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International Journal of Game Theory

, Volume 38, Issue 4, pp 553–574 | Cite as

One-way monotonicity as a form of strategy-proofness

  • M. Remzi Sanver
  • William S. Zwicker
Article

Abstract

Suppose that a vote consists of a linear ranking of alternatives, and that in a certain profile some single pivotal voter v is able to change the outcome of an election from s alone to t alone, by changing her vote from P v to \({P^\prime_{v}}\) . A voting rule \({\mathcal{F}}\) is two-way monotonic if such an effect is only possible when v moves t from below s (according to P v to above s (according to \({P^\prime_{v}}\) . One-way monotonicity is the strictly weaker requirement forbidding this effect when v makes the opposite switch, by moving s from below t to above t. Two-way monotonicity is very strong—equivalent over any domain to strategy proofness. One-way monotonicity holds for all sensible voting rules, a broad class including the scoring rules, but no Condorcet extension for four or more alternatives is one-way monotonic. These monotonicities have interpretations in terms of strategy-proofness. For a one-way monotonic rule \({\mathcal{F}}\) , each manipulation is paired with a positive response, in which \({\mathcal{F}}\) offers the pivotal voter a strictly better result when she votes sincerely.

Keywords

One-way monotonicity Monotonicity Participation No-show paradox Strategy-proofness Manipulation Scoring rule Sensible virtue Condorcet extension 

JEL Classification

D71 

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of EconomicsIstanbul Bilgi UniversityIstanbulTurkey
  2. 2.Mathematics DepartmentUnion CollegeSchenectadyUSA

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