Related papers: Approximating power by weights

Measures of voting power have been the subject of extensive research since the mid 1940s. More recently, similar measures of relative importance have been studied in other domains that include inconsistent knowledge bases, intensity of…

The ability to measure the satisfaction of (groups of) voters is a crucial prerequisite for formulating proportionality axioms in approval-based participatory budgeting elections. Two common - but very different - ways to measure the…

We analyse two-tier voting systems with voters described by a multi-group mean-field model that allows for correlated voters both within groups as well as across group boundaries. In this model voters are influenced by voters within their…

Multiwinner voting rules can be used to select a fixed-size committee from a larger set of candidates. We consider approval-based committee rules, which allow voters to approve or disapprove candidates. In this setting, several voting rules…

In this paper we address the problem of electing a committee among a set of $m$ candidates and on the basis of the preferences of a set of $n$ voters. We consider the approval voting method in which each voter can approve as many candidates…

Determining how close a winner of an election is to becoming a loser, or distinguishing between different possible winners of an election, are major problems in computational social choice. We tackle these problems for so-called weighted…

Power-law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man-made phenomena. Unfortunately, the detection and characterization of power laws is…

A continuous approximation for the results of [1] is obtained. In this approximation the energy distribution is represented in the form of the product of the Gibbs factor and superstatistics factor. The mutual weights of the factors are…

We introduce a general framework for exploring the problem of selecting a committee of representatives with the aim of studying a networked voting rule based on a decentralized large-scale platform, which can assure a strong accountability…

We study voting rules with respect to how they allow or limit a majority from dominating minorities: whether a voting rule makes a majority powerful, and whether minorities can veto the candidates they do not prefer. For a given voting…

Consider an election where N seats are distributed among parties with proportions p_1,...,p_m of the votes. We study, for the common divisor and quota methods, the asymptotic distribution, and in particular the mean, of the seat excess of a…

The power of multiple testing procedures can be increased by using weighted p-values (Genovese, Roeder and Wasserman 2005). We derive the optimal weights and we show that the power is remarkably robust to misspecification of these weights.…

A finite sum of exponential functions may be expressed by a linear combination of powers of the independent variable and by successive integrals of the sum. This is proved for the general case and the connection between the parameters in…

To choose a suitable multiwinner voting rule is a hard and ambiguous task. Depending on the context, it varies widely what constitutes the choice of an ``optimal'' subset of alternatives. In this paper, we provide a quantitative analysis of…

We describe a way to approximate the matrix elements of a real power $\alpha$ of a positive (for $\alpha \ge 0$) or non-negative (for $\alpha \in \mathbb{R}$), infinite, bounded, sparse and Hermitian matrix $W$. The approximation uses only…

We consider collective decision making when the society consists of groups endowed with voting weights. Each group chooses an internal rule that specifies the allocation of its weight to the alternatives as a function of its members'…

The division of mandates to the European Parliament posed difficulties since the beginning of its operation. Introduction of the degressive proportionality principle to legal acts intensified further discussion on this subject. The…

The Banzhaf power index was introduced in cooperative game theory to measure the real power of players in a game. The Banzhaf interaction index was then proposed to measure the interaction degree inside coalitions of players. It was shown…

This paper considers elections in which voters choose one candidate each, independently according to known probability distributions. A candidate receiving a strict majority (absolute or relative, depending on the version) wins. After the…

We approximate the solution to some linear and degenerate quasi-linear problem involving a linear elliptic operator (like the semi-discrete in time implicit Euler approximation of Richards and Stefan equations) with measure right-hand side…