Subjective expected utility on the basis of ordered categories (original) (raw)

Subjective expected utility without preferences

Journal of Mathematical Psychology, 2011

This paper proposes a theory of subjective expected utility based on primitives only involving the fact that an act can be judged either "attractive" or "unattractive". We give conditions implying that there are a utility function on the set of consequences and a probability distribution on the set of states such that attractive acts have a subjective expected utility above some threshold. The numerical representation that is obtained has strong uniqueness properties.

Classical subjective expected utility

Proceedings of the National Academy of Sciences, 2013

We consider decision makers who know that payo¤ relevant observations are generated by a process that belongs to a given class M , as postulated in Wald [36]. We incorporate this Waldean piece of objective information within an otherwise subjective setting a la Savage [33] and show that this leads to a two-stage subjective expected utility model that accounts for both state and model uncertainty.

Subjective Expected Utility with State-Dependent but Action/Observation-Independent Preferences

Risks

Under state-dependent preferences, probabilities and units of scale of state-dependent utilities are not separately identified. In standard models, only their products matter to decisions. Separate identification has been studied under implicit actions by Drèze or under explicit actions and observations by Karni. This paper complements both approaches and relates them when conditional preferences for final outcomes are independent of actions and observations. That special case permits drastic technical simplification while remaining open to some natural extensions.

Generalized Subjective Lexicographic Expected Utility Representation

arXiv, 2014

We provide foundations for decisions in face of unlikely events by extending the standard framework of Savage to include preferences indexed by a family of events. We derive a subjective lexicographic expected utility representation which allows for infinitely many lexicographically ordered levels of events and for event-dependent attitudes toward risk. Our model thus provides foundations for models in finance that rely on different attitudes toward risk (e.g. Skiadas [9]) and for off-equilibrium reasonings in infinite dynamic games, thus extending and generalizing the analysis in Blume, Brandenburger and Dekel [3].

Reference-dependent subjective expected utility

Journal of Economic Theory, 2003

A reference-dependent generalisation of subjective expected utility theory is presented. In this theory, preferences between acts depend both on final outcomes and on reference points (which may be uncertain acts). It is characterised by a set of axioms in a Savage-style framework. A restricted form of the theory separates attitudes to end states (encoded in a 'satisfaction function') from attitudes to gains and losses of satisfaction. Given weak additional assumptions, the restricted theory excludes cycles of choice, explains observed disparities between willingness-to-pay and willingness-to-accept valuations of lotteries, and predicts preference reversal. r

Testable implications of subjective expected utility theory

Games and Economic Behavior, 2005

I show that the predictive content of the hypothesis of subjective expected utility maximization critically depends on what the analyst knows about the details of the problem a particular decision maker faces. When the analyst does not know anything about the agent´s payo s or beliefs and can only observe the sequence of actions taken by the decision maker any arbitrary sequence of actions can be implemented as the choice of an agent that solves some intertemporal utility maximization problem under uncertainty. for their comments to an earlier version of this work, and especially the associate editor and the referees for making suggestions that substantially improved the quality of the paper. I also received useful comments from the participants at a Cornell seminar. All remaining shortcomings are mine.

The impossibility of compromise: some uniqueness properties of expected utility preferences

Economic Theory, 2000

We focus on the following uniqueness property of expected utility preferences: Agreement of two preferences on one interior indifference class implies their equality. We show that, besides expected utility preferences under (objective) risk, this uniqueness property holds for subjective expected utility preferences in Anscombe-Aumann's (partially subjective) and Savage's (fully subjective) settings, while it does not hold for subjective expected utility preferences in settings without rich state spaces. Indeed, when it holds the uniqueness property is even stronger than described above, as it needs only agreement on binary acts. The extension of the uniqueness property to the subjective case is possible because beliefs in the mentioned settings are shown to satisfy an analogous property: If two decision makers agree on a likelihood indifference class, they must have identical beliefs.

Subjectively weighted linear utility

Theory and Decision, 1987

An axiomatized theory of nonlinear utility and subjective probability is presented in which assessed probabilities are allowed to depend on the consequences associated with events. The representation includes the expected utility model as a special case, but can accommodate the Ellsberg paradox and other types of ambiguity sensitive behavior, while retaining familiar properties of subjective probability, such as additivity for disjoint events and multiplication of conditional probabilities. It is an extension, to the states model of decision making under uncertainty, of Chew's weighted linear utility representation for decision making under risk.