias, flagging those judges for closer
scrutiny.  Judge rating agencies might form.  Finally, "appeals" markets
can give judges a direct incentive to be careful and honest, since judges
must then bet that their verdict will be upheld on appeal.

    WON'T JUDGING COST TOO MUCH?  Through audit lotteries, one can keep the
percentage taken by judges below any given threshold, and still afford to
pay for very detailed judging, even going so far as to choose many jurors
from widely different cultures and train them in one or more specialties
before having them adjudicate some specific issue! This approach is mainly
limited by risk aversion, which limits the attractiveness of large wins.
Most people will not want to bet so much on any one question that the
amount they might win would be much more than their total wealth.  A one in
a billion chance of winning a billion dollars is not worth as much to most
people as a one in a thousand chance of winning a thousand dollars.  If the
amount one would need to bet to avoid this effect is too small, it is not
worth the bother and people will bet nothing on the question.

    WON'T WEALTHY PEOPLE HAVE TOO MUCH INFLUENCE?  Markets are not opinion
polls where the rich get more votes; to use market influence one must risk
losing it.  As in existing financial markets, rich investors who are not
specialists in some particular area will prefer to get investment advice
from someone who is a specialist, or avoid investing in that area entirely.
This is similar to the way that powerful people defer to academic
specialists now.  Rich people who carelessly throw their weight around will
lose their riches.

    Even so, the wealthier social classes will have more influence, as they
do now in most areas of life, including academia.  If this is a problem
which you are willing to invoke the force of government to solve (I am
reluctant to do so), then the natural solution is general wealth
redistribution. This is much more cost-effective than crudely trying to
keep the rich out of any particular walk of life.

    If you worry that markets would create large inequalities in academia,
don't.  Influence in academia, as measured for example by number of papers
published [Pr], is far more concentrated than in most walks of life.  It
seems unlikely that markets would make things worse, and could well make
things much better, as people would not need degrees or the blessing of the
academic elites to play as equals.

    WON'T THE MARKET BE DOMINATED BY FOOLS?  Again, markets are not opinion
polls.  Anyone can invest in any open market, but they only choose to
invest where they think they have special insight or insurance needs. Even
if they are mistaken about their special insights into, say, the gold
market, they are fairly quickly taught otherwise.  Most people who play
commodity markets, for example, lose their stake and quit within a year.
Such markets are dominated by the minority who have managed to play and not
go broke.  If you believe otherwise, and know of some market where the
prices are obviously wrong, I challenge you to "put your money where your
mouth is" and take some of that free money you believe is there for the
taking.  It's easy to bad-mouth the stupid public before you have tried to
beat them.

    WON'T ADVERTISING MANIPULATE OPINION?  Advertising, in the sense of
campaigns to persuade through evidence and arguments, exists now in
academia and would certainly persist.  Advertising, in the sense of clever
jingles and sex appeal to grab the subconscious of the impulse buyer,
should not be a problem.  People do not try to affect the price of corn
futures with clever jingles; it would be like trying to sell cars by
offering free balloons to Consumer Reports technicians. The savvy investors
who dominate markets are smarter than that.

    AREN'T MARKETS FULL OF CHEATS AND THIEVES?  Yes, but this does not
usually distort the incentives or the consensus price much.  Most cheating
is not "manipulating the price", which is rather hard to do in a liquid
market, but conflicts of interest where people who supposedly represent
others instead act in their own interest, giving poor advice to clients and
using information gained from clients.

    Insider trading is mentioned below.  But brokers and investment
advisors are the worst case.  In markets you win whenever you can get
others to do what you just did, or when you predict what they will do and
do it first. Brokers and investment advisors often tell you to buy whatever
they would like to sell, and charge you large commissions for the "advice".
Brokers often trade for themselves just before they execute trades for you;
stop orders and margin calls are especially lucrative.

    To avoid being cheated, be careful who you trust.  Avoid brokers who
trade for themselves, and advisors who do not take the same risk they
advise for you.

    As bets, idea futures markets cannot be cornered or monopolized. No
matter how many bets have been made, other people are always free to bet
more.

    WHAT ABOUT INSIDER TRADING?  When an employee of a company makes money
by trading on inside information they have about that company, or by
telling someone else so they can trade, that employee is considered to be
going against the interest of the other stockholders who own the company.
Employment contracts and laws can forbid this conflict of interest, though
price movements just before major announcements show that a substantial
amount of such trading happens anyway.

    Fortunately nature has no insiders or employees.  The only similar
problem in idea futures is when a research lab is trying to keep a result
temporarily secret before trading on it, and an employee sneaks out and
trades first.  This could be dealt with exactly as stock insider trading is
now, through private trading records accessible to criminal investigators.

