Full Implementation under Ambiguity

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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Necessary and sufficient conditions for the strategyproofness of irresolute social choice functions

Proceedings of hte 13th Conference on Theoretical Aspects of Rationality and Knowledge - TARK XIII ◽

10.1145/2000378.2000394 ◽

2011 ◽

Cited By ~ 8

Author(s):

Felix Brandt ◽

Markus Brill

Keyword(s):

Social Choice ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Choice Functions ◽

Social Choice Functions ◽

Necessary And Sufficient

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Randomized Social Choice Functions Under Metric Preferences

Journal of Artificial Intelligence Research ◽

10.1613/jair.5340 ◽

2017 ◽

Vol 58 ◽

pp. 797-827 ◽

Cited By ~ 14

Author(s):

Elliot Anshelevich ◽

John Postl

Keyword(s):

Social Choice ◽

Choice Functions ◽

Worst Case ◽

Ordinal Information ◽

Deterministic Algorithms ◽

Distortion Bounds ◽

Special Cases ◽

Agent Cost ◽

Social Choice Functions ◽

The Cost

We determine the quality of randomized social choice algorithms in a setting in which the agents have metric preferences: every agent has a cost for each alternative, and these costs form a metric. We assume that these costs are unknown to the algorithms (and possibly even to the agents themselves), which means we cannot simply select the optimal alternative, i.e. the alternative that minimizes the total agent cost (or median agent cost). However, we do assume that the agents know their ordinal preferences that are induced by the metric space. We examine randomized social choice functions that require only this ordinal information and select an alternative that is good in expectation with respect to the costs from the metric. To quantify how good a randomized social choice function is, we bound the distortion, which is the worst-case ratio between the expected cost of the alternative selected and the cost of the optimal alternative. We provide new distortion bounds for a variety of randomized algorithms, for both general metrics and for important special cases. Our results show a sizable improvement in distortion over deterministic algorithms.

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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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