BETTING MARKET: Rank Dependent Expected Utility

2013 ◽  
Vol 1 (2) ◽  
pp. 147-163
Author(s):  
Loreto Llorente
Keyword(s):  
Decision Theory ◽  
Expected Utility ◽  
Utility Maximization ◽  
Betting Market ◽  
Expected Utility Maximization ◽  
Classical Decision ◽  
Rank Dependent Expected Utility ◽  
The Way

In Pelota matches, games with two mutually exclusive and exhaustive outcomes, bets on the winner are made through a middleman who receives 16% of the finally paid amount. The classical decision theory of expected utility maximization can not explain this market assuming bettors are identical. Llorente and Aizpurua (2007) explain the existence of bets in the market under Quiggin’s rank dependent expected utility (RDEU) model. They find that bettors have to be optimistic in order to explain the existence of a bet. Analyzing the way odds are fixed in the market Llorente (2006) finds that assuming equal return on bets there are inefficiencies in the market. In this paper we show that, given an assumption that bettors are rank dependent expected utility maximizers, these inefficiencies tend to disappear.

Probability and Decision Theory

2020 ◽  
pp. 6-41
Author(s):  
Juan Comesaña
Keyword(s):  
Decision Theory ◽  
Conditional Probability ◽  
Expected Utility ◽  
Utility Maximization ◽  
Measure Theory ◽  
Dutch Book ◽  
Logical Omniscience ◽  
Probability Calculus ◽  
Expected Utility Maximization ◽  
Truth Tables

This chapter introduces the mathematics of probability and decision theory. The probability calculus is introduced in both a set-theoretic and a propositional context. Probability is also related to measure theory, and stochastic truth-tables are presented. Problems with conditional probability are examined. Two interpretations of the probability calculus are introduced: physical and normative probabilities. The problem of logical omniscience for normative probabilities is discussed. Dutch Book arguments and accuracy-based arguments for Probabilism (the claim that our credences must satisfy the probability axioms) are examined and rejected. Different interpretations of the “idealization” reply to the problem of logical omniscience are considered, and one of them is tentatively endorsed. The expected utility maximization conception of decision theory is introduced, and representation arguments are considered (and rejected) as another reply to the problem of logical omniscience.

scholarly journals Reasoning about social preferences with uncertain beliefs

2021 ◽  
Author(s):  
isaac davis ◽  
Ryan W. Carlson ◽  
Yarrow Dunham ◽  
Julian Jara-Ettinger
Keyword(s):  
Expected Utility ◽  
Utility Maximization ◽  
Social Preference ◽  
Social Preferences ◽  
Social Judgments ◽  
Social Agents ◽  
Preference Reasoning ◽  
The Face ◽  
Expected Utility Maximization ◽  
Social Uncertainty

We propose a computational model of social preference judgments that accounts for the degree of an agents’ uncertainty about the preferences of others. Underlying this model is the principle that, in the face of social uncertainty, people interpret social agents’ behavior under an assumption of expected utility maximization. We evaluate our model in two experiments which each test a different kind of social preference reasoning: predicting social choices given information about social preferences, and inferring social preferences after observing social choices. The results support our model and highlight how un- certainty influences our social judgments.

Specialist versus Generalist Decision Making

2018 ◽  
Author(s):  
Armin W. Schulz
Keyword(s):  
Decision Making ◽  
Expected Utility ◽  
Utility Maximization ◽  
Decision Rules ◽  
Mental States ◽  
Vast Array ◽  
Expected Utility Maximization

A number of scholars argue that human and animal decision making, at least to the extent that it is driven by representational mental states, should be seen to be the result of the application of a vast array of highly specialized decision rules. By contrast, other scholars argue that we should see human and animal representational decision making as the result of the application of a handful general principles—such as expected utility maximization—to a number of specific instances. This chapter shows that, using the results of chapters 5 and 6, it becomes possible to move this dispute forwards: the account of the evolution of conative representational decision making defended in chapter 6 together with the account of the evolution of cognitive representational decision making defended in chapter 5, makes clear that both sides of this dispute contain important insights, and that it is possible to put this entire dispute on a clearer and more precise foundation. Specifically, I show that differentially general decision rules are differentially adaptive in different circumstances: certain particular circumstances favor specialized decision making, and certain other circumstances favor more generalist decision making.

Conclusion

2020 ◽  
pp. 248-250
Author(s):  
Paul Weirich
Keyword(s):  
Expected Utility ◽  
Utility Maximization ◽  
Risk Principle ◽  
Expected Utility Maximization ◽  
The Mean ◽  
Mean Risk

Recognizing that an act’s risk is a consequence of the act yields a version of expected-utility maximization that does not need adjustments for risk in addition to the probabilities and utilities of possible outcomes. This treatment of an act’s risk justifies the expected-utility principle, and the mean-risk principle, for evaluation of an act. Rational attitudes to risks explain the rationality of acting in accord with the principles. They ground the separability relations that support the principles. The expected-utility principle justifies a substantive, and not just a representational, version of the decision principle of expected-utility maximization. Consequently, the principle governs a single choice and not just sets of choices. It demands more than consistency of the choices in a set. It demands that each choice follow the agent’s preferences, and these preferences explain the rationality of a choice that complies with the principle.

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