Is the preference of the majority representative?

Auteur:

Mihir Bhattacharya

Nicolas Grave

Date de publication:

03 Février 2020

Publié ici :

03 Février 2020

Mis à jour le :

16 Avril 2020

Domaines:

Economie

Langue de publication:

Anglais

Zone géographique:

Asie

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 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.

Is the preference of the majority representative?
By Mihir Bhattacharya and Nicolas Gravel, CSH-IFP Working Papers ; 12, Institut Français de Pondichéry / Centre de Sciences Humaines, Pondicherry / New Delhi, 26 p.
Language: English.(Not for sale). Available online at https://hal.archives-ouvertes.fr/hal-02281251

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