Choquet Expected Utility Representation of Preferences on Generalized Lotteries (original) (raw)

Extendibility of Choquet rational preferences on generalized lotteries

2014

Given a finite set of generalized lotteries, that is random quantities equipped with a belief function, and a partial preference relation on them, a necessary and sufficient condition (Choquet rationality) has been provided for its representation as a Choquet expected utility of a strictly increasing utility function. Here we prove that this condition assures the extension of the preference relation and it actually guides the decision maker in this process.

Rationality principles for preferences on belief functions

Kybernetika, 2015

A generalized notion of lottery is considered, where the uncertainty is expressed by a belief function. Given a partial preference relation on an arbitrary set of generalized lotteries all on the same finite totally ordered set of prizes, conditions for the representability, either by a linear utility or a Choquet expected utility are provided. Both the cases of a finite and an infinite set of generalized lotteries are investigated.

Expected utility theory without the completeness axiom

We study the problem of obtaining an expected utility representation for a potentially incomplete preference relation over lotteries by means of a set of von Neumann-Morgenstern utility functions. It is shown that, when the prize space is a compact metric space, a preference relation admits such a multi-utility representation provided that it satisfies the standard axioms of expected utility theory. Moreover, the representing set of utilities is unique in a well-defined sense. r

Preferences Representable by a Lower Expectation: Some Characterizations

Theory and Decision, 2008

We propose two different characterizations for preference relations representable by lower (upper) expectations with the aim of removing either fair price or completeness requirements. Moreover, we give an explicit characterization for comparative degrees of belief on a finite algebra of events representable by lower probabilities.

Second Thougts on Von-Neumann-Morgenstern Utility Functions

Metroeconomica, 1978

In this paper we would like to do two things: firstly, to show that the proof of the von-Neumann-Moorgenstern linear utility theorem can be simplified by noting the isomorphism of the problem with Rn secondly, we would like to argue that there is hidden within the von-Neumann-Morgenstern assumptions an unacceptable condition on commodity preferences.

Expected Utility for Probabilistic Prospects and the Common Ratio Property

We prove the existence of an expected utility function for preferences over probabilistic prospects satisfying Strict Monotonicity, Indifference, the Common Ration Property, Substitution and Reducibility of Extreme Prospects. The example in Rubinstein (1988) that is inconsistent with the existence of a von Neumann-Morgenstern for preferences over probabilistic prospects, violates the Common Ratio Property. Subsequently, we prove the existence of expected utility functions with piecewise linear Bernoulli utility functions for preferences that are piece-wise linear. For this case a weaker version of the Indifference Assumption that is used in the earlier existence theorems is sufficient. We also state analogous results for probabilistic lotteries. We do not require any compound prospects or mixture spaces to prove any of our results. In the second last section of this paper, we “argue” that the observations related to Allais paradox, do not constitute a violation of expected utility maximization by individuals, but is a likely manifestation of individuals assigning (experiment or menu-dependent?) subjective probabilities to events which disagree with their objective probabilities.

Another Characterization of Expected Scott-Suppes Utility Representation

Bogazici Journal

This paper provides a new characterization of Expected Scott-Suppes Utility Representation (ESSUR). ESSUR combines the Expected Utility Representation with the Scott-Suppes Utility Representation (ESSUR). The latter represents semiorders that formalize preferences with intransitive indifferences. Dalkıran, Dokumacı, and Kara (2018) were the first to provide an axiomatic characterization of ESSUR. Surprisingly, their characterization does not involve any separability axiom, which is essential for numerical representations of preferences on uncountable sets. Candeal and Indurain (2010) were the first to provide a characterization of SSUR on uncountably infinite sets employing a semiorder separability axiom. In this paper, we identify the axioms required on top of those of Candeal and Indurain (2010) in order to obtain a linear Scott-Suppes utility representation, i.e., another characterization of ESSUR.

On expected and von Neumann-Morgenstern utility functions

2010

In this note we analyze the relationship between the properties of von Neumann-Morgenstern utility functions and expected utility functions. More precisely, we investigate which of the regularity and concavity assumptions usually imposed on the latter transfer to the former and vice versa. In particular we obtain that, in order for the expected utility functions to fulfill such classical properties, it