Related papers: Double Majority and Generalized Brexit: Explaining…
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 notion of the voting power is illustrated by examples of the systems of voting in the European Council according to the Treaty of Nice and the more recent proposition of the European Convent. We show that both systems are not…
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 exhibit the hidden beauty of weighted voting and voting power by applying a generalization of the Penrose-Banzhaf index to social choice rules. Three players who have multiple votes in a committee decide between three options by…
Brexit and its implications are an ongoing topic of interest since the Brexit referendum in 2016. In 2019 the House of commons held a number of "indicative" and "meaningful" votes as part of the Brexit approval process. The voting behaviour…
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…
Systems of indirect voting based on the principle of qualified majority can be analysed using the methods of game theory. In particular, this applies to the voting system in the Council of the European Union, which was recently a subject of…
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…
The Council of the European Union (EU) is one of the main decision-making bodies of the EU. A number of decisions require a qualified majority, the support of 55% of the member states (currently 15) that represent at least 65% of the total…
In certain bodies, like the Council of the EU, the member states have a voting weight which depends on the population of the re- spective state. In this article we ask the question which voting weight guarantees a `fair' representation of…
We examine two aspects of the mathematical basis for two-tier voting systems, such as that of the Council of the European Union. These aspects concern the use of square-root weights and the choice of quota. Square-root weights originate in…
In recent years, enlargement of the European Union has led to increased interest in the allocation of voting weights to member states with hugely differing population numbers. While the eventually agreed voting scheme lacks any strict…
A committee's decisions on more than two alternatives much depend on the adopted voting method, and so does the distribution of power among the committee members. We investigate how different aggregation methods such as plurality runoff,…
The Brexit referendum took place in the UK in June, 2016. The unweighted percentage of leavers over the whole population was 51.9%. In this paper, first, we demonstrate that a 52%-48% split represents only a difference that is not…
The voting rules of the European Council (EU) under the Treaty of Lisbon became effective on 1 November 2014. Kurz \& Napel (2015) showed that the dimension of this voting system is between $7$ and $13,368$. The lower bound $7$ actually…
In this paper, we propose an improved version of the power index related to the Banzhaf power index for weighted voting systems. This index now takes into account the mutual persuasion power matrix(PPM) existing among the voters. This…
We investigate a class of weighted voting games for which weights are randomly distributed over the standard probability simplex. We provide close-formed formulae for the expectation and density of the distribution of weight of the $k$-th…
As of 2022, the European Union has taken several steps regarding enlargement. We focus on the accession of countries with which the Union is actively negotiating membership. This is examined under two enlargement scenarios: first, the…
Since the result of the 2016 referendum, Brexit has been an unpredictable democratic adventure, the finale of which remains unclear. This year, in the final days of March, parliamentarians seized control of the order paper from the…
We perform stochastic microsimulations of the dynamics of England and Wales population after the British referendum on EU membership, considering different possible outcomes. Employing available survey data, we model the demographics of the…