Evaluating the Properties of a First Choice Weighted Approval Voting System

TL;DR

This paper introduces a hybrid voting system called beta(k) that combines features of plurality and approval voting, analyzing its properties and potential to satisfy various voting criteria.

Contribution

The paper characterizes the behavior of the beta(k) voting system for any value of k and demonstrates how it can mimic plurality or approval voting, including tie-breaking and criterion satisfaction.

Findings

Beta(k) can mimic plurality or approval voting depending on k.

It is possible to determine winning candidates based on known votes.

Beta(k) satisfies several common voting system criteria.

Abstract

Plurality and approval voting are two well-known voting systems with different strengths and weaknesses. In this paper we consider a new voting system we call beta(k) which allows voters to select a single first-choice candidate and approve of any other number of candidates, where k denotes the relative weight given to a first choice; this system is essentially a hybrid of plurality and approval. Our primary goal is to characterize the behavior of beta(k) for any value of k. Under certain reasonable assumptions, beta(k) can be made to mimic plurality or approval voting in the event of a single winner while potentially breaking ties otherwise. Under the assumption that voters are honest, we show that it is possible to find the values of k for which a given candidate will win the election if the respective approval and plurality votes are known. Finally, we show how some of the commonly used voting system criteria are satisfied by beta(k).