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 nd 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
JournalInternational Journal of Game Theory
Publication statusAccepted/In press - 2020

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Scoring
Reinforcement
reinforcement
Monotonicity
Axiom
Axioms
Scoring rules
Vary
Imply
Alternatives
Requirements
Class

Cite this

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title = "Consistency of scoring rules: A reinvestigation of composition-consistency",
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 whichcan be formulated as a consistency axiom on its own right. We nd 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 Pluralityrule. 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-consistencyleads to a class of scoring rules that always select a Plurality winner when combined with monotonicity.",
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journal = "International Journal of Game Theory",
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Consistency of scoring rules: A reinvestigation of composition-consistency. / Öztürk, Emel.

In: International Journal of Game Theory, 2020.

Research output: Contribution to journalArticleScientificpeer-review

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AU - Öztürk, Emel

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AB - 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 whichcan be formulated as a consistency axiom on its own right. We nd 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 Pluralityrule. 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-consistencyleads to a class of scoring rules that always select a Plurality winner when combined with monotonicity.

M3 - Article

JO - International Journal of Game Theory

JF - International Journal of Game Theory

SN - 0020-7276

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