相关论文: Power index rankings in bicameral legislatures and…

Decisions in a shareholder meeting or a legislative committee are often modeled as a weighted game. Influence of a member is then measured by a power index. A large variety of different indices has been introduced in the literature. This…

This paper is a twofold contribution. First, it contributes to the problem of enumerating some classes of simple games and in particular provides the number of weighted games with minimum and the number of weighted games for the dual class…

Weighted voting games are frequently used in decision making. Each voter has a weight and a proposal is accepted if the weight sum of the supporting voters exceeds a quota. One line of research is the efficient computation of so-called…

Weighted voting games apply to a wide variety of multi-agent settings. They enable the formalization of power indices which quantify the coalitional power of players. We take a novel approach to the study of the power of big vs.~small…

Many real-world voting systems consist of voters that occur in just two different types. Indeed, each voting system with a {\lq\lq}House{\rq\rq} and a {\lq\lq}Senat{\rq\rq} is of that type. Here we present structural characterizations and…

Weighted voting games are a family of cooperative games, typically used to model voting situations where a number of agents (players) vote against or for a proposal. In such games, a proposal is accepted if an appropriately weighted sum of…

This paper studies power indices based on average representations of a weighted game. If restricted to account for the lack of power of dummy voters, average representations become coherent measures of voting power, with power distributions…

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…

Each year, the United States Congress considers thousands of legislative proposals to select bills to present to the US President to sign into law. Naturally, the decision processes of members of Congress are subject to peer influence. In…

Ranking is a ubiquitous phenomenon in the human society. By clicking the web pages of Forbes, you may find all kinds of rankings, such as world's most powerful people, world's richest people, top-paid tennis stars, and so on and so forth.…

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…

Coalitional voting games appear in different forms in multi-agent systems, social choice and threshold logic. In this paper, the complexity of comparison of influence between players in coalitional voting games is characterized. The…

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…

Representative democracy in the United States relies on election systems that transmit votes into representatives in three key bodies: the two chambers of the federal legislature (House of Representatives and Senate) and the Electoral…

Consider an election where the set of candidates is partitioned into parties, and each party must choose exactly one candidate to nominate for the election held over all nominees. The Necessary President problem asks whether a candidate, if…

Based on Holler (1982) and Armijos-Toro et al. (2021) we propose two power indices to measure the influence of the players in the class of weighted majority games in partition function form. We compare these new power indices with their…

Among two-candidate elections that treat the candidates symmetrically and never result in a tie, which voting rules are fair? A natural requirement is that each voter exerts an equal influence over the outcome, i.e., is equally likely to…

The Shapley-Shubik index is a specialization of the Shapley value and is widely applied to evaluate the power distribution in committees drawing binary decisions. It was generalized to decisions with more than two levels of approval both 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…

We introduce new power indices to measure the a priori voting power of voters in liquid democracy elections where an underlying network restricts delegations. We argue that our power indices are natural extensions of the standard…