    WHAT ABOUT "MORAL HAZARD"?  One of the advantages of a market is that
it offers incentives to anyone to come and contribute their knowledge about
the world.  A disadvantage is that, since changing the world can give one
special knowledge about it, people may have an incentive to cause harm.  If
we allow anyone to bet on your lifespan, then someone may decide to kill
you just to win a bet.  And this murder may be much harder to solve than
most since, with anonymous trading, most anyone might be a potential
suspect.  (Though criminal investigators may be able to learn who really
made what "anonymous" trades.)  For this reason, there are usually
restrictions on who may buy how much life insurance on you.

    Moral hazard should be less of a problem for basic questions about
nature that people cannot change, though it could conceivably be a problem
for short-term trading and options that bet on when information will come
out. We wouldn't want someone to blow up the latest accelerator to prevent
results from coming out, or to kill some patients to slant a medical study.

    Yet we shouldn't prevent open markets if the chance of foul play seems
small.  Anyone is allowed to trade stock, even though there is a
possibility that someone will sell short the stock of the makers of a pain
reliever, and then poison some packages to depress their sales. Only for
the rare claim where the risk of harm seemed particularly high might one
justify a prior restraint limiting who could have how much stake on the
different sides of a question.

    WHAT ABOUT INCENTIVES TO START FALSE RUMORS?  A "rumor" is just
information, perhaps false, passed informally through a social network.
Maliciously false rumors occur whenever people both have an interest in
what other socially connected people think about a question, and when there
is inadequate feedback for learning what rumors were false, so that people
can discount unreliable sources.

    In current academia, there is often enough feedback to discourage false
rumors about what results are about to be published.  Word of mouth which
discredits a junior researcher, however, can trash his or her reputation
without others ever really finding out if the rumors were right.

    Markets both encourage and discourage false rumors.  Markets give more
people an interest in fooling other people, but also improve the feedback
about what rumors were right.  And the market price offers an alternative
to informal information channels.  Again, don't believe everything you
hear; trust advisors with a good track record who take the same risk they
advise you to.

    WHAT ABOUT INCENTIVES TO KEEP INFORMATION SECRET?  If you acquired a
piece of information where it was clear which side of what questions the
information favored, then your best strategy would be to buy on those
favored sides, reveal and publicize your information (perhaps after selling
it to other traders), wait for the price to rise, and then sell at a
profit.  If, however, the implications of the information are not clear,
you might be tempted to sit tight and wait for further revelations, even
though you risk other people stumbling on to your insight in the meantime.
It is similar with incentives to publish. Unless you can connect your
insight to currently popular issues, and package enough of them together to
make a paper, you cannot get published and so you may keep the idea to
yourself.

One approach might be to formulate a question more closely related to your
information, and then try to convince some funding agency that your
question is interesting, even if its implications are not clear. Or you
could subsidize your question, in the hope that this would encourage others
to figure out its implications and create conditional offers connecting it
to other questions.  Either approach might induce enough market thickness
to make your information pay off.

WON'T AN APPARENT CONSENSUS CREATE A CROWD MENTALITY?  People might think
they agreed more than they actually did, defer to a consensus that had
little thought behind it, and so create the social analogues of anchoring
and overconfidence [Kah].  Would creativity be suppressed?

Markets with less thought behind them should give themselves away by being
thinner.  If not, and some of us catch wind of this trend, we could make
money by correcting for it.  And, for what it's worth, the market odds at
horse races actually tend to be underconfident, being biased toward
long-shots.  Markets encourage people to be contrarian; the only reason to
trade, to not own the same mix of investments as everyone else, is because
you think the consensus is wrong, or for insurance needs.

    WILL THE NEW INCENTIVES SLOW OR STOP CONVERGENCE?  This is the opposite
of the above problem.  People with a stake on a certain side may become
mentally biased toward that side, resisting the rational implications of
mounting evidence.  This is of course not a new phenomenon in academia, and
so it's hard to see why the problem would be worse.  Except for issues
closely connected to basic "ideologies" about which most everyone has an
opinion, we can hope to find impartial jurors not overwhelmingly biased by
either side.

    WON'T DIFFERENT CLAIM WORDINGS, JUDGES, AND BASE ASSETS CONFUSE THE
CONSENSUS?  Unless the performance of a base asset correlates with a claim,
the claim's market odds should be independent of base, and arbitrageurs can
easily enforce this.  If the prices on the same claim judged by different
judges were persistently different, this would constitute consensus about
judging bias, a situation that judges would want to avoid.  If different
claim wordings on an issue have very different prices, this represents
consensus that there are really several different issues to be
distinguished.  For each distinguishable issue, traders seeking liquidity
will probably congregate around one or a handful of base
asset/wording/judge combinations, thereby avoiding a combinatorial
explosion.

