We study linearly weighted versions of the least core and the (pre)nucleolus and investigatethe reduction possibilities in their computation. We slightly extend some well-known related results and establish their counterparts by using the dual game. Our main results imply, for example, that if...

We tackle the problem of partitioning players into groups of fixed size, such as allocating eligible students to shared dormitory rooms. Each student submits preferences over the other individual students. We study several settings, which differ in the size of the rooms to be filled, the...

Few elections attract so much attention as the Papal Conclave that elects the religious leader of over a billion Catholics worldwide. The Conclave is an interesting case of qualified majority voting with many participants and no formal voting blocks. Each cardinal is a wellknown public gure with...