Measuring unfairness feeling in allocation problems

In this paper, we introduce a new measure of social fairness based on unfairness feelings of the players involved in an allocation problem, e.g., cake-cutting problem or shift scheduling. We only require that each player be described by a von Neumann-Morgenstern utility function. Next, we propose a social normalization of each player׳s utility function, based on how each player sees the other players׳ shares through her own utility function. Further, we extend this normalization idea to a setting where the players are represented by a weighted oriented graph, where the weights assess the relatedness of (or similarities between) the agents. Among other results, we establish some links between our measures of fairness and those classically used in the cake-cutting-problem literature.