Limited Voting for Better Representation?

TL;DR

This paper provides a formal analysis of Limited Voting (LV), an approval-based multi-winner voting method, examining its potential to improve representation in terms of diversity and proportionality, with practical insights from a Dutch health insurance company's use case.

Contribution

It offers the first formal analysis of LV, identifying conditions where it enhances representation and quantifying its benefits or limitations in diversity and proportionality.

Findings

LV can improve representation under certain conditions.

The extent of improvement varies with election parameters.

LV's effectiveness depends on specific diversity and proportionality criteria.

Abstract

Limited Voting (LV) is an approval-based method for multi-winner elections where all ballots are required to have a same fixed size. While it appears to be used as voting method in corporate governance and has some political applications, to the best of our knowledge, no formal analysis of the rule exists to date. We provide such an analysis here, prompted by a request for advice about this voting rule by a health insurance company in the Netherlands, which uses it to elect its work council. We study conditions under which LV would improve representation over standard approval voting and when it would not. We establish the extent of such an improvement, or lack thereof, both in terms of diversity and proportionality notions. These results help us understand if, and how, LV may be used as a low-effort fix of approval voting in order to enhance representation.