In this paper we show how theorems of Borsuk-Ulam and Tucker can be used to construct a consensus-halving: a division of an object into two portions so that each of n people believe the portions are equally split. Moreover, the division takes at most n cuts, which is best possible. This extends...

We introduce the following basic voting method: voters submit both a “consensus” and a “fall-back” ballot. If all “consensus” ballots name the same option, it wins; otherwise, a randomly drawn “fall-back” ballot decides. If there is one potential consensus option that everyone...

In this paper we demonstrate a new method for computing approximate Nash equilibria in n-person games. Strategy spaces are assumed to be represented by simplices, while payoff functions are assumed to be concave. Our procedure relies on a simplicial algorithm that traces paths through the set of...