Heuristic Strategies in Uncertain Approval Voting Environments

In many collective decision making situations, agents vote to choose an alternative that best represents the preferences of the group. Agents may manipulate the vote to achieve a better outcome by voting in a way that does not reflect their true preferences. In real world voting scenarios, people often do not have complete information about other voter preferences and it can be computationally complex to identify a strategy that will maximize their expected utility. In such situations, it is often assumed that voters will vote truthfully rather than expending the effort to strategize. However, being truthful is just one possible heuristic that may be used. In this paper, we examine the effectiveness of heuristics in single winner and multi-winner approval voting scenarios with missing votes. In particular, we look at heuristics where a voter ignores information about other voting profiles and makes their decisions based solely on how much they like each candidate. In a behavioral experiment, we show that people vote truthfully in some situations and prioritize high utility candidates in others. We examine when these behaviors maximize expected utility and show how the structure of the voting environment affects both how well each heuristic performs and how humans employ these heuristics.Comment: arXiv admin note: text overlap with arXiv:1905.1210

Modeling Voters in Multi-Winner Approval Voting

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.Comment: 9 pages, 4 figures. To be published in the Proceedings of the Thirty-Fifth AAAI Conference on Artificial Intelligence, AAAI 202

Sincerity and Manipulation under Approval Voting

Under approval voting, each voter can nominate as many candidates as she wishes and the election winners are those candidates that are nominated most often. A voter is said to have voted sincerely if she prefers all those candidates she nominated to all other candidates. As there can be a set of winning candidates rather than just a single winner, a voter’s incentives to vote sincerely will depend on what assumptions we are willing to make regarding the principles by which voters extend their preferences over individual candidates to preferences over sets of candidates. We formulate two such principles, replacement and deletion, and we show that, under approval voting, a voter who accepts those two principles and who knows how the other voters will vote will never have an incentive to vote insincerely. We then discuss the consequences of this result for a number of standard principles of preference extension in view of sincere voting under approval voting

Vote manipulation in the presence of multiple sincere ballots

A classical result in voting theory, the Gibbard-Satterthwaite Theorem, states that for any non-dictatorial voting rule for choosing between three or more candidates, there will be situations that give voters an incentive to manipulate by not reporting their true preferences. However, this theorem does not immediately apply to all voting rules that are used in practice. For instance, it makes the implicit assumption that there is a unique way of casting a sincere vote, for any given preference ordering over candidates. Approval voting is an important voting rule that does not satisfy this condition. In approval voting, a ballot consists of the names of any subset of the set of candidates standing; these are the candidates the voter approves of. The candidate receiving the most approvals wins. A ballot is considered sincere if the voter prefers any of the approved candidates over any of the disapproved candidates. In this paper, we explore to what extent the presence of multiple sincere ballots allows us to circumvent the Gibbard-Satterthwaite Theorem. Our results show that there are several interesting settings in which no voter will have an incentive not to vote by means of some sincere ballot.

Vote Manipulation in the Presence of Multiple Sincere Ballots

A classical result in voting theory, the Gibbard-Satterthwaite Theorem, states that for any non-dictatorial voting rule for choosing between three or more candidates, there will be situations that give voters an incentive to manipulate by not reporting their true preferences. However, this theorem does not immediately apply to all voting rules that are used in practice. For instance, it makes the implicit assumption that there is a unique way of casting a sincere vote, for any given preference ordering over candidates. Approval voting is an important voting rule that does not satisfy this condition. In approval voting, a ballot consists of the names of any subset of the set of candidates standing; these are the candidates the voter approves of. The candidate receiving the most approvals wins. A ballot is considered sincere if the voter prefers any of the approved candidates over any of the disapproved candidates. In this paper, we explore to what extent the presence of multiple sincere ballots allows us to circumvent the Gibbard-Satterthwaite Theorem. Our results show that there are several interesting settings in which no voter will have an incentive not to vote by means of some sincere ballot.