Recipes for Structural Fairness in Games

Abstract

Although fairness is central to society and to games that are taken seriously, the structural aspect of fairness has not been addressed as a problem of games. Structural fairness in a game of multiple episodes with multiple parties contending for limited opportunities can be assured by an appropriate rotational procedure over a sufficient number of episodes. For fixed number of parties, positional rotation assures complete position fairness. In contrast, order rotation assures both complete positional fairness and complete order fairness, but only when number-of-party and number-of-episode conditions are satisfied. For variable number of parties, arrival rotation assures fairness to parties added last. Order rotation may assure fairness better than proportional allocation when opportunities cannot be distributed exactly in the proportions required. The Gold and Pray (1990) model can be adapted to include rotation. Structural fairness as equality of realized, rather than expected, opportunity cannot be assured by random selection; rotation is necessary.