This paper deals with the problem of calculating the Shapley-Shubik power index in weighted majority games. We propose an efficient Monte Carlo algorithm based on an implicit hierarchical structure of permutations of players. Our algorithm outputs a vector of power indices preserving the...

Simple games in partition function form are used to model voting situations where a coalition being winning or losing might depend on the way players outside that coalition organize themselves. Such a game is called a plurality voting game if in every partition there is at least one winning...

The Qualified Majority Voting (QMV) used by the Council of the European Union developed to a high degree of complexity from one modifying treaty to another, until the latest definition stipulated in the Treaty of Lisbon. This paper analyses this EU intra-institutional voting method using a...

Agenda-setting power is a double-edged sword that increases the likelihood that an agent is chosen to be a proposer, but may reduce the probability that the agent is included in a winning coalition. We experimentally test the theoretical prediction of potentially negative returns to...

I propose a general power index in games. The power of an agent over an outcome is understood as the equilibrium effect on the outcome of variations in the agent’s preferences. I show that the new index, ∆, has the following properties: (i) classic measures of freedom of choice are a special...

We study the efficient computation of power indices for weighted voting games with precoalitions amongst subsets of players (reflecting, e.g., ideological proximity) using the paradigm of dynamic programming. Starting from the state-of-the-art algorithms for computing the Banzhaf and...

Debates on an EU-leaving referendum arose in several member states after Brexit. We want to highlight how the exit of an additional country affects the power distribution in the Council of the European Union. We inspect the power indices of the member states both with and without the country...

We show that under suitable assumption on the number of states and the distribution of the population numbers of the states, bias of various methods of apportionment can be quantified. We also discuss the frequency of quota violations and occurrences of the Alabama Paradox. The results provide...

The exit of the United Kingdom from the European Union has had profound economic and political effects. Here, we look at a particular aspect, the power distribution in the Council of the European Union. Using the Shapley-Shubik power index, we calculate the member states' powers with and without...

The modern Condorcet jury theorem states that under weak conditions, when voters have common interests, elections will aggregate information when the population is large, in any equilibrium. Here, we study the performance of large elections with population uncertainty. We find that the modern...

This paper examines how neutral the current EU decision-making procedures are to membership and how well they obey certain transparent general constitutional principles. The paper evaluates the performance of the procedures by strategic and classical power indices. The main emphasis in the...

Traditional power indices ignore preferences and strategic interaction. Equilibrium analysis of particular non-cooperative decision procedures is unsuitable for normative analysis and assumes typically unavailable information. These points drive a lingering debate about the right approach 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 the input and the output. The corresponding games are...

We study the issue of assigning weights to players that identify winning coalitions in plurality voting democracies. For this, we consider plurality games which are simple games in partition function form such that in every partition there is at least one winning coalition. Such a game is said...

The modern Condorcet jury theorem states that under weak conditions, when voters have common interests, then elections will aggregate information when the population is large, in any responsive and symmetric equilibrium. Here, we study the performance of large elections with population...

In this article, we empirically study the survival of the ruling party in parliamentary democracies using a hazard rate model. We define survival of a crisis as being successful in a critical vote in the parliament. We develop a general probabilistic model of political crises and test it...

Among the wide variety of voting power indices, the public good index (PGI) is one of the less well-known ones. Holler (forthcoming) posits hypotheses about why this is the case. In response to these hypotheses, I share a few thoughts about voting power in general and about the popularity of the PGI

The Coleman Power of the Collectivity to Act (CPCA) is a popular statistic that reflects the ability of a committee to pass a proposal. Applying the Shapley value to this measure, we derive a new power index that indicates each voter's contribution to the CPCA. This index is characterized by...

This thesis deals with the measurement of voting power in different decision environments. After a short introduction in Chapter 1, several established concepts for power analysis are reviewed and applied in Chapters 2 and 3. Chapters 4 and 5 step on new ground by introducing a power index for a...

We consider plurality voting games being simple games in partition function form such that in every partition there is at least one winning coalition. Such a game is said to be weighted if it is possible to assign weights to the players in such a way that a winning coalition in a partition is...