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One-way monotonicity as a form of strategy-proofness


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.

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Correspondence to M. Remzi Sanver.

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Sanver, M.R., Zwicker, W.S. One-way monotonicity as a form of strategy-proofness. Int J Game Theory 38, 553–574 (2009).

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

JEL Classification

  • D71