Abstract
In the sequel we will derive sufficient and necessary conditions for the existence of certain numeric representations of simple games. In § 2 the above mentioned representation is given by a so called, “coalitionally ordered function”, i.e. a numeric function representing the desirability of each coalition in the class of all coalitions. Simple games which possess a c.o.f are called coalitionally ordered games. Sufficient and necessary criteria are given for a simple game to be a c.o.g. Analogously weighted majority games are characterized in § 3. The criteria to be presented are linked by properties of the desirability relation of a simple game. The concept of a desirability relation was introduced by Peleg 1978.
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