In many real world situations, collective decisions are made using voting. Moreover, scenarios such as committee or board elections require voting rules that return multiple winners. In multi-winner approval voting (AV), an agent may vote for as many candidates as they wish. Winners are chosen by tallying up the votes and choosing the top- @math candidates receiving the most votes. An agent may manipulate the vote 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 to strategize, instead of incurring the additional effort required to compute the manipulation which most favors this http URL this paper, we examine voting behavior in multi-winner approval voting scenarios with complete information. We show that people generally manipulate their vote to obtain a better outcome, but often do not identify the optimal manipulation. Instead, voters tend to prioritize the candidates with the highest utilities. Using simulations, we demonstrate the effectiveness of these heuristics in situations where agents only have access to partial information.
Approval voting is a set of methods for aggregating group preferences that are particularly popular among economists, computer scientists, psychologists, and beyond @cite_23 @cite_6 . There are even multiple political action committees (PACs) in the United States, e.g., The Center for Election Science https: www.electionscience.org , that are committed to seeing the United States change voting procedures from plurality to approval voting. Perhaps one reason for this popularity is the idea that participants are allowed to express preference over a set of candidates and not just a single one. In France, a large study was run parallel to the 2002 election showing that many voters would have preferred approval ballots to traditional plurality ballots @cite_28 .
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Approval voting is a well-known voting procedure for single-winner elections. Voters approve of as many candidates as they like, and the candidate with the most approvals wins (Brams and Fishburn 1978, 1983, 2005). But Merrill and Nagel (1987) point out that there are many ways to aggregate approval votes to determine a winner, justifying a distinction between approval balloting, in which each voter submits a ballot that identifies the candidates the voter approves of, and approval voting, the procedure of ranking the candidates according to their total numbers of approvals. to the Handbook on Approval Voting.- History of Approval Voting.- Acclamation Voting in Sparta: An Early Use of Approval Voting.- Going from Theory to Practice: The Mixed Success of Approval Voting.- Axiomatic Theory.- Collective Choice for Simple Preferences.- Axiomatizations of Approval Voting.- Committees.- Approval Balloting for Multi-winner Elections.- Does Choosing Committees from Approval Balloting Fulfill the Electorate's Will?.- Strategic Voting.- The Basic Approval Voting Game.- Approval Voting in Large Electorates.- Computational Aspects of Approval Voting.- Probabilistic Exercises.- On the Condorcet Efficiency of Approval Voting and Extended Scoring Rules for Three Alternatives.- Behavioral Heterogeneity Under Approval and Plurality Voting.- In Silico Voting Experiments.- Experiments.- Laboratory Experiments on Approval Voting.- Framed Field Experiments on Approval Voting: Lessons from the 2002 and 2007 French Presidential Elections.- Approval Voting in Germany: Description of a Field Experiment.- Electoral Competition.- Classical Electoral Competition Under Approval Voting.- Policy Moderation and Endogenous Candidacy in Approval Voting Elections.- Meaning for Individual and Society.- Describing Society Through Approval Data.- Approval as an Intrinsic Part of Preference. This paper presents a large-scale experiment on the Approval Voting rule that took place during the 2002 French presidential election. We describe the experiment and its main results. The findings are as follows: (i) Such an experiment is feasible, and very well accepted by voters. (ii) The principle of approval voting is easily understood and accepted. (iii) Within the observed political context, compared to the official first-round vote, approval voting modifies the overall ranking of candidates. (iv) The candidates Le Pen and Chirac, more than the others, were able to convert approval votes into official first-round votes. We consider approval voting elections in which each voter votes for a (possibly empty) set of candidates and the outcome consists of a set of k candidates for some parameter k, e.g., committee elections. We are interested in the min-imax approval voting rule in which the outcome represents a compromise among the voters, in the sense that the maximum distance between the preference of any voter and the outcome is as small as possible. This voting rule has two main drawbacks. First, computing an outcome that minimizes the maximum distance is computationally hard. Furthermore, any algorithm that always returns such an outcome provides incentives to voters to misreport their true preferences. In order to circumvent these drawbacks, we consider approximation algorithms, i.e., algorithms that produce an outcome that approximates the minimax distance for any given instance. Such algorithms can be considered as alternative voting rules. We present a polynomial-time 2-approximation algorithm that uses a natural linear programming relaxation for the underlying optimization problem and deterministically rounds the fractional solution in order to compute the outcome; this result improves upon the previously best known algorithm that has an approximation ratio of 3. We are furthermore interested in approximation algorithms that are resistant to manipulation by (coalitions of) voters, i.e., algorithms that do not motivate voters to misreport their true preferences in order to improve their distance from the outcome. We complement previous results in the literature with new upper and lower bounds on strategyproof and group-strategyproof algorithms.