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Research paper topic: Could Gambling Save Science: Encouraging An Honest Consensus - 4913 words

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.. 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 relate.

Related: compulsive gambling, consensus, encouraging, gambling, honest

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