Game Mechanisms & Procedural Fairness

The main paper to which this abstract refers models procedural fairness and procedural justice, crucial concepts in the design and appraisal of social interaction [1]. Argumentation systems in particular owe the quality of their inferences to the quality of the procedure that produces them. We are interested in both games that can be justified without reference to substantive social purposes, such as tournaments, and games that are fair, even if they are formally asymmetric, because they are appropriate to their social purposes, such as litigation and prosecution games. A mathematical theory of procedural fairness has eluded theorists (much informal discussion in this regard has centered around the work of Rawls [2]). Such a theory would give formal standing to devices such as anonymization through chance and turnswapping, equality of opportunity, symmetry of rules, and exchangeable asymmetries. It would understand the fundamental role of fair procedure: to construct justifiable ex post asymmetries that could not be justified except by reference to the procedure that produced them. Such a procedure begins with a justifiable ex ante position, and constructs its outcome on serendipity of play and chance, under an independently justifiable regimen. We have developed a preliminary formal framework for exploring some mathematical properties of procedural fairness. The framework encompasses deterministic and stochastic games and player strategies, and contains formal devices for recursively composing complex games from simple components, including devices concerned with modifying/introducing procedural fairness properties. We also define allocation games as a special case, and may then invoke familiar game-theoretic concepts. Consider