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Social Choice and Welfare

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22-03-2017 | Original Paper

On societies choosing social outcomes, and their memberships: strategy-proofness

Authors: Gustavo Bergantiños, Jordi Massó, Alejandro Neme

Published in: Social Choice and Welfare | Issue 4/2017

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Abstract

We consider a society whose members have to choose not only an outcome from a given set of outcomes but also the subset of agents that will remain members of the society. We assume that each agent is indifferent between any two alternatives (pairs of final societies and outcomes) provided that the agent does not belong to any of the two final societies, regardless of the chosen outcome. Under this preference domain restriction we characterize the class of all strategy-proof, unanimous and outsider independent rules as the family of all serial dictator rules.

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All these examples will be included as particular instances of our model. However, the strong incentive requirement of strategy-proofness will be incompatible with any stability notion related to voluntary membership.

See the last section of the paper for a discussion about the consequences of requiring stronger domain restrictions.

For instance, complex and sequential algorithms defined for matching problems induce rules mapping preference profiles into alternatives.

Note that we are admitting the possibility that the society selects all outcomes with no agent in the final society; i.e., for all \(x\in X\) , \((\varnothing ,x)\in A\).

See the final section of the paper for an indication of the class of strategy-proof and unanimous rules that are not outsider independent.

Observe again that the preferences we are considering satisfy (P.1) and hence, rules do not operate on the universal domain of preferences over A. Thus, the Gibbard–Satterthwaite theorem can not be applied.

The preference \(R_{N^{*},\succ _{i}}\) may not depend on \(\succ _{i},\) but for simplicity we maintain the notation \(R_{N^{*},\succ _{i}}\) .

We thank a referee of this journal for suggesting us these two domain restrictions. However, to obtain full characterizations of interesting classes of non-trivial and strategy-proof rules, on the two corresponding domains, seems to require a complete analysis, which is outside the scope of the present paper.

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Title: On societies choosing social outcomes, and their memberships: strategy-proofness
Authors: Gustavo Bergantiños
Jordi Massó
Alejandro Neme
Publication date: 22-03-2017
Publisher: Springer Berlin Heidelberg
Published in: Social Choice and Welfare / Issue 4/2017
Print ISSN: 0176-1714
Electronic ISSN: 1432-217X
DOI: https://doi.org/10.1007/s00355-017-1041-0

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