Fair allocation of disputed properties

We model problems of allocating disputed properties as generalized exchange economies in which agents have preferences and claims over multiple goods, and the social endowment of each good may not be sufficient to satisfy all individual claims. In this context, we investigate procedural and end-state principles of fairness, their implications and relations. To do so, we explore “procedural” allocation rules represented by a composition of a rights-assignment mechanism (to assign each profile of claims individual property rights over the endowment) and Walrasian, or other individually rational, exchange rule. Using variants of fairness based on no-envy as end-state principles, we provide axiomatic characterizations of the three focal egalitarian mechanisms, known in the literature on rationing problems as constrained equal awards, constrained equal losses, and proportional mechanisms. Our results are connected to focal contributions in political philosophy, and also provide rationale for market-based environ- mental policy instruments (such as cap-and-trade schemes and personal carbon trading) and moral foundation for the three proposals to allocate GHG emission rights known as the equal per capita sharing, the polluter pays principle and the equal burden sharing (the victims pay principle).