    WON'T THE CONSENSUS REFLECT RISK PREFERENCES AS WELL AS BELIEFS? Yes,
the amount one should bet depends on one's beliefs, attitude toward risk,
and the stake one already has in a question [Kad]. Risk-avoiders bet less
than risk-takers, and bet less on the side that they already have a stake
in. Price distortions from this should be minor, unless most everyone has
substantial non-betting stakes on the same side, or if beliefs correlate
significantly with such stakes, and if the stakes held approach each
person's total wealth.  One exception is that few people would bet for
"Technology will soon make us all too rich to care about money", even if
they believed it.

    It might seem that questions with extremely lop-sided odds would also
be a problem.  Too few people might bet that "energy is conserved" (EC) if
they very confidently expecting to win very little.  But by splitting EC
assets along other questions, people could jointly support EC, debate other
questions, and get a higher average return.  In general, traders should
keep splitting until liquidity or risk considerations dominate.

    Some people have worried that opinionated yet extremely risk averse
people, unwilling to bet on anything, would be unfairly labeled "insincere"
debaters.  But it is hard for me to imagine that they could not afford to
risk even $10 a year so that we could develop a reputation score for them.
If it is the risk of a low reputation score that scares them, perhaps they
should not act so opinionated.

    WON'T BETTING CHALLENGES DISCOURAGE CREATIVITY?  If people were
expected to bet on every idea that comes out of their mouth, they would be
more reluctant to think up wild ideas, most of which are going to be bad.
Hopefully we can maintain a distinction between saying "Here is an
interesting idea to think about" and "This is the way it is, why won't you
agree?", only expecting people to put up or shut up in the second case.

    WHAT'S THE POINT OF A "CONSENSUS" THAT PEOPLE DISAGREE WITH? Regardless
of the name used, people often want to pool their differing individual
estimates on some issue into a composite estimate.  This is most clearly
needed in the "public choice" problem, where citizen estimates must be
combined into government policy.  But we also have a more general need for
social institutions where experts combine their estimates on some subject
into composite estimates, estimates that non-experts can use to make
individual choices.  Several such institutions may compete for attention,
but the need remains.

    Most work on consensus measures [Gen,Gr,Syn] focuses on various
explicit functions for combining individual beliefs, and some simple
variations of these [Man] are now used as academic consensus mechanisms.
Compared to these, betting markets not only offer superior incentives [Ei]
for people to bother to make their beliefs explicit and honest, but betting
markets have the following unique claim to the word "consensus".

    It is in the personal interest of an ideal decision theory agent to
make all external actions as if they agreed with the market consensus
[Kad,Na], without any coercion.  Agents should buy contingent assets up to
the point where their marginal rates of substitution are the same, i.e.
where they all agree on the relative value of getting one more dollar for
sure vs. even more dollars in some contingency.  An external observer, who
can offer agents trades or choices but cannot tell how much each agent has
already bet, cannot tell that the agents internally disagree.

    Insurance-based proposals [Fa] are similar in spirit to the betting
markets proposed here, as is the following proposal for dealing with the
public choice problem [Mu].  If a government threatens to make a change,
sells insurance on the change either way, and then makes the choice that is
cheapest for them, they produce an efficient "Pareto optimal" result.

    ISN'T IT BETTER FOR PEOPLE TO ARGUE OUT THEIR OWN DISPUTES?  Yes, which
is why we want incentives, such as audit lotteries, for parties to settle
out of court and avoid judging.  Idea futures is only intended to
discourage insincere debaters.

    Another way to avoid judging is to hold "argue lotteries" which are
like audit lotteries except that judges are not invoked.  The idea is to
focus attention on a smaller number of markets where more is at stake. This
should induce more discussion and examination of such questions, perhaps
resulting in more related questions being formed. Hopefully, opinions would
naturally converge, and people would leave the market. Judges are really
only there to discourage self-deception and strategic bargaining, so that
the market odds eventually reflect the "obvious".

    WON'T THIS HAVE THE SAME PROBLEMS AS PATENTS?  No [Hir].  With patents
we must decide who owns an idea, and so a centralized legal system must
make a great many subtle decisions with insufficient evidence and
expertise.  We must examine history to decide who contributed how much to
the idea.  We must define some sharp legal boundaries that determine what
it is to use the idea.  With present patent law, we must also decide if an
idea is true, if it is "original", if it is "obvious", if it is a
"process", if it was revealed properly, etc.  Bets are much more flexible;
we need only decide if an idea is right, and we can each choose who is to
judge that question.  Government intervention and international agreement
are not needed.

