Aggregation of Monotonic Bernoullian Archimedean Preferences: Arrovian Impossibility Results

Herzberg, Frederik

doi:10.2139/ssrn.2342431

Cited by 5 publications

(3 citation statements)

References 21 publications

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“…When individuals and society have ambiguity-sensitive preferences and individual tastes are heterogeneous, respecting Pareto dominance becomes impossible even when all individuals have identical beliefs. This has been shown in various settings covering in particular the class of MBA preferences (Gajdos et al, 2008;Herzberg, 2013;Chambers and Hayashi, 2014;Mongin and Pivato, 2015;Zuber, 2015). In contrast, Theorems 1 and 2 show that unambiguous preferences allow the aggregation of imprecise beliefs.…”

Section: Social Decisions With Ambiguity-sensitive Preferencesmentioning

confidence: 89%

Robust Social Decisions

Danan

Gajdos

Hill

et al. 2016

American Economic Review

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International audienceWe propose and operationalize normative principles to guide social decisions when individuals potentially have imprecise and heterogeneous beliefs, in addition to conflicting tastes or interests. To do so we adapt the standard Pareto principle to those preference comparisons that are robust to belief imprecision and characterize social preferences that respect this robust principle. We also characterize a suitable restriction of this principle. The former principle provides stronger guidance when it can be satisfied; when it cannot, the latter always provides minimal guidance

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Section: Social Decisions With Ambiguity-sensitive Preferencesmentioning

confidence: 89%

Robust Social Decisions

Danan

Gajdos

Hill

et al. 2016

American Economic Review

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“…the set of all expected-utility preferences for some set of states of the world or the set of all multiple-prior preferences) into a single variational preference ordering (e.g. an expected-utility preference ordering on that set of states of the world), there will be no aggregation rule satisfying the analogues of Arrow's responsiveness axioms, as was shown in Herzberg [23,22]. Note that these impossibility statements can be established both for the case of profiles of a given finite length (the analogue of Arrow's [2] theorem) and for the case of profiles of any given infinite length (the analogue of Campbell's [5] theorem), using a model-theoretic approach to aggregation theory inspired by Lauwers and Van Liedekerke [35] and systematically elaborated by Herzberg and Eckert [25,26].…”

Section: The Aggregation Of Probability Measuresmentioning

confidence: 99%

Aggregating Infinitely Many Probability Measures

Herzberg

2014

SSRN Journal

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Abstract. The problem of how to rationally aggregate probability measures occurs in particular (i) when a group of agents, each holding probabilistic beliefs, needs to rationalise a collective decision on the basis of a single 'aggregate belief system' and (ii) when an individual whose belief system is compatible with several (possibly infinitely many) probability measures wishes to evaluate her options on the basis of a single aggregate prior via classical expected utility theory (a psychologically plausible account of individual decisions).We investigate this problem by first recalling some negative results from preference and judgment aggregation theory which show that the aggregate of several probability measures should not be conceived as the probability measure induced by the aggregate of the corresponding expected-utility preferences. We describe how McConway's (Journal of the American Statistical Association, vol. 76, no. 374, pp. 410-414, 1981) theory of probabilistic opinion pooling can be generalised to cover the case of the aggregation of infinite profiles of finitelyadditive probability measures, too; we prove the existence of aggregation functionals satisfying responsiveness axioms à la McConway plus additional desiderata even for infinite electorates. On the basis of the theory of propositional-attitude aggregation, we argue that this is the most natural aggregation theory for probability measures.Our aggregation functionals for the case of infinite electorates are neither oligarchic nor integral-based and satisfy (at least) a weak anonymity condition. The delicate set-theoretic status of integral-based aggregation functionals for infinite electorates is discussed.

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“…Herzberg (2013) studies aggregation of MBA preferences in a multi-profile setup and gives an extension of Arrow's impossibility theorem to infinite electorates.…”

Section: Related Literaturementioning

confidence: 99%

Aggregating Tastes, Beliefs, and Attitudes Under Uncertainty

et al. 2014

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We provide possibility results on the aggregation of beliefs and tastes for Monotone, Bernoullian and Archimedian preferences of Cerreia-Vioglio, Ghirardato, Maccheroni, Marinacci, and Siniscalchi (2011). We propose a new axiom, Unambiguous Pareto Dominance, which requires that if the unambiguous part of individuals' preferences over a pair of acts agree, then society should follow them. We characterize the resulting social preferences and show that it is enough that individuals share a prior to allow non dictatorial aggregation. A further weakening of this axiom on common-taste acts, where cardinal preferences are identical, is also characterized. It gives rise to a set of relevant priors at the social level that can be any subset of the convex hull of the individuals' sets of relevant priors. We then apply these general results to the Maxmin Expected Utility model, the Choquet Expected Utility model and the Smooth Ambiguity model. We end with a characterization of the aggregation of ambiguity attitudes.

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Aggregation of Monotonic Bernoullian Archimedean Preferences: Arrovian Impossibility Results

Cited by 5 publications

References 21 publications

Robust Social Decisions

Robust Social Decisions

Aggregating Infinitely Many Probability Measures

Aggregating Tastes, Beliefs, and Attitudes Under Uncertainty

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