Balancedness, nonemptiness of the core and the existence of a majority equilibrium
Consider a society with a finite number, n, of individuals who have to choose an alternative from a compact, convex set A in the m-dimensional Euclidean space, \({\mathbb{R}}^ m\). Assume that the preference relation over A of every individual is represented by a quasi-concave and continuous function. If the set of winning coalitions (i.e. those that have the veto power) consists of all coalitions with more than \(mn/(m+1)\) individuals, then there exists an alternative a*\(\in A\) which is a majority equilibrium, or equivalently, that the core of the induced game is nonempty. The main step of the proof is to show that the game is balanced. This is a slight strengthening of a previous result by the first author.
scientific article; zbMATH DE number 3854741