    WOULDN'T ANONYMOUS TRADING SCREW UP REPUTATION STATISTICS? Perhaps
people could make private trades to move prices out of line, and then make
public trades on the other side to bring them back, so that those trades do
better than average.  This is somewhat like giving someone a wad of money
by dropping it in the park and having them wander by an hour later to pick
it up.  If the park is crowded enough, someone else will have found it by
then.  In the market, anyone else could make money by stopping the price
from moving out of line.  The problem is more serious, however, if everyone
accepts that only one trader has any information about a question, and so
no one else wants to bet there. If identifiable, such markets should be
excluded from reputation scores.

    IF THIS IS SO GREAT, WHY HASN'T IT HAPPENED ALREADY?  If it was in
people's interest, wouldn't there be such markets by now?  Well, if we
always assumed this we might never do anything new, but it's important to
ask this question.  The fact that science bets have been legal only in
Britain, and then only in the last three decades is only part of an
explanation.

    English bookmakers perceive little demand for science bets, and so take
them mainly to induce popular articles mentioning the going odds on unusual
subjects [ShG].  This publicity brings in new clients, who may then be
switched to the "real" betting on sports. Because of this, bookies prefer
small bets on subjects "in good taste" that anyone can understand, like
UFOs, Yetis, and Moon landings.  They avoid subjects that seem too esoteric
for the general public, like the recent "cold fusion" claims, and subjects
that won't very clearly resolve themselves, as a judging industry has not
yet evolved.

    Bookmakers traditionally prefer to set prices and stick to them, rather
than setting up markets in order to play market-maker with the fluctuating
prices.  Because of this, they are usually unwilling to offer bets on
claims where they do not know how to estimate the odds, and few bookies
have advanced science educations.  As a result, they mainly take safe bets,
siding with the scientific establishment against "crazy" outside theories,
which doesn't help the image problem betting has in many quarters.

    English bookmakers do not seem to have seriously tried to sell
imagine-conscious academics on science bets, through arguments like those
in this paper.  Nor, to my knowledge, has the possibility for betting
markets as a funding mechanism been pointed out. Questions of interest to
academics are now avoided and no visible influenceable consensus is formed;
one cannot even subscribe to a publication listing the going prices on
science questions.  It should be possible to improve on this.

    CAN NATIONS FUNDING RESEARCH THIS WAY APPROPRIATE THE BENEFITS? A
popular argument for government-funded research says that, left to
themselves, people won't produce enough basic knowledge [Pa].  If a
knowledge producer publishes its results, then "free riders" can use this
knowledge without paying the producer.  Patents on basic knowledge are
considered too fuzzy to enforce, and trade secrets are said to fail because
of difficulties keeping basic information secret, and in figuring out who
would find basic knowledge useful.

    Of course if nations do subsidize research, they can fall victim to
international free riders, i.e., countries that mainly apply research done
elsewhere.   Some discount this by saying that most research knowledge is
never published, but tacit and embodied in the skills of the researchers.
Thus subsidies largely benefit researchers and companies located near
enough to easily collaborate with and hire such researchers.  Of course
such a locality of benefits would suggest that research is best funded at a
local level, or even privately within a large university campus.

    A need for local appropriation of benefit argues against indirect
funding methods, like prizes or idea futures, which cannot as easily
control where the research they induce is performed.  But such mechanisms
might be well suited for science-for-its-own-sake philanthropy and for
international funding of research, as such indirect methods can better
avoid favoritism toward any particular nation.

    SHOULDN'T WE APPEAL TO HIGHER MOTIVES THAN GREED?  The very formulation
of the patron's problem, how to best promote scientific progress given a
fixed pile of money, forces one to deal with money.  Money is what the
patron has to offer.  So the patron can only influence people that care to
some degree about money, or that care about something else controlled by
people who care about money.

STRATEGY

    It's a lot easier to sketch a grand utopian vision than it is to figure
out how to get there from here.  An ideal development strategy would show
how to grow incrementally, with each self-supporting step leading naturally
to the next one.  Most utopian visions fail because they, instead, require
too many things to change all at once.

    One advantage of idea futures is that, if not legally prohibited or
socially shunned, it can co-exist with existing academic institutions and
incrementally attract investors, patrons, and controversies. Papers would
still be published and elite committees would still convene. Professors
would gradually make more side bets, and begin to challenge each other to
bets.  Journalists would gradually rely more on the market odds for news
stories, and funding agencies would gradually try larger levels of
subsidies.  Idea futures could rise or fall on its own merits, as people
studied how well its predictions compared to other consensus measures, and
how the rate of progress in a field depends on the fraction of funding
channeled through the markets.

