Is the preference of the majority representative ?

Nicolas Gravel () and Mihir Bhattacharya

No 12, CSH-IFP Working Papers from Centre de Sciences Humaines, New Delhi

Abstract: Given a profile of preferences on a set of alternatives, a majority relation is a complete binary relation that agrees with the strict preference of a strict majority of these preferences whenever such strict majority is observed. We show that a majority binary relation is, among all conceivable binary relations, the most representative of the profile of preferences from which it emanates. We define “the most representative” to mean “the closest in the aggregate”. This requires a definition of what it means for a pair of preferences to be closer to each other then another. We assume that this definition takes the form of a distance function defined over the set of all conceivable preferences. We identify a necessary and sufficient condition for such a distance to be minimized by the preference of the majority. This condition requires the distance to be additive with respect to a plausible notion of compromise between preferences. The well-known Kemeny distance between preference does satisfy this property. We also provide a characterization of the class of distances satisfying this property as numerical representations of a primitive qualitative proximity relation between preferences.

Keywords: preferences; majority; dissimilarity; distance; aggregation (search for similar items in EconPapers)
JEL-codes: D71 D72 (search for similar items in EconPapers)
Pages: 30 pages
Date: 2019-08, Revised 2019-08
New Economics Papers: this item is included in nep-mic
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Published in the CSH-IFP Working Papers series

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Related works:
Journal Article: Is the preference of the majority representative ? (2021)
Working Paper: Is the preference of the majority representative ? (2021)
Working Paper: Is the preference of the majority representative? (2019)
Working Paper: Is the Preference of the Majority Representative? (2019)
Working Paper: Is the preference of the majority representative? (2019)
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