Proportional Rankings

TL;DR

This paper extends the concept of proportional representation to rankings based on approval preferences, analyzing various methods to ensure fair representation of cohesive voter groups in initial ranking segments.

Contribution

It introduces the concept of proportional rankings, studies multiple ranking methods, and provides theoretical guarantees and experimental evaluation for their effectiveness.

Findings

Certain ranking methods guarantee proportional representation.

Experimental results identify the most suitable methods for proportional rankings.

Theoretical analysis confirms proportionality guarantees for specific algorithms.

Abstract

In this paper we extend the principle of proportional representation to rankings. We consider the setting where alternatives need to be ranked based on approval preferences. In this setting, proportional representation requires that cohesive groups of voters are represented proportionally in each initial segment of the ranking. Proportional rankings are desirable in situations where initial segments of different lengths may be relevant, e.g., hiring decisions (if it is unclear how many positions are to be filled), the presentation of competing proposals on a liquid democracy platform (if it is unclear how many proposals participants are taking into consideration), or recommender systems (if a ranking has to accommodate different user types). We study the proportional representation provided by several ranking methods and prove theoretical guarantees. Furthermore, we experimentally evaluate these methods and present preliminary evidence as to which methods are most suitable for producing proportional rankings.