In search of characterization of the preference for safety under the Choquet model

Michèle Cohen and Isaac Meilijson ()
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Isaac Meilijson: TAU - School of Mathematical Sciences [Tel Aviv] - TAU - Raymond and Beverly Sackler Faculty of Exact Sciences [Tel Aviv] - TAU - Tel Aviv University

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Abstract: Victor prefers safety more than Ursula if whenever Ursula prefers some constant to some uncertain act, so does Victor. This paradigm, whose Expected Utility version takes the form of Arrow & Pratt's more risk averse concept, will be studied in the Choquet Uncertainty model, letting u and μ (v and ν) be Ursula's (Victor's) utility and capacity. A necessary and sufficient condition (A) on the pairs (u, μ) and (v, ν) will be presented for dichotomous weak increased uncertainty aversion, the preference by Victor of a constant over a dichotomous act whenever such is the preference of Ursula. This condition, pointwise inequality between a function defined in terms of v (u-1(⋅)) and another defined purely in terms of the capacities, preserves the flavor of the "more pessimism than greediness" characterization of monotone risk aversion by Chateauneuf, Cohen & Meilijson in the Rank-dependent Utility Model and its extension by Grant & Quiggin to the Choquet Utility Model. A sufficient condition (B) in terms of the capacities only, satisfied in particular if ν (⋅) = f (μ (⋅)) for some convex f, will be presented for more simplicity seeking, the preference by Victor over any act for some dichotomous act, that leaves Ursula indifferent. Condition A is thus a characterization of weak increased uncertainty aversion for convex f. An example will be exhibited disproving the more far reaching conjecture under which the dichotomous case implies the general case.

Keywords: Modèle de Choquet; avidité; pessimisme; utilité dépendant du rang; aversion pour le risque; incertain.; Choquet Utility; greediness; pessimism; Rank-dependent Utility; Risk aversion; uncertainty. (search for similar items in EconPapers)
Date: 2011-05
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00594082v1
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Published in 2011

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Working Paper: In search of characterization of the preference for safety under the Choquet model (2011)
Working Paper: In search of a characterization of the preference for safety under the Choquet model (2011)
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