Comparability of coalitions in committees with permission of voters by using desirability relation and hopefulness relation

摘要

In this paper, we treat committees with permission of voters, and examine comparability of the effectiveness and the efficiency of coalitions in a committee by using formal ways, that is, the desirability relation and the hopefulness relation. Consequently, we obtain a necessary and sufficient condition for desirability relation of the permission game of a committee with permission of voters to be complete, that is, the desirability relation is complete if and only if there is no pair of coalitions whose supporters are mutually different. Moreover, we give an example of committees in which there are coalitions whose effectiveness and efficiency cannot be compared.