In parliaments elected by proportional systems the seats are allocated to the elected political parties roughly proportionally to the shares of votes for the party lists. Assuming that members of the parliament representing the same party are voting together, it has sense to require that distribution of the influence of the parties in parliamentary decision making is proportional to the distribution of seats. There exist measures (so called voting power indices) reflecting an ability of each party...

The computation of leastcore and prenucleolus is an efficient way of allocating a common resource among n players. It has, however, the drawback being a linear programming problem with 2n - 2 constraints. In this paper we show how, in the case of convex production games, generate constraints by solving small size linear programming problems, with both continuous and integer variables. The approach is extended to games with symmetries (identical players), and to games with partially continuous...

Applying the Owen construction of value of games with a priori unions to the normalized Banzhaf value gives a new type of the normalized Banzhaf value for games with a priori unions. Using a simple example of a four-person voting game with a priori unions, it is shown that this value is different from those known in the literature: the normalized Owen-Banzhaf value, the Banzhaf share function defined by van der Laan and van den Brink and the Banzhaf index for simple games with a priori unions introduced...

The uncertainty of expectations and vagueness of the interests belong to natural components of cooperative situations, in general. Therefore, some kind of formalization of uncertainty and vagueness should be included in realistic models of cooperative behaviour. This paper attempts to contribute to the endeavour of designing a universal model of vagueness in cooperative situations. Namely, some initial auxiliary steps toward the development of such a model are described. We use the concept of fuzzy...