    Unfortunately, there seem to be some obstacles to overcome before
gradual growth is possible.  Economies of scale in forming reputable
judging organizations or building secure computerized marketplaces may mean
that certain levels of participation may be required before idea futures
can "take off".  But the major hurdle seems to be attitudes toward the very
idea, attitudes reflected in the world-wide legal prohibitions.  There are
several possible strategies here.

    One approach is more discussions, like those in this paper, of the need
for alternative academic institutions, and of betting markets as a
particular alternative.  Perhaps we need simple word tricks, like insurance
and stock bets have used, to disassociate idea futures from ordinary
betting, though the concept of bets is very useful in explaining how it
works.

    Also helpful is further research on markets in conditional assets, such
as recent attempts to show them superior to opinion polls at predicting
elections [Fo].  Laboratory experiments [SmV] comparing betting markets to
some mockup of existing peer review institutions would be very interesting,
though not of course decisive.

    A different approach, which I am also pursuing, would be to create an
electronic mail-based reputation game, where people play for "bragging
rights" instead of money.  This would avoid legal problems and the
discomfort academics have in dealing explicitly with money, and would allow
many people from around the world to participate in a less-threatening
partial test of markets as an academic consensus mechanism.  However,
avoiding money makes the incentives suspect, and precludes many of the
advantages, like insurance, that idea futures offer.  In particular, it
makes it hard to pay judges enough to do a careful job.  If enough people
played, the scores would mean something to observers, and so people might
have an incentive to play and play well.  But building a game up to this
status would be hard, probably requiring some "big name" players to attract
others.

    If the basic idea became plausible enough to enough private patrons in
Britain (because that's where it's legal) or government patrons anywhere,
idea futures could be seriously tried.  The initial field would preferably
be one where bets are easier to settle, like number theory, though such
subjects tend to be ones where existing institutions also work better, and
so perceive less of a need for change.  A socially important question with
minimal opportunities for conflict of interest would also be nice.
Attractive initial candidate fields include number theory, meteorology,
remote sensing, and particle properties.

    Idea futures will have "made it" when it becomes known as a good place
to find out the latest thinking on certain issues, reliably predicting what
will later become consensus in other social contexts.

ADVANTAGES

    If its potential problems can be overcome, and a development path
charted and followed, idea futures offers many advantages, most of which
have already been mentioned.

    There would be a clear incentive to be careful, honest, and expert when
making public statements.  Opinion holders could be rewarded for being
right, rather than just for being liked by academic insiders. Those who
invest wisely would accumulate capital and gain influence, which they could
reinvest in discretionary research or in influencing future consensuses.

    Funding agencies would only need to pick important questions, not who
would be good to research them, what methods aught to be used, nor whenrthe
research should be done.  Diverse approaches could be tried to research a
question, without arbitrary penalties against crossing disciplinary
boundaries, ignoring fashion and insiders, integrating pre-existing
knowledge, violating methodological ideologies, or using insights too small
or inarticulate to make a publishable unit. Any approach by which one could
reliably make the consensus odds better informed could be financially
rewarded.

    Anyone, not just articulate Ph.D.s, could contribute directly to the
world's corpus of knowledge.  Easily published science odds and amateur
betting should increase popular interest in science.  And even if the
"great unwashed" turn out to be poor contributors, they would subsidize
professional efforts on questions of popular interest, and perhaps increase
the general savings rate.  And I suspect they will do better than most
elites expect.

    Clear market odds would ease science reporting.  A visible scientific
consensus would be available to guide public policy, a consensus which
would be self-consistent across a wide range of issues and harder for media
campaigns to distort.  Compared to competing consensus mechanisms, idea
futures should be relatively simple, cheap, decentralized, egalitarian,
responsive to new information, and at least as informative. This consensus
should correct for many current biases, such as overconfidence.

    The mere threat of betting challenges could improve incentives in
discussions and debates.  If the market consensus carried social weight, it
could serve as a coordination point for thousand of independent
conversations.  A rejected visionary would have a new way to get publicity
for his ideas, and a reward for being right against the establishment; true
cranks would subsidize leveler heads. As debates became settled, they would
leave a trail of agreed-upon statements which could be used to counter
bogus claims made by those ignorant of solid expert consensus.

    Businesses could make insurance hedges against technological risk, as
in the cold fusion case.  While such insurance may be legal now, the
introduction of speculators would increase market thickness to a point
where it might be practical.

    Reputation scores offer an new way to evaluate people's ability to
separate the wheat from the chaff in ideas and arguments, and these scores
should depend less on whether one has curried favor from the right people.

