Minimax apportionments

The method of apportionment proposed in this paper reverses the approach of classical methods, where techniques for the assignment of electoral seats are developed, and then the fairness criteria which are met by this techniq ue are established. In this paper, however, an order of priority of the cri teria is first established and then a "customized" solution is developed fo r each individual case following the approaches of Balinski and Young. By u sing suitable relations of dominance between seat distributions and Coopera tive Game Theory, it is possible to obtain a "minimax apportionment", i.e. a distribution which minimizes the gravest possible distorsions. This metho d can also be easily applied to multiordered apportionments.