Voter control problems model situations in which an external agent tries to affect the result of an election by adding or deleting the fewest number of voters. The goal of the agent is to make a specific candidate either win (constructive control) or lose (destructive control) the election. We study the constructive and destructive voter control problems when adding and deleting voters have a c...

A median (antimedian) of a profile of vertices on a graph G is a vertex that minimizes (maximizes) the sum of the distances to the elements in the profile. The median (antimedian) function has as output the set of medians (antimedians) of a profile. It is one of the basic models for the location of a desirable (obnoxious) facility in a network. The median function is well studied. For instance ...

The synchronized bit communication model, defined recently by Impagliazzo and Williams in [1], is a communication model which allows the participants to share a common clock. The main open problem posed in this paper was the following: does the synchronized bit model allow a logarithmic speed-up for all functions over the standard deterministic model of communication? We resolve this question i...

New proofs are given for Monjardet’s theorem that all strong simple games (i.e., ipsodual elements of the free distributive lattice) can be generated by the median operation. Tighter limits are placed on the number of iterations necessary. Comparison is drawn with the χ function which also generates all strong simple games.

Voting research is rich in empirical regularities yet a parsimonious theory of voter turnout that can match the facts has proven to be elusive. This paper argues that voter turnout patterns can be explained by extending the traditional rational voter model to include limited information. A model is presented in which utility-ma~ximizing consumers receive higher payoffs from voting the more conf...

Audit logs are an important tool for post-election investigations, in the event of an election dispute or problem. We propose a new approach to logging that is designed to provide a record of all interactions between each voter and the voting machine. Our audit logs provide a comprehensive, trustworthy, replayable record of essentially everything the voter saw and did in the voting booth, provi...

We extend Valiant's construction of monotone formulae for the majority function to obtain an eecient probabilistic construction of small monotone formulae for arbitrary positive linear threshold functions. We show that any positive linear threshold function on n boolean variables which has weight complexity q(n) can be computed by a monotone boolean formula of size O(q(n) 3:3 n 2): Our techniqu...

The fair way to decide an election between two candidates a and b is majority rule; if more than half the electorate prefer a to b, then a is elected; otherwise b is elected. Arrow’s theorem asserts that no fair election procedure exists for choosing from among three or more candidates. This note gives an exposition of Arrow’s theorem. It also describes the relation of election procedures betwe...