Consistency of scoring rules: A reinvestigation of composition-consistency

Emel Öztürk*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

Abstract

We consider a collective choice problem in which the number of alternatives and the number of voters vary. Two fundamental axioms of consistency in such a setting, reinforcement and composition-consistency, are incompatible. We first observe that the latter implies four conditions each of which can be formulated as a consistency axiom on its own right. We find that two of these conditions are compatible with reinforcement. In fact, one of these, called composition-consistency with respect to non-clone winners, turns out to characterize a class of scoring rules which contains the Plurality rule. When combined with a requirement of monotonicity, composition-consistency with respect to non-clone winners uniquely characterizes the Plurality rule. A second implication of composition-consistency leads to a class of scoring rules that always select a Plurality winner when combined with monotonicity.
Original languageEnglish
Pages (from-to)801-831
JournalInternational Journal of Game Theory
Volume49
Issue number3
DOIs
Publication statusPublished - Sep 2020

Keywords

  • plurality rule
  • cloning-consistency
  • composition-consistency
  • reinforcement
  • scoring rules
  • monotonicity

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