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Consistency of scoring rules: a reinvestigation of composition-consistency

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  • Z. Emel Öztürk

    () (Tilburg University)

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.

Suggested Citation

  • Z. Emel Öztürk, 2020. "Consistency of scoring rules: a reinvestigation of composition-consistency," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(3), pages 801-831, September.
  • Handle: RePEc:spr:jogath:v:49:y:2020:i:3:d:10.1007_s00182-020-00711-7
    DOI: 10.1007/s00182-020-00711-7
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    References listed on IDEAS

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    More about this item

    Keywords

    Plurality rule; Cloning-consistency; Composition-consistency; Reinforcement; Scoring rules; Monotonicity;
    All these keywords.

    JEL classification:

    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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