Related papers: On the inverse power index problem
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…
Feature attribution methods have become essential for explaining machine learning models. Many popular approaches, such as SHAP and Banzhaf values, are grounded in power indices from cooperative game theory, which measure the contribution…
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,…
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.,…
We study a basic sequential model for the discovery of winning coalitions in a simple game, well known from its use in defining the Shapley-Shubik power index. We derive in a uniform way a family of measures of collective and individual…
Online social networks are used to diffuse opinions and ideas among users, enabling a faster communication and a wider audience. The way in which opinions are conditioned by social interactions is usually called social influence. Social…
In simple games, larger coalitions typically wield more power, but do all players align their efforts effectively? Consider a voting scenario where a coalition forms, but needs more voters to pass a bill. The cohesion of the new group of…
The concept of power among players can be expressed as a combination of their utilities. A player who obeys another takes into account the utility of the dominant one. Technically it is a matter of superimposing some weighted sum or product…
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 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…
In an election, we are given a set of voters, each having a preference list over a set of candidates, that are distributed on a social network. We consider a scenario where voters may change their preference lists as a consequence of the…
We examine two aspects of the mathematical basis for two-tier voting systems, such as that of the Council of the European Union. These aspects concern the use of square-root weights and the choice of quota. Square-root weights originate in…
Members of a shareholder meeting or legislative committee have greater or smaller voting power than meets the eye if the nucleolus of the induced majority game differs from the voting weight distribution. We establish a new sufficient…
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…
We introduce a natural variant of weighted voting games, which we refer to as k-Prize Weighted Voting Games. Such games consist of n players with weights, and k prizes, of possibly differing values. The players form coalitions, and the i-th…
Election control considers the problem of an adversary who attempts to tamper with a voting process, in order to either ensure that their favored candidate wins (constructive control) or another candidate loses (destructive control). As…
Shapley value is a popular approach for measuring the influence of individual features. While Shapley feature attribution is built upon desiderata from game theory, some of its constraints may be less natural in certain machine learning…
A proposed measure of voting power should satisfy two conditions to be plausible: first, it must be conceptually justified, capturing the intuitive meaning of what voting power is; second, it must satisfy reasonable postulates. This paper…
We introduce a class of cooperative games induced by weighted directed graphs. Specifically, the coalitional value combines an internal interaction term given by the induced subgraph game with an external component based on minimal incoming…
We study minimum integer representations of weighted games, i.e., representations where the weights are integers and every other integer representation is at least as large in each component. Those minimum integer representations, if the…