Characterization of tie-breaking plurality rules
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Abstract We introduce a new condition for social choice functions, called “equal treatment of congruent distributions.” It requires some invariance between two preference profiles that share a type of congruity property with respect to the associated distributions of votes. It also implies two equal treatment conditions: one is a natural weakening of anonymity , which is the most standard equal treatment condition for individuals, and the other is a natural weakening of neutrality , which is the most standard equal treatment one for alternatives. Thus, equal treatment of congruent distributions plays the role of weak equal treatment conditions both for individuals and for alternatives. As our main results, we characterize a class of social choice functions that satisfy equal treatment of congruent distributions and some mild positive responsiveness conditions, and it is shown to coincide with the class of tie-breaking plurality rules , which are selections of the well-known plurality rule .Keywords:
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We consider an axiomatic characterization of the plurality rule, which selects the alternative(s) most preferred by the largest number of individuals. We strengthen the characterization result of Yeh (Economic Theory 34: 575{583, 2008) by replacing effciency axiom by the weaker axiom called faithfulness . Formally, we show that the plurality rule is the only rule satisfying anonymity, neutrality, reinforcement, tops-only , and faithfulness .
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We consider axiomatic characterization of social choice functions when there exist a fixed number of voters. Our particular interest is in social choice functions that reflect, to some extent, positional information in voters' preference rankings as well as orders between two alternatives. More specifically, we look for social choice functions that satisfy Neutrality, Positive Responsiveness, and Invariance for Average-Position Preserving Reversals. It turns out that there exists one and only one social choice function satisfying the three axioms, namely, Borda rule.
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Many classical social preference (multiwinner social choice) correspondences are resolute only when two alternatives and an odd number of individuals are considered. Thus, they generally admit several resolute refinements, each of them naturally interpreted as a tie-breaking rule. In this paper we find out conditions which make a social preference (multiwinner social choice) correspondence admit a resolute refinement fulfilling suitable weak versions of the anonymity and neutrality principles, as well as reversal symmetry (immunity to the reversal bias).
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In a social choice model with an infinite number of agents, there may occur coalitions that a preference aggregation rule should treat in the same manner. We introduce an axiom of equal treatment with respect to a measure of coalition size and explore its interaction with common axioms of social choice. We show that, provided the measure space is sufficiently rich in coalitions of the same measure, the new axiom is the natural extension of the concept of anonymity, and in particular plays a similar role in the characterization of preference aggregation rules.
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Many classical social preference (multiwinner social choice) correspondences are resolute only when two alternatives and an odd number of individuals are considered. Thus, they generally admit several resolute refinements, each of them naturally interpreted as a tie-breaking rule. In this paper we find out conditions which make a social preference (multiwinner social choice) correspondence admit a resolute refinement fulfilling suitable weak versions of the anonymity and neutrality principles, as well as reversal symmetry (immunity to the reversal bias).
Neutrality
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Arrow's impossibility theorem
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