    Idea futures is well-grounded in our best theories of decision and
incentives.  Once legal and accepted, idea futures could grow
incrementally, and perhaps dramatically increase our rate of scientific
progress per funding spent.

CONCLUSION

    Markets in contingent assets, more commonly known as "bets", offer a
needed alternative to existing academic institutions. Betting markets
cannot solve all current problems, or replace all current institutions. But
if this paper has been successful, the potential of such markets should be
clear, and most of the obvious problems with such markets should have been
addressed in enough detail that we can say the idea still seems plausible
on a closer examination.   If so, more serious intellectual discussion is
justified, and perhaps some small-scale experiments.  We could do much
worse than having intellectual institutions as open, flexible, diverse, and
egalitarian as the stock market, with incentives as well-grounded and with
estimates on important issues as unbiased and predictive.

ACKNOWLEDGEMENTS

    These ideas germinated in the fertile ground of discussions with
friends interested in similar problems, most of whom are associated in one
way or another with the company Xanadu.  K. Eric Drexler, Mark Miller, and
Phil Salin have been particularly influential.  And my wife Peggy Jackson
has influenced me in more ways than I know.  Several hundred people, more
than I can list here, have provided useful comments and criticisms on all
aspects of the idea.

REFERENCES

[APA] (1987) Diagnostic and Statistical Manual of Mental Disorders Third
  Edition, Revised, American Psychiatric Association, Washington D.C.
[Be] Bernal, J. (1989) "After Twenty-Five Years", Science and Public
  Policy, 16:3, June, pp.143-151.
[By] Byrne, G. (1989) "A Modest Proposal", Science, 244, April 2, p.290.
[Bre] Brenner,R., Brenner, G. (1990)Gambling and Speculation, Cambridge
  Univ. Press, NY.
[Bru] Brunner, J. (1975) The Shockwave Rider, Harper & Row, NY.
[Ch] Chubin, D., Hackett, E., (1990) Peerless Science, SUNY Press, NY.
[Cia] Cialdini, R. (1988) Influence, Science and Practice, Scott, Foresman
  and Co., Boston.
[Cic] Cicchetti, D. "The reliability of peer review for manuscript and
  grant submissions: A cross-disciplinary investigation", Behavioral and
  Brain Sciences, 14:1, pp.119-135.
[Co] Cole, S., Cole, J., (1987) "Testing the Ortega Hypothesis: Milestone
  or Millstone?", Scientometrics, 12:5-6 pp.345-353.
[De] Debus, A. (1970) Science and Education in the Seventeenth Century,
  MacDonald, London.
[Dr] Drexler, K.E. (1986) Engines of Creation, Doubleday, New York.
[Do] Dowie, J. (1982) "Gambling in Education and Education in Gambling",
  Proc. Fifth Intl. Conf. on Gambling and Risk Taking, ed. William
  Eadington, pp.23-39.
[Ec] Economides, N., Siow, A. (1988) "The Division of Markets is Limited by
  the Extent of Liquidity (Spatial Competition with Externalities)",
  American Economic Review, March, pp.108-121.
[Ei] Eisenberg, E., Gale, D. (1959) "Consensus of Subjective Probabilities.
  The Pari-mutuel Method" Ann. Math. Statist. 30. pp.165-168.
[Ev] Evans, D. (1991) "Atom Priests", San Jose Mercury News, Oct. 28, p.7B.
[Fa] Fairley, W., Meyer, M., Chernick, P. (1984) "Insurance Market
  Assessment of Technological Risk", Proc. Soc. for Risk Analysis Internl.
  Workshop on Uncertainty in Risk Assessment, Risk Management, and Decision
  Making, Sept. 30, pp.89-102.
[Fe] Feyerabend, P., (1975) "How to Defend Society Against Science",
  Radical Philosophy, 2, Summer, pp.4-8.
[Fo] Forsythe, R., Nelson, F., Neumann, G., Wright, J. (1990) "The
  Explanation and Prediction of Presidential Elections:  A Market
  Alternative to Polls" Economics Working Paper 90-11, April 12. Univ. of
  Iowa, Iowa City.
[Gal] Galileo, Dialogue Concerning the Two Chief World Systems, transl. by
