A continuous rating method for preferential voting. The incomplete case

TL;DR

This paper introduces a continuous rating method for preferential voting that handles incomplete individual preferences, ensuring desirable properties like continuity, clone consistency, and the Condorcet-Smith principle in the social acceptance ratings.

Contribution

It extends previous methods to accommodate incomplete votes, distinguishing lack of information from ties, and proves the method's desirable properties in this more general setting.

Findings

Method handles incomplete votes effectively.

Ensures continuity and clone consistency.

Satisfies Condorcet-Smith principle.

Abstract

A method is given for quantitatively rating the social acceptance of different options which are the matter of a preferential vote. In contrast to a previous article, here the individual votes are allowed to be incomplete, that is, they need not express a comparison between every pair of options. This includes the case where each voter gives an ordered list restricted to a subset of most preferred options. In this connection, the proposed method (except for one of the given variants) carefully distinguishes a lack of information about a given pair of options from a proper tie between them. As in the special case of complete individual votes, the proposed generalization is proved to have certain desirable properties, which include: the continuity of the rates with respect to the data, a decomposition property that characterizes certain situations opposite to a tie, the Condorcet-Smith principle, and clone consistency