相关论文: Power Indices and minimal winning Coalitions

Coalition setting among a set of actors (countries, firms, individuals) is studied using concepts from the theory of spin glasses. Given the distribution of respective bilateral propensities to either cooperation or conflict, the phenomenon…

We present theoretical and empirical results demonstrating the usefulness of voting rules for participatory democracies. We first give algorithms which efficiently elicit \epsilon-approximations to two prominent voting rules: the Borda rule…

There are many factors that can influence the outcome of an election. We here identify two dominant effects that can affect the votes obtained by a candidate, namely, the Majority Effect and the Media Effect. We mimic these two effects in a…

Most work on manipulation assumes that all preferences are known to the manipulators. However, in many settings elections are open and sequential, and manipulators may know the already cast votes but may not know the future votes. We…

We consider the problem of computing Shapley values for points in the plane, where each point is interpreted as a player, and the value of a coalition is defined by the area of usual geometric objects, such as the convex hull or the minimum…

Various peer-to-peer energy markets have emerged in recent years in an attempt to manage distributed energy resources in a more efficient way. One of the main challenges these models face is how to create and allocate incentives to…

The balancing index of a polynomial $f \in \mathbb{Z}[x_1,\dots,x_n]$ is the least positive sum of coefficients in an integer linear combination of permuted copies of $f$ which produces a symmetric polynomial. Here we consider 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…

Bayesian inference affords scientists with powerful tools for testing hypotheses. One of these tools is the Bayes factor, which indexes the extent to which support for one hypothesis over another is updated after seeing the data. Part of…

This article describes an efficient procedure for computing approximate confidence levels for searches for new particles where the expected signal and background levels are small enough to require the use of Poisson statistics. The results…

We use the topology of simplicial complexes to model political structures following [1]. Simplicial complexes are a natural tool to encode interactions in the structures since a simplex can be used to represent a subset of compatible…

In Bayesian hypothesis testing, evidence for a statistical model is quantified by the Bayes factor, which represents the relative likelihood of observed data under that model compared to another competing model. In general, computing Bayes…

We propose a simple method for combining together voting rules that performs a run-off between the different winners of each voting rule. We prove that this combinator has several good properties. For instance, even if just one of the base…

In this paper, we propose a pseudo polynomial size LP formulation for finding a payoff vector in the least core of a weighted voting game. The numbers of variables and constraints in our formulation are both bounded by $\mbox{O}(n W_+)$,…

A social system is susceptible to perturbation when its collective properties depend sensitively on a few pivotal components. Using the information geometry of minimal models from statistical physics, we develop an approach to identify…

Let the group $G = AB$ be the product of the subgroups $A$ and $B$. We determine some structural properties of $G$ when the $p$-elements in $A\cup B$ have prime power indices in $G$, for some prime $p$. More generally, we also consider the…

We improve results of Kahn, Kalai, and Linial from the late 80s on the existence of influential large coalitions for Boolean functions, and we give counterexamples to conjectures (of Benny Chor and others) also from the late 80s, by…

In this paper, we consider the consistency of the desirability relation with the ranking of the players in a simple game provided by some well-known solutions, in particular the Public Good Index [14] and the criticality-based ranking [1].…

While most useful information theoretic inequalities can be deduced from the basic properties of entropy or mutual information, Shannon's entropy power inequality (EPI) seems to be an exception: available information theoretic proofs of the…

We propose a variant of the Shapley value, the group Shapley value, to interpret counterfactual simulations in structural economic models by quantifying the importance of different components. Our framework compares two sets of parameters,…