  Stillman Drake, 2nd ed., Berkeley, Univ. of California Press, 1967.
[Gar] Garwin, R. (1989) "Consensus on Cold fusion still elusive" Nature,
  338, April 20.
[Gei] Geis, G. (1974) One Eyed Justice, Drake Publ. Inc. NY.
[Gen] Genest, C., Zidek, J. (1986) "Combining Probability Distributions: A
  Critique and Annotated Bibliography", Statistical Science 1:1,
  pp.114-148.
[Gh] Ghiselin, Michael T. (1989) Intellectual Compromise: The Bottom Line,
  Paragon House Publ., NY.
[Gi] Gilmore, J.B. (1991) "On Forecasting validity and finessing
  reliability", Behavioral and Brain Sciences, 14:1, pp.148-149.
[Gr] Grofman, B., Owen, G. eds. (1986) Information Pooling and Group
  Decision Making: Proc of the Second Univ. Cal. Irvine Conf. on Political
  Economy, JAI Press, Inc. London.
[Hak] Hakansson, N., Beja, A., Kale, J. (1985) "On the Feasibility of
  Automated Market Making by a Programmed Specialist", J. Finance, March.
[Hal] Hall, S. (1989) "Professor Thorne's Time Machine" California,
  October, pp.68-77.
[Han88] Hanson, R. (1988) "Toward Hypertext Publishing, Issues and Choices
  in Database Design", ACM SIGIR Forum, 22:1,2 Winter 1988.
[Han90] Hanson, R. (1990) "Market-Based Foresight - A Proposal", Foresight
  Update, 10, publ. of Foresight Institute, P.O. Box 61058, Palo Alto, CA
  94306.
[Han90b] Hanson, R. (1990) "Could Gambling Save Science? Encouraging an
  Honest Consensus" Proc. Eighth Intl. Conf. on Risk and Gambling, July,
  London.
[He] Heilbron, J. (1982) Elements of Early Modern Physics, U. California
  Press.
[Hir] Hirshleifer, J. (1971) "The Private and Social Value of Information
  and the Reward to Inventive Activity", American Economics Review, 61:4,
  Sept., pp. 561-74.
[He] Henrion, M., Fischhoff, B. (1986) "Assessing Uncertainty in Physical
  Constants", Am. J. Phys. 54:9, September, pp.791-798.
[Ho84] Hofstee, W. (1984) "Methodological Decision Rules As Research
  Policies: A Betting Reconstruction of Empirical Research", Acta
  Psychologica, 56, pp93-109.
[Ho81] Hofstee, W., Nevels, K., (1981) "Do not take the betting
  model literally", Kwantitatieve Methoden, 3, pp70-72.
[Jac] Jacobs, J. (1991) "Fremont, Film Capital", San Jose Mercury News West
  Magazine, Sept. 1, p. 3.
[Jaf] Jaffray, J. (1989) "Coherent Bets Under Partially Resolving
  Uncertainty and Belief Functions", Theory and Decision, 26, 99-105.
[Kad] Kadane, J., Winkler, R. (1988) "Separating Probability Elicitation
  from Utilities" J. American Stat. Assoc., June, 83:402, Theory and
  Methods, pp. 357-363.
[Kah] Kahneman, D., Tversky, A., eds., (1982) Judgment under uncertainty:
  Heuristics and biases, Cambridge Univ. Press, NY.
[Kan] Kantrowitz, A. (1977) "The Science Court Experiment: Criticisms and
  Responses", Bulletin of the Atomic Scientists, April, pp.44-50.
[Ke] Kelley, J. (1988) "Compulsive Gambling in Britain", J. Gambling
  Behavior, 4:4 Winter, p.291
[La] Laffont, J.J. (1989) The Economics of Uncertainty and Information, MIT
  Press.
[Lea] Leamer, E. (1986) "Bid-Ask Spreads For Subjective Probabilities",
  Bayesian Inference and Decision Techniques, ed. P. Goel, A. Zellner,
  Elsevier Sci. Publ., pp.217-232
[Led] Lederberg, J. (1989) "Does Scientific Progress Come from Projects or
  People?" Current Contents, 48, November 27, pp.4-12.
[Lew] Lewis, H.W., (1989) "Fusion isn't just around the corner" San Jose
  Mercury News, April 7, Opinion page.
[Li] Linstone, L., Turoff, M., ed. (1975) The Delphi Method,
  Addison-Wesley, London.
[Mal] Malkiel, B. (1989) "Is the Stock Market Efficient?" Science, 243,
  March 10, pp.1313-1318.
[Man] Mann, C. (1990) "Meta-Analysis in the Breech" Science 249, August 3,
  pp.476-480.
[Mar] Marshall, E. (1990) "Science Beyond the Pale", Science 249, July 6,
  pp.14-16.
[May] Mayer, M. (1988) Markets, Norton & Co., NY.
