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32
Logarithmic Market Scoring Rules for Modular Combinatorial Information Aggregation
 Journal of Prediction Markets
, 2002
"... In practice, scoring rules elicit good probability estimates from individuals, while betting markets elicit good consensus estimates from groups. Market scoring rules combine these features, eliciting estimates from individuals or groups, with groups costing no more than individuals. ..."
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Cited by 71 (5 self)
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In practice, scoring rules elicit good probability estimates from individuals, while betting markets elicit good consensus estimates from groups. Market scoring rules combine these features, eliciting estimates from individuals or groups, with groups costing no more than individuals.
A utility framework for boundedloss market makers
 In Proceedings of the 23rd Conference on Uncertainty in Artificial Intelligence
, 2007
"... We introduce a class of utilitybased market makers that always accept orders at their riskneutral prices. We derive necessary and sufficient conditions for such market makers to have bounded loss. We prove that hyperbolic absolute risk aversion utility market makers are equivalent to weighted pseu ..."
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Cited by 47 (21 self)
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We introduce a class of utilitybased market makers that always accept orders at their riskneutral prices. We derive necessary and sufficient conditions for such market makers to have bounded loss. We prove that hyperbolic absolute risk aversion utility market makers are equivalent to weighted pseudospherical scoring rule market makers. In particular, Hanson’s logarithmic scoring rule market maker corresponds to a negative exponential utility market maker in our framework. We describe a third equivalent formulation based on maintaining a cost function that seems most natural for implementation purposes, and we illustrate how to translate among the three equivalent formulations. We examine the tradeoff between the market’s liquidity and the market maker’s worstcase loss. For a fixed bound on worstcase loss, some market makers exhibit greater liquidity near uniform prices and some exhibit greater liquidity near extreme prices, but no market maker can exhibit uniformly greater liquidity in all regimes. For a fixed minimum liquidity level, we give the lower bound of market maker’s worstcase loss under some regularity conditions. 1
A dynamic parimutuel market for hedging, wagering, and information aggregation
 In Proceedings of the Fifth ACM Conference on Electronic Commerce (EC’04
, 2004
"... I develop a new mechanism for risk allocation and information speculation called a dynamic parimutuel market (DPM). A DPM acts as hybrid between a parimutuel market and a continuous double auction (CDA), inheriting some of the advantages of both. Like a parimutuel market, a DPM offers infinite bu ..."
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Cited by 34 (7 self)
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I develop a new mechanism for risk allocation and information speculation called a dynamic parimutuel market (DPM). A DPM acts as hybrid between a parimutuel market and a continuous double auction (CDA), inheriting some of the advantages of both. Like a parimutuel market, a DPM offers infinite buyin liquidity and zero risk for the market institution; like a CDA, a DPM can continuously react to new information, dynamically incorporate information into prices, and allow traders to lock in gains or limit losses by selling prior to event resolution. The trader interface can be designed to mimic the familiar double auction format with bidask queues, though with an addition variable called the payoff per share. The DPM price function can be viewed as an automated market maker always offering to sell at some price, and moving the price appropriately according to demand. Since the mechanism is parimutuel (i.e., redistributive), it is guaranteed to pay out exactly the amount of money taken in. I explore a number of variations on the basic DPM, analyzing the properties of each, and solving in closed form for their respective price functions.
Statistical Methods for Eliciting Probability Distributions
 Journal of the American Statistical Association
, 2005
"... Elicitation is a key task for subjectivist Bayesians. While skeptics hold that it cannot (or perhaps should not) be done, in practice it brings statisticians closer to their clients and subjectmatterexpert colleagues. This paper reviews the stateoftheart, reflecting the experience of statisticia ..."
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Cited by 32 (1 self)
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Elicitation is a key task for subjectivist Bayesians. While skeptics hold that it cannot (or perhaps should not) be done, in practice it brings statisticians closer to their clients and subjectmatterexpert colleagues. This paper reviews the stateoftheart, reflecting the experience of statisticians informed by the fruits of a long line of psychological research into how people represent uncertain information cognitively, and how they respond to questions about that information. In a discussion of the elicitation process, the first issue to address is what it means for an elicitation to be successful, i.e. what criteria should be employed? Our answer is that a successful elicitation faithfully represents the opinion of the person being elicited. It is not necessarily “true ” in some objectivistic sense, and cannot be judged that way. We see elicitation as simply part of the process of statistical modeling. Indeed in a hierarchical model it is ambiguous at which point the likelihood ends and the prior begins. Thus the same kinds of judgment that inform statistical modeling in general also inform elicitation of prior distributions.
Betting BooleanStyle: A Framework for Trading in Securities Based on Logical Formulas
, 2003
"... We develop a framework for trading in compound securities: financial instruments that pay off contingent on the outcomes of arbitrary statements in propositional logic. Buying or selling securities  which can be thought of as betting on or against a particular future outcome  allows agents both ..."
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Cited by 30 (17 self)
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We develop a framework for trading in compound securities: financial instruments that pay off contingent on the outcomes of arbitrary statements in propositional logic. Buying or selling securities  which can be thought of as betting on or against a particular future outcome  allows agents both to hedge risk and to profit (in expectation) on subjective predictions. A compound securities market allows agents to place bets on arbitrary boolean combinations of events, enabling them to more closely achieve their optimal risk exposure, and enabling the market as a whole to more closely achieve the social optimum. The tradeoff for allowing such expressivity is in the complexity of the agents' and auctioneer's optimization problems.
