Mixture Symmetry and Quadratic Utility

Chew, Soo Hong; Epstein, Larry G.; Segal, Uzi

doi:10.2307/2938244

Cited by 166 publications

(94 citation statements)

References 21 publications

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“…These findings and other data showing violations of coalescing (Birnbaum, 2004a(Birnbaum, , 2007b refute CPT and all theories that satisfy coalescing, including those of Lopes and Oden (1999); Becker and Sarin (1987); Chew (1983);and Chew, Epstein, and Segal (1991), among others (see Luce, 1998Luce, , 2000. Birnbaum (1997) deduced that RAM and TAX would violate stochastic dominance when choices were constructed from a special recipe, illustrated in Choice Problem 2 of Table 1.…”

Section: Violations Of Coalescing: Splitting Effectsmentioning

confidence: 83%

New paradoxes of risky decision making.

Birnbaum¹

2008

Psychological Review

343

387

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During the last 25 years, prospect theory and its successor, cumulative prospect theory, replaced expected utility as the dominant descriptive theories of risky decision making. Although these models account for the original Allais paradoxes, 11 new paradoxes show where prospect theories lead to self-contradiction or systematic false predictions. The new findings are consistent with and, in several cases, were predicted in advance by simple "configural weight" models in which probability-consequence branches are weighted by a function that depends on branch probability and ranks of consequences on discrete branches. Although they have some similarities to later models called "rank-dependent utility," configural weight models do not satisfy coalescing, the assumption that branches leading to the same consequence can be combined by adding their probabilities. Nor do they satisfy cancellation, the "independence" assumption that branches common to both alternatives can be removed. The transfer of attention exchange model, with parameters estimated from previous data, correctly predicts results with all 11 new paradoxes. Apparently, people do not frame choices as prospects but, instead, as trees with branches.

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Section: Violations Of Coalescing: Splitting Effectsmentioning

confidence: 83%

New paradoxes of risky decision making.

Birnbaum¹

2008

Psychological Review

343

387

View full text Add to dashboard Cite

show abstract

“…Note that this implication does not depend on the assumption of SEU, but only on stochastic dominance. In contrast, it is possible for general non-expected utility preferences, for example, quadratic preference (Chew, Epstein, and Segal (1991)), to exhibit non-monotone behavior in interval and two-point ambiguity. See Chew, Miao, and Zhong (2013) for a discussion of Chew and Sagi's (2008) source preference model without reduction.…”

Section: A2 Recursive Rank-dependent Utilitymentioning

confidence: 99%

Partial Ambiguity

Chew¹,

Miao²,

Zhong³

2017

Econometrica

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We extend Ellsberg's two‐urn paradox and propose three symmetric forms of partial ambiguity by limiting the possible compositions in a deck of 100 red and black cards in three ways. Interval ambiguity involves a symmetric range of 50 − n to 50 + n red cards. Complementarily, disjoint ambiguity arises from two nonintersecting intervals of 0 to n and 100 − n to 100 red cards. Two‐point ambiguity involves n or 100 − n red cards. We investigate experimentally attitudes towards partial ambiguity and the corresponding compound lotteries in which the possible compositions are drawn with equal objective probabilities. This yields three key findings: distinct attitudes towards the three forms of partial ambiguity, significant association across attitudes towards partial ambiguity and compound risk, and source preference between two‐point ambiguity and two‐point compound risk. Our findings help discriminate among models of ambiguity in the literature.

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“…Thus, other than our model of mixture-averse preferences, most of the non-expectedutility preferences considered in the literature are encompassed by this result. The only prominent theory that we are aware of that is not covered by this result is the quadratic utility model of Chew, Epstein, and Segal (1991). To our knowledge, it remains an open question whether quadratic utility can violate PD while still respecting SOSD.…”

Section: S32 Preference For Diversification and Sosdmentioning

confidence: 93%

Dynamic Mixture-Averse Preferences

Sarver¹

2018

Econometrica

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IN THIS SUPPLEMENT, we provide several supporting results that are used in the main paper. In Section S.1, we provide a general local expected-utility result for mixture-averse preferences that nests Proposition 1 in the main paper as a special case. In Section S.2, we establish the relationship between mixture-averse preferences and several prominent non-expected-utility theories, including rank-dependent utility, betweenness, disappointment aversion, and cautious expected utility. Section S.3 describes the implications of preference for diversification for insurance demand, and discusses how preference for diversification is equivalent to risk aversion for either rank-dependent utility or any preference that is quasiconcave in probabilities. Section S.4 establishes the existence of a value function for the optimal risk attitude representation. Proofs are contained in Section S.5. S.1. LOCAL EXPECTED-UTILITY ANALYSISWhen applying the optimal risk attitude model, one important consideration is how properties of the set of transformations in the representation relate to properties of the corresponding risk preference. In this section, we show that the certainty equivalent for an ORA representation respects a stochastic order if and only if each of the transformations φ ∈ also respects this order. This result is similar in spirit to the local expected-utility analysis introduced in the influential paper by Machina (1982). After presenting the main theorem of this section, we will make precise connections to Machina's results and the many generalizations and extensions that appeared in the literature that followed. We will also describe how the expected-utility core recently developed by Cerreia-Vioglio, Maccheroni, and Marinacci (2017) can be related to the ORA representation.The main result of this section applies to any convex utility representation on a set of lotteries (X), where X is any compact metric space. Of particular interest is the special case where X is an interval, for example, a set of monetary outcomes or the set of continuation values for an ORA representation. We first state a general definition of stochastic orders generated by sets of functions. DEFINITION S.1: Let C be a set in the space of real-valued continuous functions C(X) for some compact metric space X. The order ≥ C on (X) generated by C is defined by μ ≥ C η ⇐⇒ φ(x) dμ(x) ≥ φ(x) dη(x) ∀φ ∈ C A function W : (X) → R is monotone with respect to the order ≥ C if μ ≥ C η implies W (μ) ≥ W (η).

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Mixture Symmetry and Quadratic Utility

Cited by 166 publications

References 21 publications

New paradoxes of risky decision making.

New paradoxes of risky decision making.

Partial Ambiguity

Dynamic Mixture-Averse Preferences

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