Boolean Representations of Preferences under Ambiguity

Frick, Mira; Iijima, Ryota; Yaouanq, Yves Le

doi:10.2139/ssrn.3423802

Cited by 3 publications

(3 citation statements)

References 45 publications

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“…Lehrer and Teper (2011) studied a representation called the multiple multiple-priors representation, which allows for violations of completeness and transitivity. Frick, Iijima, and Le Yaouanq (2019) proposed the Boolean expected utility representation, in which the belief the individual uses to evaluate an act is the most pessimistic prior from the most optimistic set of priors.…”

Section: Preview Of Resultsmentioning

confidence: 99%

“…Then the choice domain (F ) can be reduced to F , in which case only statewise randomization needs to be considered. Many papers on ambiguity have been built on this reduced version of AA's domain, either for the reason above or because randomization is not considered from the beginning; these include Gilboa and Schmeidler (1989), Schmeidler (1989), Ghirardato and Marinacci (2001), Maccheroni, Marinacci, and Rustichini (2006), Siniscalchi (2009), Cerreia-Vioglio, Maccheroni, Marinacci, and Montrucchio (2011), Lehrer and Teper (2011), and Frick, Iijima, and Le Yaouanq (2019). In contrast, Seo (2009), Saito (2011), and our paper adopt the original choice domain of AA without imposing Strong Dominance.…”

Section: Discussionmentioning

confidence: 99%

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Randomization and Ambiguity Aversion

Zhang²

2020

ECTA

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We propose a model of preferences in which the effect of randomization on ambiguity depends on how the unknown probability law is determined. We adopt the framework of Anscombe and Aumann (1963) and relax the axioms. In the resulting representation of the individual's preference, the individual has a collection of sets of priors M . She believes that before she moves, nature has chosen an unknown scenario (a set of priors) from M , and from that scenario, nature will choose a prior after she moves. The representation illustrates how randomization may partially eliminate the effect of ambiguity.

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Section: Preview Of Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Randomization and Ambiguity Aversion

Zhang²

2020

ECTA

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“…17 E c ). Corollary 2 in Frick, Iijima, and Le Yaouanq (2019) shows that if % admits an ↵-MEU representation (u, P, ↵) where P is not a singleton, then ↵ 1/2 (resp. ↵  1/2) if and only if AA(E) 0 (resp.…”

Section: A1 Preliminariesmentioning

confidence: 99%

Objective rationality foundations for (dynamic) α-MEU

Frick

Iijima

Yaouanq

2022

Journal of Economic Theory

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We show how incorporating Gilboa, Maccheroni, Marinacci, and Schmeidler's (2010) notion of objective rationality into the ↵-MEU model of choice under ambiguity (Hurwicz, 1951) can overcome several challenges faced by the baseline model without objective rationality. The decision-maker (DM) has a subjectively rational preference % ^, which captures the complete ranking over acts the DM expresses when forced to make a choice; in addition, we endow the DM with a (possibly incomplete) objectively rational preference % ⇤ , which captures the rankings the DM deems uncontroversial. Under the objectively founded ↵-MEU model, % ^has an ↵-MEU representation and % ⇤ has a unanimity representation à la Bewley (2002), where both representations feature the same utility index and set of beliefs. While the axiomatic foundations of the baseline ↵-MEU model are still not fully understood, we provide a simple characterization of its objectively founded counterpart. Moreover, in contrast with the baseline model, the model parameters are uniquely identified. Finally, we provide axiomatic foundations for prior-by-prior Bayesian updating of the objectively founded ↵-MEU model, while we show that, for the baseline model, standard updating rules can be ill-defined.

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Dual‐Self Representations of Ambiguity Preferences

Chandrasekher

Frick

Iijima

et al. 2022

ECTA

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We propose a class of multiple‐prior representations of preferences under ambiguity, where the belief the decision‐maker (DM) uses to evaluate an uncertain prospect is the outcome of a game played by two conflicting forces, Pessimism and Optimism. The model does not restrict the sign of the DM's ambiguity attitude, and we show that it provides a unified framework through which to characterize different degrees of ambiguity aversion, and to represent the co‐existence of negative and positive ambiguity attitudes within individuals as documented in experiments. We prove that our baseline representation, dual‐self expected utility (DSEU), yields a novel representation of the class of invariant biseparable preferences (Ghirardato, Maccheroni, and Marinacci (2004)), which drops uncertainty aversion from maxmin expected utility (Gilboa and Schmeidler (1989)), while extensions of DSEU allow for more general departures from independence. We also provide foundations for a generalization of prior‐by‐prior belief updating to our model.

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Boolean Representations of Preferences under Ambiguity

Cited by 3 publications

References 45 publications

Randomization and Ambiguity Aversion

Randomization and Ambiguity Aversion

Objective rationality foundations for (dynamic) α-MEU

Dual‐Self Representations of Ambiguity Preferences

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