The General Theory of Random Choices in Relation to the Invariant Cardinal Utility Function and the Specific Probability Function. The (U, θ) Model A General Overview

Allais, Maurice

doi:10.1007/978-94-009-4019-2_16

Cited by 103 publications

(51 citation statements)

References 8 publications

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“…Machina (1982) has developed a very general theory of 'smooth' non-expected utility preferences over probability distributions. A special case 1 of Machina's model, which maintains some independence properties, is the rank-dependent expected utility (RDEU) model (Quiggin 1981, 1982a, Allais 1987,Yaari 1987, see also Gilboa 1987, Schmeidler 1989and Segal 1989.…”

Section: Comparative Statics For Rank-dependent Expected Utility Theorymentioning

confidence: 99%

Comparative statics for rank-dependent expected utility theory

Quiggin

1991

J Risk Uncertainty

137

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Section: Comparative Statics For Rank-dependent Expected Utility Theorymentioning

confidence: 99%

Comparative statics for rank-dependent expected utility theory

Quiggin

1991

J Risk Uncertainty

137

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“…(Allais 1988) and (Yaari 1987)). This model was, however, first presented and axiomatized by (Quiggin 1982) under the name of Anticipated Utility theory; the preference function in the RDU model has the form of a Choquet integral (Choquet 1953).…”

Section: A Non-eu Model: Rank Dependent Utility (Rdu)mentioning

confidence: 99%

Dynamic decision making without expected utility: An operational approach

Nielsen

Jaffray²

2006

European Journal of Operational Research

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Non-expected utility theories, such as rank dependent utility (RDU) theory, have been proposed as alternative models to EU theory in decision making under risk.These models do not share the separability property of expected utility theory. This implies that, in a decision tree, if the reduction of compound lotteries assumption is made (so that preferences at each decision node reduce to RDU preferences among lotteries) and that preferences at different decision nodes are identical (same utility function and same weighting function), then the preferences are not dynamically consistent; in particular, the sophisticated strategy, i.e., the strategy generated by a standard rolling back of the decision tree, is likely to be dominated w.r.t. stochastic dominance. Dynamic consistency of choices remains feasible, and the decision maker can avoid dominated choices, by adopting a non-consequentialist behavior, with his choices in a subtree possibly depending on what happens in the rest of the tree. We propose a procedure which: i) although adopting a non-consequentialist behavior, involves a form of rolling back of the decision tree; and ii) selects a non-dominated strategy that realizes a compromise between the decision maker's discordant goals at the different decision nodes. Relative to the computations involved in the standard expected utility evaluation of a decision problem, the main computational increase is due to the identification of non-dominated strategies by linear programming. A simulation, using the rank dependent utility criterion, confirms the computational tractability of the model.

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“…In particular, RDEU explains the behaviour observed in the Allais paradox by weakening the independence axiom. RDEU was first axiomatized by Quiggin (1982) as anticipated utility theory, and was further studied by Yaari (1987), Segal (1989), Allais (1987), and Wakker (1990), amongst others.…”

Section: Diversification Preferences In Eutmentioning

confidence: 99%

Diversification preferences in the theory of choice

Giorgi

Mahmoud

2016

Decisions Econ Finan

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Diversification represents the idea of choosing variety over uniformity. Within the theory of choice, desirability of diversification is axiomatized as preference for a convex combination of choices that are equivalently ranked. This corresponds to the notion of risk aversion when one assumes the von-Neumann-Morgenstern expected utility model, but the equivalence fails to hold in other models. This paper analyzes axiomatizations of the concept of diversification and their relationship to the related notions of risk aversion and convex preferences within different choice theoretic models. Implications of these notions on portfolio choice are discussed. We cover model-independent diversification preferences, preferences within models of choice under risk, including expected utility theory and the more general rank-dependent expected utility theory, as well as models of choice under uncertainty axiomatized via Choquet expected utility theory. Remarks on interpretations of diversification preferences within models of behavioral choice are given in the conclusion.

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The General Theory of Random Choices in Relation to the Invariant Cardinal Utility Function and the Specific Probability Function. The (U, θ) Model A General Overview

Cited by 103 publications

References 8 publications

Comparative statics for rank-dependent expected utility theory

Comparative statics for rank-dependent expected utility theory

Dynamic decision making without expected utility: An operational approach

Diversification preferences in the theory of choice

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