Modeling Voters in Multi-Winner Approval Voting

TL;DR

This paper investigates how voters behave in multi-winner approval voting, revealing that people often manipulate their votes but do not always do so optimally, and introduces a new model that better predicts real-world voting behavior.

Contribution

The paper introduces a novel behavioral model for multi-winner approval voting that accounts for human cognitive constraints and the size of the winning set, improving prediction accuracy.

Findings

Voters tend to manipulate their votes to improve outcomes.

Most voters do not identify the optimal manipulation.

The new model outperforms existing heuristics in predicting behavior.

Abstract

In many real world situations, collective decisions are made using voting and, in scenarios such as committee or board elections, employing voting rules that return multiple winners. In multi-winner approval voting (AV), an agent submits a ballot consisting of approvals for as many candidates as they wish, and winners are chosen by tallying up the votes and choosing the top-$k$ candidates receiving the most approvals. In many scenarios, an agent may manipulate the ballot they submit in order to achieve a better outcome by voting in a way that does not reflect their true preferences. In complex and uncertain situations, agents may use heuristics instead of incurring the additional effort required to compute the manipulation which most favors them. In this paper, we examine voting behavior in single-winner and multi-winner approval voting scenarios with varying degrees of uncertainty using behavioral data obtained from Mechanical Turk. We find that people generally manipulate their vote to obtain a better outcome, but often do not identify the optimal manipulation. There are a number of predictive models of agent behavior in the COMSOC and psychology literature that are based on cognitively plausible heuristic strategies. We show that the existing approaches do not adequately model real-world data. We propose a novel model that takes into account the size of the winning set and human cognitive constraints, and demonstrate that this model is more effective at capturing real-world behaviors in multi-winner approval voting scenarios.