[Mu] Mueller, D. (1979) Public Choice, Cambridge Univ. Press, Cambridge.
[My] Myers, D. (1983) Social Psychology, 2nd ed., McGraw-Hill.
[Na] Nau, R., McCardle, K., "Arbitrage, Rationality, and Equilibrium",
  Theory and Decision, to appear.
[NS] (1990) "Feedback Column", New Scientist, July 14. See also 2/10, 7/28.
[Pa] Pavitt, K. (1991) "What makes basic research economically useful?"
  Research Policy, 20, pp.109-119.
[Pe] Pearl, J. (1988) Probabilistic Reasoning in Intelligent Systems:
  Networks of Plausible Inference, Morgan Kaufmann Publ., Inc., San Mateo,
  CA.
[Pol] Polinsky, M, (1983) An Introduction to Law and Economics, LittleBrown
  and Co., Boston.
[Poo] Pool, R. (1989) "Bulls Outpace Bears - For Now!" Science,244,
  April 28, p.421.
[Pop] Popper, K. (1985) Popper Selections, ed D. Miller, Princeton Univ.
  Press.
[Pow] Power, W. (1989) "Hottest Commodity In Wall Street Pits?
  Georgetown Hoyas", Wall Street Journal, March 24, p.A1.
[Pr] Price, D.J. de Solla (1963) Little Science, Big Science, and
  Beyond, Colombia Univ. Press, NY.
[Red] Redner, H. (1987) "Pathologies of Science", Social Epistemology, 1:3,
  pp.215-247.
[Res] Rescher, N. (1978) Scientific Progress, Camelot Press, London.
[Ros] Rose, I.N. (1986) Gambling and the Law, Gambling Times Incorporated,
  Hollywood.
[Roy] Roy, R. (1985) "Funding Science: The Real Defects of Peer Review and
  An Alternative To It", Science, Technology and Human Values, 10:3 Summer,
  pp.73-81.
[Se] Seidenfeld, T. (1990) "Two Perspectives on Consensus for (Bayesian)
  Inference and Decisions" Knowledge Representation and Defeasible
  Reasoning, H. Kyburg, et. al. eds. pp267-286.
[ShW] Sharpe, W. (1985) Investments, 3rd Ed., Prentice Hall, NJ.
[ShG] Sharpe, G. (1990) phone conversations, William Hill Org. Ltd. 19
  Valentine Pl. London SE1 8QH, July.
[ShS] Shapin, S., Schaffer, S. (1985) Leviathan and the Air-Pump,
  Princeton U. Press.
[Si] Simon, J. (1991) Here's An Offer You Ought to Refuse, Feb. 25, open
  letter available from author, 110 Primrose St., Chevy Chase, MD 20815.
[SmP] Smith, P. (1990) Killing the Spirit, Viking/Penguin, NY.
[SmV] Smith, V. (1986) "Experimental Methods in the Political Economy of
  Exchange", Science, 234, October 10, pp.167-173.
[So] Sobey, P., Maddess, T. (1991) "You can bet on it", New Scientist,
  August.
[St] Stoll, H. (1989) "Inferring the Components of the Bid-Ask Spread:
  Theory and Empirical Tests", J. Finance, 44:1, March. pp.115-134.
[Syk] Sykes, C. (1988) ProfScam, St. Martin's Press, NY.
[Syn] (1985) Synthese, "Consensus" issue, 62:1, Jan
[Th] Thayer, H. (1980) "Peirce on Truth", Two Centuries of Philosophy in
  America, ed. P. Caws. Towman & Littlefield, Totowa NJ.
[Ti] Tierney, J. (1991) "A Bet On Planet Earth", Reader's Digest, March,
  pp.61-64.
[Tr] Trumpbour, J. (1989) How Harvard Rules, South End Press, Boston.
[Ts] Tsao, J. (1989) "Consumer preferences and funding priorities in
  scientific research", Science and Public Policy, 16:5, October,
  pp.294-298.
[Tul] Tullock, G. (1966) The Organization of Inquiry, Duke Univ. Press,
  London.
[Tur] Turner, S. (1990) "Forms of Patronage", Theories of Science in
  Society, ed. S. Cozzens, T. Gieryn, Indiana U. Press, pp.185-21.
[Ve] Verne, J. (1872) Around the World in Eighty Days
[Wa] Wade, N. (1980) "Why Government Should Not Fund Science", Science,
  210:3, October, p.33.
[Whe] Wheeler, S., (1990) "Betting on Futures in Financial Markets: A
  Variation on Old Institutions", Proc. Eighth Intl. Conf. on Risk and
  Gambling, July, London.
[Whi] White, F. (1946) Famous Utopias of the Renaissance, Hendricks House
  Inc, Putney Vermont.
[WSJ] (1989) "Fusion Fuss Is Turning Scientists Into Gamblers" Wall Street
  Journal, April 18.
[Ze] Zeckhauser, R., Viscusi, W. (1990) "Risk Within Reason", Science, 248,
  May 4, pp.559-564.
