Von Neumann-Morgenstern solution social choice functions: An impossibility theorem

It has become accepted that social choice is impossible in the absence of interpersonal comparisons of well-being. This view is challenged here. Arrow obtained an impossibility theorem only by making unreasonable demands on social choice functions. With reasonable requirements, one can get very attractive possibilities and derive social preferences on the basis of non-comparable individual preferences. This new approach makes it possible to design optimal second-best institutions inspired by principles of fairness, while traditionally the analysis of optimal second-best institutions was thought to require interpersonal comparisons of well-being. In particular, this approach turns out to be especially suitable for the application of recent philosophical theories of justice formulated in terms of fairness, such as equality of resources.

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A REPRESENTATION THEOREM FOR VOTING WITH LOGICAL CONSEQUENCES

Economics and Philosophy ◽

10.1017/s026626710600085x ◽

2006 ◽

Vol 22 (2) ◽

pp. 181-190 ◽

Cited By ~ 45

Author(s):

PETER GÄRDENFORS

Keyword(s):

Social Choice ◽

Representation Theorem ◽

Impossibility Theorem ◽

Choice Functions ◽

Natural Conditions ◽

Independence Of Irrelevant Alternatives ◽

The Social ◽

Social Choice Functions ◽

Central Result ◽

Choice Set

This paper concerns voting with logical consequences, which means that anybody voting for an alternative x should vote for the logical consequences of x as well. Similarly, the social choice set is also supposed to be closed under logical consequences. The central result of the paper is that, given a set of fairly natural conditions, the only social choice functions that satisfy social logical closure are oligarchic (where a subset of the voters are decisive for the social choice). The set of conditions needed for the proof include a version of Independence of Irrelevant Alternatives that also plays a central role in Arrow's impossibility theorem.

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A Comment on Arrow’s Impossibility Theorem

The B E Journal of Theoretical Economics ◽

10.1515/bejte-2019-0175 ◽

2020 ◽

Vol 0 (0) ◽

Cited By ~ 1

Author(s):

Alec Sandroni ◽

Alvaro Sandroni

Keyword(s):

Social Choice ◽

Choice Function ◽

Social Preference ◽

Social Choice Function ◽

Individual Preference ◽

Impossibility Theorem ◽

Preference Order ◽

Individual Choice ◽

Choice Functions ◽

Preference Orders

AbstractArrow (1950) famously showed the impossibility of aggregating individual preference orders into a social preference order (together with basic desiderata). This paper shows that it is possible to aggregate individual choice functions, that satisfy almost any condition weaker than WARP, into a social choice function that satisfy the same condition (and also Arrow’s desiderata).

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Full Implementation under Ambiguity

American Economic Journal Microeconomics ◽

10.1257/mic.20180184 ◽

2021 ◽

Vol 13 (1) ◽

pp. 148-178

Author(s):

Huiyi Guo ◽

Nicholas C. Yannelis

Keyword(s):

Social Choice ◽

Expected Utility ◽

Sufficient Conditions ◽

Choice Functions ◽

Maxmin Expected Utility ◽

Special Cases ◽

Social Choice Functions ◽

Bayesian Implementation ◽

Pareto Efficient ◽

Choice Set

This paper introduces the maxmin expected utility framework into the problem of fully implementing a social choice set as ambiguous equilibria. Our model incorporates the Bayesian framework and the Wald-type maxmin preferences as special cases and provides insights beyond the Bayesian implementation literature. We establish necessary and almost sufficient conditions for a social choice set to be fully implementable. Under the Wald-type maxmin preferences, we provide easy-to-check sufficient conditions for implementation. As applications, we implement the set of ambiguous Pareto-efficient and individually rational social choice functions, the maxmin core, the maxmin weak core, and the maxmin value. (JEL D71, D81, D82)

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