Related papers: Representation-Compatible Power Indices
We consider a simple and altruistic multiagent system in which the agents are eager to perform a collective task but where their real engagement depends on the willingness to perform the task of other influential agents. We model this…
Classical power index analysis considers the individual's ability to influence the aggregated group decision by changing its own vote, where all decisions and votes are assumed to be binary. In many practical applications we have more…
We study the inverse power index problem for weighted voting games: the problem of finding a weighted voting game in which the power of the players is as close as possible to a certain target distribution. Our goal is to find algorithms…
In many applications of cooperative game theory -- from corporate governance and cartel formation to parliamentary voting -- not all winning coalitions are feasible. Ideological distances, institutional constraints, or pre-electoral…
Voting power determines the "power" of individuals who cast votes; their power is based on their ability to influence the winning-ness of a coalition. Usually each individual acts alone, casting either all or none of their votes and is…
A proposal in a weighted voting game is accepted if the sum of the (non-negative) weights of the "yea" voters is at least as large as a given quota. Several authors have considered representations of weighted voting games with minimum sum,…
In approval-based multiwinner voting, voters express approval preferences over a set of candidates, and the goal is to return a winning committee. This model captures a broad range of subset selection problems under preferences. Prior work…
Power law or generalized polynomial regressions with unknown real-valued exponents and coefficients, and weakly dependent errors, are considered for observations over time, space or space--time. Consistency and asymptotic normality of…
The Banzhaf Power Index (BPI) is a method of measuring the power of voters in determining the outcome of a voting game. Some voting games exhibit a hierarchical structure, including the US electoral college and ensemble learning methods; we…
The Shapley value is commonly illustrated by roll call votes in which players support or reject a proposal in sequence. If all sequences are equiprobable, a voter's Shapley value can be interpreted as the probability of being pivotal, i.e.,…
In this paper we study rankings induced by power indices of players in simple game models of bicameral legislatures. For a bicameral legislature where bills are passed with a simple majority vote in each house we give a condition involving…
When selecting multiple candidates based on approval preferences of agents, the proportional representation of agents' opinions is an important and well-studied desideratum. Existing criteria for evaluating the representativeness of…
We study multiwinner elections with approval-based preferences. An instance of a multiwinner election consists of a set of alternatives, a population of voters---each voter approves a subset of alternatives, and the desired committee size…
We consider weighted averages of the number of representations of an even integer as a sum of two prime numbers, where each summand lies in a given arithmetic progression modulo a common integer $q$. Our result is uniform in a suitable…
Election data represent a precious source of information to study human behavior at a large scale. In proportional elections with open lists, the number of votes received by a candidate, rescaled by the average performance of all…
Voting systems typically treat all voters equally. We argue that perhaps they should not: Voters who have supported good choices in the past should be given higher weight than voters who have supported bad ones. To develop a formal…
Many binary collective choice situations can be described as weighted simple voting games. We introduce weighted committee games to model decisions on an arbitrary number of alternatives in analogous fashion. We compare the effect of…
Despite extensive theoretical research on proportionality in approval-based multiwinner voting, its impact on which committees and candidates can be selected in practice remains poorly understood. We address this gap by (i) analyzing the…
Systems of indirect voting based on the principle of qualified majority can be analysed using the methods of game theory. In particular, this applies to the voting system in the Council of the European Union, which was recently a subject of…
In this paper we extend the principle of proportional representation to rankings. We consider the setting where alternatives need to be ranked based on approval preferences. In this setting, proportional representation requires that…