An approach to the solution of a conflict situation with $n$ participants

Zimmermann, Karel

Applications of Mathematics, Tome 21 (1976) no. 2, pp. 81-91.

Résumé

In this article an attempt is made to find in a certain sense reasonable probabilistic preference group order. The criterion of reasonability of the group preference order is the value of a real function (the so called function of discontent) defined on a set of feasible group decision rules, each of which determines a probabilistic preference ordering on a given set of alternatives. The decision rules minimizing the value of the function $f$ over the set of feasible group decisoin rules are supposed to be reasonable for the whole group and can be recommended to the leader of the group as a "reasonable dictate". The members of the group, who tend to minimize the value of the function $f$, if appointed leaders of the whole group, are called reasonable dictators (the set $\Cal D_r(f)$ in the text). The problem of choosing in a sense the "most suitable reasonable dictators" is considered (the set $\Cal D_r(f, \phi)$ in the text). The solution of a given conflict situation is then a pair $(P;j)$, where $P$ is a reasonable group decision rule ("reasonable dictate" for the whole group) and $j$ is a suitable reasonable dictator, i.e. a person from the group, who can apply this reasonable dictate if appointed the leader of the group. Existence conditions for the solution of the conflict situation are given and various possibilities of extension of the proposed models are considered. A small numerical example is solved.

Détail

DOI : 10.21136/AM.1976.103626

Classification : 90A99, 90D12, 91A35, 91B06, 91B16, 91B99, 91D99