Scoring rules over subsets of alternatives: Consistency and paradoxes

Eric Kamwa and Vincent Merlin ()

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Abstract: We know since the works of Gehrlein and Fishburn (1980, 1981), Fishburn (1981) and Saari (1987, 1988, 1990) that, the collective rankings of scoring rules are not stable when some alternatives are dropped from the set of alternatives. However, in the literature, attention has been mainly devoted to the relationship between pairwise majority vote and scoring rules rankings. In this paper, we focus on the relationships between four-candidate and three-candidate rankings. More precisely, given a collective ranking over a set of four candidates, we determine under the impartial culture condition, the probability of each of the six possible rankings to occur when one candidate is dropped. As a consequence, we derive from our computations, the likelihood of two paradoxes of committee elections, the Leaving Member Paradox (Staring, 1986) and the Prior Successor Paradox which occur when an elected candidate steps down from a two-member committee.

Keywords: Committee; Paradox; Collective ranking; Consistency; Scoring rule; Impartial Culture (search for similar items in EconPapers)
Date: 2015-12
Note: View the original document on HAL open archive server: https://hal.univ-antilles.fr/hal-01702492v1
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Citations: View citations in EconPapers (21)

Published in Journal of Mathematical Economics, 2015, 61, pp.130 - 138. ⟨10.1016/j.jmateco.2015.08.008⟩

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Journal Article: Scoring rules over subsets of alternatives: Consistency and paradoxes (2015)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01702492

DOI: 10.1016/j.jmateco.2015.08.008

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