A continuous rating method for preferential voting. The complete case

TL;DR

This paper introduces a continuous rating method for complete preferential voting that ensures desirable properties like continuity, clone consistency, and adherence to the Condorcet-Smith principle, complementing existing ranking methods.

Contribution

The paper presents a novel quantitative rating method for complete preferential votes with proven desirable properties, enhancing the analysis of social acceptance.

Findings

Method satisfies continuity and clone consistency.

It adheres to the Condorcet-Smith principle.

It complements existing ranking methods like Schulze's.

Abstract

A method is given for quantitatively rating the social acceptance of different options which are the matter of a complete preferential vote. Completeness means that every voter expresses a comparison (a preference or a tie) about each pair of options. The proposed method 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 a property of clone consistency. One can view this rating method as a complement for the ranking method introduced in 1997 by Markus Schulze. It is also related to certain methods of one-dimensional scaling or cluster analysis.