Topological aggregation of inequality preorders

Breton, Michel Le; Trannoy, Alain; Uriarte, José Ramón

doi:10.1007/bf00437312

Cited by 8 publications

(2 citation statements)

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“…The space of continuous and strictly Schur-convex preferences, i.e. continuous preferences P such that for all x 2 IR k with P x i xed and for all bistochastic matrices B we have: x; Bx 2 P implies that B is a permutation matrix, equipped with a suitable topology Le Breton et al, 1985.…”

Section: 44mentioning

confidence: 99%

Topological social choice

Lauwers

2000

Mathematical Social Sciences

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The topological approach to social choice was developed by Graciela Chichilnisky in the beginning of the eighties. The main result in this area known as the resolution of the topological social choice paradox shows that a space of preferences admits of a continuous, anonymous, and unanimous aggregation rule for every numb e rof individuals if and only if this space is contractible. Furthermore, connections b e t ween the Pareto principle, dictatorship, and manipulation were established. Recently, Baryshnikov used the topological approach to demonstrate that Arrow's impossibility theorem can b ereformulated in terms of the non-contractibility of spheres. This paper discusses these results in a self-contained way, emphasizes the social choice interpretation of some topological concepts, and surveys the area of topological aggregation. 1

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Section: 44mentioning

confidence: 99%

Topological social choice

Lauwers

2000

Mathematical Social Sciences

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“…In this framework, Le Breton et al (1985) have proved the existence of Chichilnisky aggregation rules on the class of all continuous and strictly Schur-convex inequality preorders.…”

Section: Applications To Topological Social Choice Modelsmentioning

confidence: 99%