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 study divisor methods, the primary class to solve apportionment problems, based upon Stolarsky means S(alphabeta). These encompass the five traditional methods. We disclose a one-to-one relation between methods of the form S(alpha1) and aggregate measures of seat/vote disproportionality of...

In the current FIFA penalty shootout mechanism, a coin toss decides which team will kick first. Empirical evidence suggests that the team taking the first kick has a higher probability to win a shootout. We design sequentially fair shootout mechanisms such that in all symmetric Markov-perfect...

In a dynamic model of assignment problems, small deviations suffice to move between stable outcomes. This result is used to obtain no-selection and almost-no-selection results under the stochastic stability concept for uniform and payoff-dependent errors. There is no-selection of partner or...

We evaluate the goal of maximizing the number of individually rational assignments. We show that it implies incentive, fairness, and implementation impossibilities. Despite that, we present two classes of mechanisms that maximize assignments. The first are Pareto efficient, and undominated –...

Social optimization problems typically maximize the sum of individual weighted utilities over feasible allocations that satisfy certain constraints. While social optimization problems are at the heart of economic analysis, it is not always clear how to choose individual welfare weights. In this...

Recently there has been a resurgence of interest in the study of optimal monetary policy under uncertainty. This book provides a thorough survey of the literature that has resulted from this renewed interest. The authors ground recent contributions on the 'science of monetary policy' in the...