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...

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...