A re-characterization of the Kemeny distance

Burak Can; Ton Storcken

doi:10.1016/j.jmateco.2018.04.007

A re-characterization of the Kemeny distance

Burak Can^*, Ton Storcken

^*Corresponding author for this work

QE Math. Economics & Game Theory

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

The well-known swap distance (Kemeny, 1959; Kendall, 1938 and Hamming, 1950) is analyzed. On weak preferences, this function was characterized by Kemeny (1959) with five conditions; metric, betweenness, neutrality, reducibility, and normalization. We show that the same result can be achieved without the reducibility condition, which shows the Kemeny distance is much less demanding than it seems. We provide a new and logically independent characterization of the Kemeny distance and provide some insight to further analyze distance functions on preferences. (C) 2018 Elsevier B.V. All rights reserved.

Original language	English
Pages (from-to)	112-116
Number of pages	5
Journal	Journal of Mathematical Economics
Volume	79
Issue number	December
DOIs	https://doi.org/10.1016/j.jmateco.2018.04.007
Publication status	Published - Dec 2018

Keywords

Kemeny distance
Swap distance
Inversion metric
Preferences

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10.1016/j.jmateco.2018.04.007

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abstract = "The well-known swap distance (Kemeny, 1959; Kendall, 1938 and Hamming, 1950) is analyzed. On weak preferences, this function was characterized by Kemeny (1959) with five conditions; metric, betweenness, neutrality, reducibility, and normalization. We show that the same result can be achieved without the reducibility condition, which shows the Kemeny distance is much less demanding than it seems. We provide a new and logically independent characterization of the Kemeny distance and provide some insight to further analyze distance functions on preferences. (C) 2018 Elsevier B.V. All rights reserved.",

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AU - Storcken, Ton

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AB - The well-known swap distance (Kemeny, 1959; Kendall, 1938 and Hamming, 1950) is analyzed. On weak preferences, this function was characterized by Kemeny (1959) with five conditions; metric, betweenness, neutrality, reducibility, and normalization. We show that the same result can be achieved without the reducibility condition, which shows the Kemeny distance is much less demanding than it seems. We provide a new and logically independent characterization of the Kemeny distance and provide some insight to further analyze distance functions on preferences. (C) 2018 Elsevier B.V. All rights reserved.

KW - Kemeny distance

KW - Swap distance

KW - Inversion metric

KW - Preferences

U2 - 10.1016/j.jmateco.2018.04.007

DO - 10.1016/j.jmateco.2018.04.007

M3 - Article

SN - 0304-4068

VL - 79

SP - 112

EP - 116

JO - Journal of Mathematical Economics

JF - Journal of Mathematical Economics

IS - December

ER -

A re-characterization of the Kemeny distance

Abstract

Keywords

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