We define and study a general framework for approval-based budgeting methods and compare certain methods within this framework by their axiomatic and computational properties. Furthermore, we visualize their behavior on certain Euclidean distributions and analyze them experimentally.
We characterize the class of committee scoring rules that satisfy the fixedmajority criterion. We argue that rules in this class are multiwinner analogues of the single-winner Plurality rule, which is uniquely characterized as the only single-winner scoring rule that satisfies the simple majority criterion. We define top-k-counting committee scoring rules and show that the fixed-majority consistent rules are a subclass of the top-k-counting rules. We give necessary and sufficient conditions for a top-kcounting rule to satisfy the fixed-majority criterion. We show that, for many top-kcounting rules, the complexity of winner determination is high (formally, we show that the problem of deciding if there exists a committee with at least a given score is NPhard), but we also show examples of rules with polynomial-time winner determination procedures. For some of the computationally hard rules, we provide either exact FPT algorithms or approximate polynomial-time algorithms.A preliminary version of this paper was presented at AAAI-2016).Nimrod Talmon: Most of the work was done while the author was affiliated with TU Berlin (Berlin, Germany) and Weizmann Institute of Science (Rehovot, Israel).
In a liquid democracy, voters can either vote directly or delegate their vote to another voter of their choice. We consider ordinal elections, and study a model of liquid democracy in which voters specify partial orders and use several delegates to refine them. This flexibility, however, comes at a price, as individual rationality (in the form of transitive preferences) can no longer be guaranteed. We discuss ways to detect and overcome such complications. Based on the framework of distance rationalization, we introduce novel variants of voting rules that are tailored to the liquid democracy context.
International audienceVoter control problems model situations such as an external agent trying to affect the result of an election by adding voters, for example by convincing some voters to vote who would otherwise not attend the election. Traditionally , voters are added one at a time, with the goal of making a distinguished alternative win by adding a minimum number of voters. In this paper, we initiate the study of combinatorial variants of control by adding voters. In our setting, when we choose to add a voter v, we also have to add a whole bundle κ(v) of voters associated with v. We study the computational complexity of this problem for two of the most basic voting rules, namely the Plurality rule and the Condorcet rule
The classical multiwinner rules are designed for particular purposes. For example, variants of kBorda are used to find k best competitors in judging contests while the Chamberlin-Courant rule is used to select a diverse set of k products. These rules represent two extremes of the multiwinner world. At times, however, one might need to find an appropriate trade-off between these two extremes. We explore continuous transitions from k-Borda to Chamberlin-Courant and study intermediate rules.
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