Related papers: On influence and compromise in two-tier voting sys…
We investigate systems of indirect voting based on the law of Penrose, in which each representative in the voting body receives the number of votes (voting weight) proportional to the square root of the population he or she represents. For…
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…
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…
The problem of designing an optimal weighted voting system for the two-tier voting, applicable in the case of the Council of Ministers of the European Union (EU), is investigated. Various arguments in favour of the square root voting…
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…
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…
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…
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…
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…
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,…
We study the Shapley value in weighted voting games. The Shapley value has been used as an index for measuring the power of individual agents in decision-making bodies and political organizations, where decisions are made by a majority vote…
We propose and study a new class of polynomial voting rules for a general decentralized decision/consensus system, and more specifically for the PoS (Proof of Stake) protocol. The main idea, inspired by the Penrose square-root law and the…
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…
Consider an election between two candidates in which the voters' choices are random and independent and the probability of a voter choosing the first candidate is $p>1/2$. Condorcet's Jury Theorem which he derived from the weak law of large…
Weighted voting games are frequently used in decision making. Each voter has a weight and a proposal is accepted if the weight sum of the supporting voters exceeds a quota. One line of research is the efficient computation of so-called…
We analyse optimal voting weights in two-tier voting systems. In our model, the overall population (or union) is split in groups (or member states) of different sizes. The individuals comprising the overall population constitute the first…
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…
Weighted voting games are a well-known and useful class of succinctly representable simple games that have many real-world applications, e.g., to model collective decision-making in legislative bodies or shareholder voting. Among the…
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…
We investigate the voting rules in the Council of the European Union. It is known that the current system, according to the Treaty of Nice, and the voting system proposed in the Lisbon treaty both strongly deviate from the square root law…