We critically discuss the Jefferson/D'Hondt and Webster/Sainte-Laguë methods, which are used to allocate parliament seats to parties in the mixed-member proportional representation systems in Germany, New Zealand, Bolivia, South Africa, South Korea, Scotland and Wales, as well as in the...

We study the problem of determining memberships to the groups in a Boolean algebra. The Boolean algebra is composed of basic groups (e.g., “J” and “K”) and the other groups that are derived from basic groups through the conjunction, disjunction, or negation operations (e.g., “J and...

In ordinal (probabilistic) assignment problems, each agent reports his preference rankings over objects and receives a lottery defined over those objects. A common efficiency notion, sd-efficiency, is obtained by extending the preference rankings to preferences over lotteries by means of...

This study investigates efficient and strategy‐proof mechanisms for allocating indivisible goods under constraints. First, we examine a setting without endowments. In this setting, we introduce a class of constraints-ordered accessibility-for which the serial dictatorship (SD) mechanism is...

This paper contains two results. The first result says that given any efficient non-monetary allocation there is a balanced vector of transfers so that the resulting allocation is fair. The second result says that given any efficient non-monetary allocation there is a pricing function defined on...

We study the problem of how to allocate a set of indivisible objects like jobs or houses and an amount of money among a group of people as fairly and as efficiently as possible. A particular constraint for such an allocation is that every person should be assigned with the same number of objects...

In the real world many social and economic decisions have to be made with imperfect information and uncertainty. In the past two decades, economists and mathematicians have devoted a great deal of time and effort into the study of ambiguity and much progress has been made in modeling ambiguity....

We solve the problem of a social planner who seeks to minimize inequality via transfers with a fixed public budget in a distribution of exogenously given incomes. The appropriate solution method depends on the objective function: If it is convex, as in the case of the absolute mean deviation, it...