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24
From decision theory to decision aiding methodology (my very personal version of this history and some related reflections)
, 2003
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De Finetti was right: probability does not exist. Theory and Decision
, 2001
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2001a), A Generalization of PrattArrow Measure to NonExpectedUtility Preferences and Inseparable Probability and Utility. Working paper, Fuqua School of Business
 Preferences And Inseparable Probability And Utility. Management Science 49:8, 1089
, 2003
"... The PrattArrow measure of local risk aversion is generalized for the ndimensional statepreference model of choice under uncertainty in which the decision maker may have inseparable subjective probabilities and utilities, unobservable stochastic prior wealth, and/or smoothnonexpectedutility prefe ..."
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Cited by 12 (7 self)
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The PrattArrow measure of local risk aversion is generalized for the ndimensional statepreference model of choice under uncertainty in which the decision maker may have inseparable subjective probabilities and utilities, unobservable stochastic prior wealth, and/or smoothnonexpectedutility preferences. Local risk aversion is measured by the matrix of derivatives of the decision maker’s riskneutral probabilities, without reference to true subjective probabilities or riskless wealthpositions, and comparative risk aversion is measured without requiring agreement on true probabilities. Riskneutral probabilities and their derivatives are shown to be sufficient statistics for approximately optimal investment and financing decisions in complete markets for contingent claims.
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.
Editors. Advances in decision analysis: from foundations to applications
, 2007
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Compact Securities Markets for Pareto Optimal Reallocation of Risk
, 2000
"... The securities market is the fundamental theoretical framework in economics and finance for resource allocation under uncertainty. Securities serve both to reallocate risk and to disseminate probabilistic information. Complete securities marketswhich contain one security for every possible ..."
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Cited by 5 (4 self)
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The securities market is the fundamental theoretical framework in economics and finance for resource allocation under uncertainty. Securities serve both to reallocate risk and to disseminate probabilistic information. Complete securities marketswhich contain one security for every possible state of naturesupport Pareto optimal allocations of risk. Complete markets suffer from the same exponential dependence on the number of underlying events as do joint probability distributions. We examine whether markets can be structured and "compacted" in the same manner as Bayesian network representations of joint distributions. We show that, if all agents' riskneutral independencies agree with the independencies encoded in the market structure, then the market is operationally complete: risk is still Pareto optimally allocated, yet the number of securities can be exponentially smaller. For collections of agents of a certain type, agreement on Markov independencies is su...
A Market Framework for Pooling Opinions
, 1998
"... Consider a group of Bayesians, each with a subjective probability distribution over a set of uncertain events. An opinion pool derives a single consensus distribution over the events, representative of the group as a whole. Several pooling functions have been proposed, each sensible under particular ..."
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Cited by 4 (4 self)
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Consider a group of Bayesians, each with a subjective probability distribution over a set of uncertain events. An opinion pool derives a single consensus distribution over the events, representative of the group as a whole. Several pooling functions have been proposed, each sensible under particular assumptions or measures. Many researchers over many years have failed to form a consensus on which method is best. We propose a marketbased pooling procedure, and analyze its properties. Participants bet on securities, each paying off contingent on an uncertain event, so as to maximize their own expected utilities. The consensus probability of each event is defined as the corresponding security's equilibrium price. The market framework provides explicit monetary incentives for participation and honesty, and allows agents to maintain individual rationality and limited privacy. "No arbitrage" arguments ensure that the equilibrium prices form legal probabilities. We show that, when events are...
Disagreement as SelfDeception About MetaRationality
 Department of Mechanical and Aerospace Engineering, Princeton University
, 2001
"... Honest truthseeking agents, Bayesian and otherwise, should not agree to disagree. This result is robust to many perturbations. Such agents are "metarational" when they are aware of and act on this result. The ubiquity of disagreement, however, suggests that very few people, academics inc ..."
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Cited by 1 (0 self)
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Honest truthseeking agents, Bayesian and otherwise, should not agree to disagree. This result is robust to many perturbations. Such agents are "metarational" when they are aware of and act on this result. The ubiquity of disagreement, however, suggests that very few people, academics included, are justified in thinking ourselves to be very metarational. We are instead selfdeceived in thinking ourselves to be more metarational than others. Since alerting us to this fact does not much change our behavior, we must not really want to know the truth, or simply cannot be any other way. 3 I.
Eliciting Objective Probabilities via Lottery Insurance Games
 Computational Mathematics Laboratory, Rice University
, 1993
"... Since utilities and probabilities jointly determine choices, eventdependent utilities complicate the elicitation of subjective event probabilities. However, for the usual purpose of obtaining the information embodied in agent beliefs, it is su#cient to elicit objective probabilities, i.e., proba ..."
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Cited by 1 (1 self)
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Since utilities and probabilities jointly determine choices, eventdependent utilities complicate the elicitation of subjective event probabilities. However, for the usual purpose of obtaining the information embodied in agent beliefs, it is su#cient to elicit objective probabilities, i.e., probabilities obtained by updating a known common prior with that agent's further information. Bayesians who play a Nash equilibrium of a certain insurance game before they obtain relevant information will afterward act regarding lottery ticket payments as if they had eventindependent riskneutral utility and a known common prior. Proper scoring rules paid in lottery tickets can then elicit objective probabilities.