Fuzzy coalitional structures (alternatives)

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 coalitions suggested in [1], discuss the concepts of superadditivity and convexity, and introduce a concept of the coalitional structure of fuzzy coalitions. The first version of this paper [10] was presented at the Czech-Japan Seminar in Valtice 2003. It was obvious that the roots of some open questions can be found in the concept of superadditivity (with consequences on some other related concepts), which deserve more attention. This version of the paper extends the previous one by discussion of alternative approaches to this topic

Power analysis of voting by count and account

summary:Using players’ Shapley–Shubik power indices, Peleg [4] proved that voting by count and account is more egalitarian than voting by account. In this paper, we show that a stronger shift in power takes place when the voting power of players is measured by their Shapley–Shubik indices. Moreover, we prove that analogous power shifts also occur with respect to the absolute Banzhaf and the absolute Johnston power indices

Representation of Convex Preferences in a Nonatomic Measure Space : ε-Pareto Optimality and ε-Core in Cake Division

The purpose of this paper is threefold. First, we represent preferencerelations on σ-fields in terms of nonadditive set functions thatsatisfy convexity and continuity in an appropriate sense. To this end,we introduce the convexity and continuity axioms for preferences ona σ-field with a metric topology and show the existence of a utilityfunction representing a convex continuous preference relation. Second,we prove the existence of ε-Pareto-optimal partitions, show howthey approximate Pareto-optimal partitions and provide their characterization.Third, we prove the existence of ε-core partitions withnontransferable utility arising in a pure exchange economy and showhow they approximate core partitions

A historical note on the complexity of scheduling problems

In 1972 E.M. Livshits and V.I. Rublinetsky published a paper in Russian, in which they presented linear-time reductions of the partition problem to a number of scheduling problems. Unaware of complexity theory, they argued that, since partition is not known to have a simple algorithm, one cannot expect to find simple algorithms for these scheduling problems either. Their work did not go completely unnoticed, but it received little recognition. We describe the approach and review the results