Candidate Monotonicity and Proportionality for Lotteries and Non-Resolute Rules

TL;DR

This paper investigates the design of multiwinner voting rules that ensure candidate monotonicity and proportionality, demonstrating that certain rules can be adapted to satisfy both properties simultaneously.

Contribution

It proves that committees satisfying proportionality for solid coalitions are candidate monotone and adapts Phragmén's Ordered Rule into a candidate monotone probabilistic rule.

Findings

Proportional committees are candidate monotone.

Phragmén's Ordered Rule can be made candidate monotone.

The study advances multiwinner voting rule design.

Abstract

We study the problem of designing multiwinner voting rules that are candidate monotone and proportional. We show that the set of committees satisfying the proportionality axiom of proportionality for solid coalitions is candidate monotone. We further show that Phragm\'en's Ordered Rule can be turned into a candidate monotone probabilistic rule which randomizes over committees satisfying proportionality for solid coalitions.