Revealed Likelihood and Knightian Uncertainty
 JOURNAL OF RISK AND UNCERTAINTY, 16:223–250 (1998) © 1998 KLUWER ACADEMIC PUBLISHERS
, 1998
"... Nonadditive expected utility models were developed for explaining preferences in settings where probabilities cannot be assigned to events. In the absence of probabilities, difficulties arise in the interpretation of likelihoods of events. In this paper we introduce a notion of revealed likelihood t ..."
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Cited by 15 (1 self)
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Nonadditive expected utility models were developed for explaining preferences in settings where probabilities cannot be assigned to events. In the absence of probabilities, difficulties arise in the interpretation of likelihoods of events. In this paper we introduce a notion of revealed likelihood that is defined entirely in terms of preferences and that does not require the existence of (subjective) probabilities. Our proposal is that decision weights rather than capacities are more suitable measures of revealed likelihood in rankdependent expected utility models and prospect theory. Applications of our proposal to the updating of beliefs and to the description of attitudes towards ambiguity are presented.
De Finetti Was Right: Probability Does Not Exist
, 2001
"... De Finetti's treatise on the theory of probability begins with the provocative statement PROBABILITY DOES NOT EXIST, meaning that probability does not exist in an objective sense. Rather, probability exists only subjectively within the minds of individuals. De Finetti defined subjective probabilitie ..."
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Cited by 14 (7 self)
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De Finetti's treatise on the theory of probability begins with the provocative statement PROBABILITY DOES NOT EXIST, meaning that probability does not exist in an objective sense. Rather, probability exists only subjectively within the minds of individuals. De Finetti defined subjective probabilities in terms of the rates at which individuals are willing to bet money on events, even though, in principle, such betting rates could depend on statedependent marginal utility for money as well as on beliefs. Most later authors, from Savage onward, have attempted to disentangle beliefs from values by introducing hypothetical bets whose payoffs are abstract consequences that are assumed to have stateindependent utility. In this paper, I argue that de Finetti was right all along: PROBABILITY, considered as a numerical measure of pure belief uncontaminated by attitudes toward money, does not exist. Rather, what exist are de Finetti's "previsions," or betting rates for money, otherwise known in the literature as "risk neutral probabilities." But the fact that previsions are not measures of pure belief turns out not to be problematic for statistical inference, decision analysis, or economic modeling.
THE SHAPE OF INCOMPLETE PREFERENCES
, 2006
"... Incomplete preferences provide the epistemic foundation for models of imprecise subjective probabilities and utilities that are used in robust Bayesian analysis and in theories of bounded rationality. This paper presents a simple axiomatization of incomplete preferences and characterizes the shape o ..."
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Cited by 10 (2 self)
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Incomplete preferences provide the epistemic foundation for models of imprecise subjective probabilities and utilities that are used in robust Bayesian analysis and in theories of bounded rationality. This paper presents a simple axiomatization of incomplete preferences and characterizes the shape of their representing sets of probabilities and utilities. Deletion of the completeness assumption from the axiom system of Anscombe and Aumann yields preferences represented by a convex set of statedependent expected utilities, of which at least one must be a probability/utility pair. A strengthening of the stateindependence axiom is needed to obtain a representation purely in terms of a set of probability/utility pairs.
Arbitrage, rationality, and equilibrium
 Theory and Decision
, 1991
"... ABSTRACT. Noarbitrage is the fundamental principle of economic rationality which unifies normative decision theory, game theory, and market theory. In economic environments where money is available as a medium of measurement and exchange, noarbitrage is synonymous with subjective expected utility ..."
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Cited by 6 (0 self)
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ABSTRACT. Noarbitrage is the fundamental principle of economic rationality which unifies normative decision theory, game theory, and market theory. In economic environments where money is available as a medium of measurement and exchange, noarbitrage is synonymous with subjective expected utility maximization in personal decisions, competitive equilibria in capital markets and exchange economies, and correlated equilibria in noncooperative games. The arbitrage principle directly characterizes rationality at the market level; the appearance of deliberate optimization by individual agents is a consequence of their adaptation to the market. Concepts of equilibrium behavior in games and markets can thus be reconciled with the ideas that individual rationality is bounded, that agents use evolutionarilyshaped decision rules rather than numerical optimization algorithms, and that personal probabilities and utilities are inseparable and to some extent indeterminate. Riskneutral probability distributions, interpretable as products of probabilities and marginal utilities, play a central role as observable quantities in economic systems.
Forthcoming in Advances in Decision Analysis: From Foundations to Applications
"... Abstract: The subjective expected utility (SEU) model rests on very strong assumptions about the consistency of decision making across a wide range of situations. The descriptive validity of these assumptions has been extensively challenged by behavioral psychologists during the last few decades, an ..."
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Abstract: The subjective expected utility (SEU) model rests on very strong assumptions about the consistency of decision making across a wide range of situations. The descriptive validity of these assumptions has been extensively challenged by behavioral psychologists during the last few decades, and the normative validity of the assumptions has also been reappraised by many statisticians, philosophers, and economists, motivating the development of more general utility theories and decision models. These generalized models are characterized by features such as imprecise probabilities, nonlinearly weighted probabilities, sourcedependent risk attitudes, and statedependent utilities, permitting the pattern of the decision maker’s behavior to change with the decision context and to perhaps satisfy the usual SEU assumptions only locally. Recent research in the emerging field of neuroeconomics sheds light on the physiological basis of decision making, the nature of preferences and beliefs, and interpersonal differences in decision competence. These findings do not necessarily invalidate the use of SEUbased decision analysis tools, but they suggest that care needs to be taken to structure preferences and to assess beliefs and risk attitudes in a manner that is appropriate for the decision and also for the decision maker. Key words: subjective probability, expected utility, nonexpected utility, Savage's axioms, surething