Related papers: Average Weights and Power in Weighted Voting Games

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,…

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…

We generalize the notion of convexity and average-convexity to the notion of weighted average-convexity. We show several results on the relation between weighted average-convexity and cooperative games. First, we prove that if a game is…

A simple game $(N,v)$ is given by a set $N$ of $n$ players and a partition of~$2^N$ into a set~$\mathcal{L}$ of losing coalitions~$L$ with value $v(L)=0$ that is closed under taking subsets and a set $\mathcal{W}$ of winning coalitions $W$…

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…

In a weighted majority voting game, the players' weights are determined based on the constitutional planner's intentions. The weights are challenging to change in numerous cases, as they represent some desired disparity. However, the voting…

We consider two-tier voting system and try to determine optimal weights for a fair representation in such systems. A prominent example of such a voting system is the Council of Ministers of the European Union. Under the assumption of…

We consider the Banzhaf-Coleman and Owen power indices for weighted majority games modified by a coalition configuration. We present calculation algorithms of them that make use of the method of generating functions. We programmed the…

Power indices are mappings that quantify the influence of the members of a voting body on collective decisions a priori. Their nonlinearity and discontinuity makes it difficult to compute inverse images, i.e., to determine a voting system…

In this paper new algorithm for calculating power indices is described. The complexity class of the problem is #P-complete and even calculating power index of the biggest player is NP-hard task. Constructed algorithm is a mix of ideas of…

This paper contributes to the program of numerical characterisation and classification of simple games outlined in the classical monograph of von Neumann and Morgenstern (1944). One of the most fundamental questions of this program is what…

Several power indices have been introduced in the literature in order to measure the influence of individual committee members on the aggregated decision. Here we ask the inverse question and aim to design voting rules for a committee such…

Binary yes-no decisions in a legislative committee or a shareholder meeting are commonly modeled as a weighted game. However, there are noteworthy exceptions. E.g., the voting rules of the European Council according to the Treaty of Lisbon…

This paper studies the allocation of voting weights in a committee representing groups of different sizes. We introduce a partial ordering of weight allocations based on stochastic comparison of social welfare. We show that when the number…

A mathematical analysis of the distribution of voting power in the Council of the European Union operating according to the Treaty of Lisbon is presented. We study the effects of Brexit on the voting power of the remaining members, measured…

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…

Consider an election between k candidates in which each voter votes randomly (but not necessarily independently) and suppose that there is a single candidate that every voter prefers (in the sense that each voter is more likely to vote for…

We consider weighted sums of independent random variables regulated by an increment sequence. We provide operative conditions that ensure strong law of large numbers for such sums to hold in both the centered and non-centered case. The…

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…

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…