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Social Choice and Welfare
Published in: Social Choice and Welfare 2/2015

01-02-2015

Maskin-monotonic scoring rules

Authors: Battal Doğan, Semih Koray

Published in: Social Choice and Welfare | Issue 2/2015

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Abstract

We characterize which scoring rules are Maskin-monotonic for each social choice problem as a function of the number of agents and the number of alternatives. We show that a scoring rule is Maskin-monotonic if and only if it satisfies a certain unanimity condition. Since scoring rules are neutral, Maskin-monotonicity turns out to be equivalent to Nash-implementability within the class of scoring rules. We propose a class of mechanisms such that each Nash-implementable scoring rule can be implemented via a mechanism in that class. Moreover, we investigate the class of generalized scoring rules and show that with a restriction on score vectors, our results for the standard case are still valid.
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Footnotes
1
A linear order is a transitive, anti-symmetric and complete binary relation.
 
2
\(\lfloor x\rfloor \) denotes the maximal integer that does not exceed \(x\).
 
3
The result is Lemma 4 in Chapter 3 of Moulin (1983).
 
4
The result is Theorem 2.3.22 of Peleg (1984).
 
Literature
Borda JC (1781) Memoire sur les elections au scrutiny. Historoire de lAcademie Royals des Sciences, Paris
Doğan B, Koray S (2007) Explorations on monotonicity in social choice theory. Bilkent University, Mimeo
Erdem O, Sanver R (2005) Minimal monotonic extensions of scoring rules. Soc Choice Welf 25:31–42CrossRef
Maskin E (1977) Nash equilibrium and welfare optimality. MIT, Cambridge
Moulin H (1983) The strategy of social choice. North-Holland, Amsterdam
Muller E, Satterthwaite M (1977) The equivalence of strong positive association and strategy-proofness. J Econ Theory 14:412–418CrossRef
Peleg B (1984) Game theoretic analysis of voting in committees. Cambridge University Press, CambridgeCrossRef
Puppe C, Tasnádi A (2008) Nash implementable domains for the borda count. Soc Choice Welf 31:367–392CrossRef
Sen A (1995) The implementation of social choice functions via social choice correspondences; a general formulation and a limit result. Soc Choice Welf 12:277–292CrossRef
Young HP (1974) An axiomatization of Borda’s rule. J Econ Theory 9:43–52CrossRef
Young HP (1975) Social choice scoring functions. SIAM J Appl Math 28:824–838CrossRef
Metadata
Title
Maskin-monotonic scoring rules
Authors
Battal Doğan
Semih Koray
Publication date
01-02-2015
Publisher
Springer Berlin Heidelberg
Published in
Social Choice and Welfare / Issue 2/2015
Print ISSN: 0176-1714
Electronic ISSN: 1432-217X
DOI
https://doi.org/10.1007/s00355-014-0835-6

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