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.
The complexity of manipulation for various types of approval voting (AV) has received considerable attention in the Computational Social Choice (COMSOC) literature @cite_35 . COMSOC is an area of research that investigates computational issues surrounding the aggregation of individual preferences. To start, assuming that agents act rationally and have full information about the votes of other agents, when agents have , i.e., when all agents either have utility 1 or 0 for candidates they approve or disapprove of, respectively, AV is strategy-proof. When agents have general utilities, finding a vote that maximizes the agent's utilities can be computed in polynomial time @cite_3 @cite_4 . For variants of AV including Proportional Approval Voting, Satisfaction Approval Voting, and the Repeated Approval Voting, the complexity of finding utility maximizing votes, even if they are manipulations, ranges in complexity from easy to coNP-complete @cite_29 .
@cite_35 @cite_29 @cite_4 @cite_3
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The rapidly growing field of computational social choice, at the intersection of computer science and economics, deals with the computational aspects of collective decision making. This handbook, written by thirty-six prominent members of the computational social choice community, covers the field comprehensively. Chapters devoted to each of the field's major themes offer detailed introductions. Topics include voting theory (such as the computational complexity of winner determination and manipulation in elections), fair allocation (such as algorithms for dividing divisible and indivisible goods), coalition formation (such as matching and hedonic games), and many more. Graduate students, researchers, and professionals in computer science, economics, mathematics, political science, and philosophy will benefit from this accessible and self-contained book. We study computational aspects of three prominent voting rules that use approval ballots to select multiple winners. These rules are proportional approval voting, reweighted approval voting, and satisfaction approval voting. Each rule is designed with the intention to compute a representative winning set. We show that computing the winner for proportional approval voting is NP-hard, closing an open problem (Kilgour, 2010). As none of the rules we examine are strategy-proof, we study various strategic aspects of the rules. In particular, we examine the computational complexity of computing a best response for both a single agent and a group of agents. In many settings, we show that it is NP-hard for an agent or agents to compute how best to vote given a fixed set of approval ballots of the other agents. Although recent years have seen a surge of interest in the computational aspects of social choice, no specific attention has previously been devoted to elections with multiple winners, e.g., elections of an assembly or committee. In this paper, we characterize the worst-case complexity of manipulation and control in the context of four prominent multiwinner voting systems, under different formulations of the strategic agent's goal. Recent work by Procaccia, Rosenschein and Zohar [14] established some results regarding the complexity of manipulation and control in elections with multiple winners, such as elections of an assembly or committee; that work provided an initial understanding of the topic. In this paper, we paint a more complete picture of the topic, investigating four prominent multi-winner voting rules. First, we characterize the complexity of manipulation and control in these voting rules under various kinds of formalizations of the manipulator's goal. Second, we extend the results about complexity of control to various well-known types of control. This work enhances our comprehension of which multi-winner voting rules should be employed in various settings.