Related papers: Penrose voting system and optimal quota
We consider an odd-sized "jury", which votes sequentially between two states of Nature (say A and B, or Innocent and Guilty) with the majority opinion determining the verdict. Jurors have private information in the form of a signal in…
In multiwinner approval voting, the goal is to select $k$-member committees based on voters' approval ballots. A well-studied concept of proportionality in this context is the justified representation (JR) axiom, which demands that no large…
Motivated by the difficulty of specifying complete ordinal preferences over a large set of $m$ candidates, we study voting rules that are computable by querying voters about $t < m$ candidates. Generalizing prior works that focused on…
A weighted game or a threshold function in general admits different weighted representations even if the sum of non-negative weights is fixed to one. Here we study bounds for the diameter of the corresponding weight polytope. It turns out…
In an election campaign, candidates must decide how to optimally allocate their efforts/resources optimally among the regions of a country. As a result, the outcome of the election will depend on the players' strategies and the voters'…
Justified representation (JR) and extended justified representation (EJR) are well-established proportionality axioms in approval-based multiwinner voting. Both axioms are always satisfiable, but they rely on a fixed quota (typically Hare…
The ability to measure the satisfaction of (groups of) voters is a crucial prerequisite for formulating proportionality axioms in approval-based participatory budgeting elections. Two common - but very different - ways to measure the…
We study in details the turnout rate statistics for 77 elections in 11 different countries. We show that the empirical results established in a previous paper for French elections appear to hold much more generally. We find in particular…
We consider an agent community wishing to decide on several binary issues by means of issue-by-issue majority voting. For each issue and each agent, one of the two options is better than the other. However, some of the agents may be…
In the United States electoral system, a candidate is elected indirectly by winning a majority of electoral votes cast by individual states, the election usually being decided by the votes cast by a small number of "swing states" where the…
Distributed voting is a fundamental topic in distributed computing. In pull voting, in each step every vertex chooses a neighbour uniformly at random, and adopts its opinion. The voting is completed when all vertices hold the same opinion.…
We study statistics of the knockout tournament, where only the winner of a fixture progresses to the next. We assign a real number called competitiveness to each contestant and find that the resulting distribution of prize money follows a…
Data of proportional elections show a striking feature: If the parties are ranked according to the number of their voters, the number of votes grows exponentially with the rank of the party. This so-called Zipf's law has been reported…
We introduce an evolutionary game with feedback between perception and reality, which we call the reality game. It is a game of chance in which the probabilities for different objective outcomes (e.g., heads or tails in a coin toss) depend…
The game of best choice (also known as the secretary problem) is a model for sequential decision making with a long history and many variations. The classical setup assumes that the sequence of candidate rankings are uniformly distributed.…
We study a model of a population making a binary decision based on information spreading within the population, which is fully connected or covering a square grid. We assume that a fraction of the population wants to make the choice of the…
The paper proposes a natural measure space of zero-sum perfect information games with upper semicontinuous payoffs. Each game is specified by the game tree, and by the assignment of the active player and of the capacity to each node of the…
We study proportional representation in the framework of temporal voting with approval ballots. Prior work adapted basic proportional representation concepts -- justified representation (JR), proportional JR (PJR), and extended JR (EJR) --…
Weighted voting games are ubiquitous mathematical models which are used in economics, political science, neuroscience, threshold logic, reliability theory and distributed systems. They model situations where agents with variable voting…
A group of privately informed agents chooses between two alternatives. How should the decision rule be designed if agents are known to be biased in favor of one of the options? We address this question by considering the Condorcet Jury…