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Social Choice and Welfare
Published in: Social Choice and Welfare 4/2020

01-10-2019 | Original Paper

On strategy-proof social choice between two alternatives

Authors: Abhinaba Lahiri, Anup Pramanik

Published in: Social Choice and Welfare | Issue 4/2020

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Abstract

We study strategy-proof rules for choosing between two alternatives. We consider the full preference domain which allows for indifference. In this framework, for strategy-proof rules, ontoness does not imply efficiency. We weaken the requirement of efficiency to ontoness and characterize the class of strategy-proof rules. We argue that the notion of efficiency is not desirable always. Further, we provide a simple description of the class of onto, anonymous and strategy-proof rules in this framework. The key feature of our characterization results brings out the role played by indifferent agents.
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Appendix
Available only for authorised users
Footnotes
1
For instance, see Dogan and Sanver (2007) for three or more alternatives with strict preferences. For two alternatives with strict preferences, see Theorem 1 of Barberà et al. (1991) and Corollary 3 of Ju (2003) for the case of single object.
 
2
If we restrict our attention to strong group strategy-proof rules, then ontoness implies efficiency [see Barberà et al. (2012), Manjunath (2012) and Harless (2015)].
 
3
See Section 3 in Núñez and Sanver (2017) for the case of two alternatives.
 
4
The participation property was introduced in Moulin (1991) to avoid the no-show paradox. The no-show paradox can be viewed as a way to manipulate social choice rules by abstaining from voting.
 
5
A profile \(R\in {\mathcal {R}}^n\) is called disagreement profile if \(N_a(R)\ne \emptyset \) and \(N_b(R)\ne \emptyset \).
 
Literature
Barberà S, Berga D, Moreno B (2012) Group strategy-proof social choice functions with binary ranges and arbitrary domains: characterization results. Int J Game Theory 41:791–808CrossRef
Barberà S, Sonnenschein H, Zhou L (1991) Voting by committees. Econometrica 59:595–609CrossRef
Dogan E, Sanver MR (2007) On the alternating use of “unanimity” and “surjectivity” in the Gibbard-Satterthwaite theorem. Econ Lett 96:140–143CrossRef
Fishburn PC (1973) The theory of social choice. Princeton University Press, Princeton
Harless P (2015) Reaching consensus: solidarity and strategic properties in binary social choice. Soc Choice Welfare 45:97–121CrossRef
Ju B-G (2003) A characterization of strategy-proof voting rules for separable weak orderings. Soc Choice Welfare 21:469–499CrossRef
Larsson B, Svensson L-G (2006) Strategy-proof voting on the full preference domain. Math Soc Sci 52:272–287CrossRef
Manjunath V (2012) Group strategy-proofness and voting between two alternatives. Math Soc Sci 63:239–242CrossRef
Moulin H (1991) Axioms of cooperative decision making, 15. Cambridge University Press, Cambridge
Núñez M, Sanver MR (2017) Revisiting the connection between the no-show paradox and monotonicity. Math Soc Sci 90:9–17CrossRef
Metadata
Title
On strategy-proof social choice between two alternatives
Authors
Abhinaba Lahiri
Anup Pramanik
Publication date
01-10-2019
Publisher
Springer Berlin Heidelberg
Published in
Social Choice and Welfare / Issue 4/2020
Print ISSN: 0176-1714
Electronic ISSN: 1432-217X
DOI
https://doi.org/10.1007/s00355-019-01220-7

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