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 language | English |
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Pages (from-to) | 801-831 |
Journal | International Journal of Game Theory |
Volume | 49 |
Issue number | 3 |
DOIs | |
Publication status | Published - Sep 2020 |
Keywords
- plurality rule
- cloning-consistency
- composition-consistency
- reinforcement
- scoring rules
- monotonicity