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This article presents a new model aimed at predicting behavior in games involving a randomized allocation procedure. It is designed to capture the relative importance and interaction between procedural justice (defined crudely in terms of the difference between one’s expected payoff and average expected payoff in the group) and distributive justice (difference between own and average actual payoffs). The model is applied to experimental games, including “randomized” variations of simple sequential bargaining games, and delivers qualitatively correct predictions. In view of the model redistribution of income can be seen as a substitute for vertical social mobility. This contributes to the explanation of greater demand for redistribution in European countries vis-a-vis the United States. I conclude with suggestions for further verification of the model and possible extensions.