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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 introduce a voting model that is similar to a Keynesian beauty contest and analyze it from a mathematical point of view. There are two types of voters-copycat and independent-and two candidates. Our voting model is a binomial…

We consider the complexity of deciding the winner of an election under the Slater rule. In this setting we are given a tournament $T = (V, A)$, where the vertices of V represent candidates and the direction of each arc indicates which of…

We propose a secure voting protocol for score-based voting rules, where independent talliers perform the tallying procedure. The protocol outputs the winning candidate(s) while preserving the privacy of the voters and the secrecy of the…

In the single winner determination problem, we have n voters and m candidates and each voter j incurs a cost c(i, j) if candidate i is chosen. Our objective is to choose a candidate that minimizes the expected total cost incurred by the…

At the end, the house always wins! This simple truth holds for all public games of chance. Nevertheless, since lotteries have existed, people have tried everything to give luck a helping hand. This article compares objective scientific…

Professor Sir Karl Popper (1902-1994) was one of the most influential philosophers of science of the twentieth century, best known for his doctrine of falsifiability. His axiomatic formulation of probability, however, is unknown to current…

Several election districts in the US have recently moved to ranked-choice voting (RCV) to decide the results of local elections. RCV allows voters to rank their choices, and the results are computed in rounds, eliminating one candidate at a…

Most democratic countries use election methods to transform election results into whole numbers which usually give the number of seats in a legislative body the parties obtained. Which election method does this best can be specified by…

From the perspective of social choice theory, ranked-choice voting (RCV) is known to have many flaws. RCV can fail to elect a Condorcet winner and is susceptible to monotonicity paradoxes and the spoiler effect, for example. We use a…

In this paper, we consider lightweight decentralised algorithms for achieving consensus in distributed systems. Each member of a distributed group has a private value from a fixed set consisting of, say, two elements, and the goal is for…

The DLG root-squaring iterations, due to Dandelin 1826 and rediscovered by Lobachevsky 1834 and Graeffe 1837, have been the main approach to root-finding for a univariate polynomial p(x) in the 19th century and beyond, but not so nowadays…

This paper is part of an ongoing investigation of "pragmatic information", defined in Weinberger (2002) as "the amount of information actually used in making a decision". Because a study of information rates led to the Noiseless and Noisy…

The classic Gibbard-Satterthwaite theorem says that every strategy-proof voting rule with at least three possible candidates must be dictatorial. In \cite{McL11}, McLennan showed that a similar impossibility result holds even if we consider…

As was shown recently, many important AI problems require counting the number of models of propositional formulas. The problem of counting models of such formulas is, according to present knowledge, computationally intractable in a worst…

The winner determination problems of many attractive multi-winner voting rules are NP-complete. However, they often admit polynomial-time algorithms when restricting inputs to be single-peaked. Commonly, such algorithms employ dynamic…

The setting of the classic prophet inequality is as follows: a gambler is shown the probability distributions of $n$ independent, non-negative random variables with finite expectations. In their indexed order, a value is drawn from each…

The Colonel Blotto game is a deeply studied theoretical model for competitive allocation environments including elections, advertising, and ecology. However, the original formulation of Colonel Blotto has had few practical implications due…

Condorcet's jury theorem states that the correct outcome is reached in direct majority voting systems with sufficiently large electorates as long as each voter's independent probability of voting for that outcome is greater than 0.5. Yet,…

Let $D$ be an integral domain. Two players, Nora and Wanda, alternately choose coefficients from $D$ for a polynomial of degree $d$. When they are done, if the polynomial has a root in the field of fractions of $D$, then Wanda wins. If not,…