Related papers: Dodgson's Rule Approximations and Absurdity

The Rev. Dodgson's determinant condensation rule is given a bijective proof.

Election rules are formal processes that aggregate voters preferences, typically to select a single candidate, called the winner. Most of the election rules studied in the literature require the voters to rank the candidates from the most…

One of the central economic paradigms in multi-agent systems is that agents should not be better off by acting dishonestly. In the context of collective decision-making, this axiom is known as strategyproofness and turns out to be rather…

Apportionment is the act of distributing the seats of a legislature among political parties (or states) in proportion to their vote shares (or populations). A famous impossibility by Balinski and Young (2001) shows that no apportionment…

The Condorcet criterion (CC) is a classical and well-accepted criterion for voting. Unfortunately, it is incompatible with many other desiderata including participation (Par), half-way monotonicity (HM), Maskin monotonicity (MM), and…

Social decision schemes (SDSs) map the preferences of a group of voters over some set of $m$ alternatives to a probability distribution over the alternatives. A seminal characterization of strategyproof SDSs by Gibbard implies that there…

In this paper, we study the metric distortion of deterministic social choice rules that choose a winning candidate from a set of candidates based on voter preferences. Voters and candidates are located in an underlying metric space. A voter…

We study positional voting rules when candidates and voters are embedded in a common metric space, and cardinal preferences are naturally given by distances in the metric space. In a positional voting rule, each candidate receives a score…

Voting can abstractly model any decision-making scenario and as such it has been extensively studied over the decades. Recently, the related literature has focused on quantifying the impact of utilizing only limited information in the…

We introduce and study isomorphic distances between ordinal elections (with the same numbers of candidates and voters). The main feature of these distances is that they are invariant to renaming the candidates and voters, and two elections…

We study electoral campaign management scenarios in which an external party can buy votes, i.e., pay the voters to promote its preferred candidate in their preference rankings. The external party's goal is to make its preferred candidate a…

Condorcet's paradox is a fundamental result in social choice theory which states that there exist elections in which, no matter which candidate wins, a majority of voters prefer a different candidate. In fact, even if we can select any $k$…

We consider elections where both voters and candidates can be associated with points in a metric space and voters prefer candidates that are closer to those that are farther away. It is often assumed that the optimal candidate is the one…

Social decision schemes (SDSs) map the ordinal preferences of individual voters over multiple alternatives to a probability distribution over the alternatives. In order to study the axiomatic properties of SDSs, we lift preferences over…

We introduce two-crossing elections as a generalization of single-crossing elections, showing a number of new results. First, we show that two-crossing elections can be recognized in polynomial time, by reduction to the well-studied…

It is well known that no reasonable voting rule is strategyproof. Moreover, the common Plurality rule is particularly prone to strategic behavior of the voters and empirical studies show that people often vote strategically in practice.…

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…

We characterize the class of committee scoring rules that satisfy the fixed-majority criterion. In some sense, the committee scoring rules in this class are multiwinner analogues of the single-winner Plurality rule, which is uniquely…

In 1866, Charles Ludwidge Dodgson published a paper concerning a method for evaluating determinants called the condensation method. His paper documented a new method to calculate determinants that was based on Jacobi's Theorem. The…

Despite the highest classification accuracy in wide varieties of application areas, artificial neural network has one disadvantage. The way this Network comes to a decision is not easily comprehensible. The lack of explanation ability…