Related papers: A Law of Large Numbers for Weighted Majority
We study the problem of designing multiwinner voting rules that are candidate monotone and proportional. We show that the set of committees satisfying the proportionality axiom of proportionality for solid coalitions is candidate monotone.…
Is it more effective to have a strong influence over a small domain, or a weaker influence over a larger one? Here, we introduce and analyse an off-lattice generalisation of the voter model, in which the range and strength of agents'…
We study two concepts of proportionality in the model of approval-based committee elections. In degressive proportionality small minorities of voters are favored in comparison with the standard linear proportionality. Regressive…
In this article, we study the effect of vector-valued interventions in votes under a binary voter model, where each voter expresses their vote as a $0-1$ valued random variable to choose between two candidates. We assume that the outcome is…
We consider the sum of power weighted nearest neighbor distances in a sample of size n from a multivariate density f of possibly unbounded support. We give various criteria guaranteeing that this sum satisfies a law of large numbers for…
The metric distortion framework posits that n voters and m candidates are jointly embedded in a metric space such that voters rank candidates that are closer to them higher. A voting rule's purpose is to pick a candidate with minimum total…
Nanson's and Baldwin's voting rules select a winner by successively eliminating candidates with low Borda scores. We show that these rules have a number of desirable computational properties. In particular, with unweighted votes, it is…
Consider an odd-sized jury, which determines a majority verdict between two equiprobable states of Nature. If each juror independently receives a binary signal identifying the correct state with identical probability $p$, then the…
Nowadays there is an increasing interest of physicists in finding regularities related to social phenomena. This interest is clearly motivated by applications that a statistical mechanical description of the human behavior may have in our…
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 investigate a variation of the classical voter model in which the set of influencing agents depends on an individual's current opinion. The initial population consists of a random sample of equally sized sub-populations for each state,…
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…
We analyse strategic, complete information, sequential voting with ordinal preferences over the alternatives. We consider several voting mechanisms: plurality voting and approval voting with deterministic or uniform tie-breaking rules. We…
A large amount of literature in social choice theory deals with quantifying the probability of certain election outcomes. One way of computing the probability of a specific voting situation under the Impartial Anonymous Culture assumption…
Weak selection, which means a phenotype is slightly advantageous over another, is an important limiting case in evolutionary biology. Recently it has been introduced into evolutionary game theory. In evolutionary game dynamics, the…
In 1977, Young proposed a voting scheme that extends the Condorcet Principle based on the fewest possible number of voters whose removal yields a Condorcet winner. We prove that both the winner and the ranking problem for Young elections is…
We discuss voting scenarios in which the set of voters (agents) and the set of alternatives are the same; that is, voters select a single representative from among themselves. Such a scenario happens, for instance, when a committee selects…
This note proves a law of large numbers for predicting several steps ahead, which, in the case of uniformly bounded random variables, generalizes the standard law of large numbers for martingales; the standard law of large numbers…
This paper presents mathematics relevant to the question whether voting should be mandatory. Assuming a static distribution of voters' political beliefs, we model how politicians might adjust their positions to raise their share of the…
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…