Scoring rules over subsets of alternatives: Consistency and paradoxes
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.
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|Date of creation:||Dec 2015|
|Publication status:||Published in Journal of Mathematical Economics, Elsevier, 2015, 61, pp.130-138. <10.1016/j.jmateco.2015.08.008>|
|Note:||View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-01238563|
|Contact details of provider:|| Web page: https://hal.archives-ouvertes.fr/|
References listed on IDEAS
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