22 March 2019, Computational Social Choice Seminar, Z. Emel Öztürk
A group of agents is ordered along a linear river. Each agent has quasilinear preferences over water and money. A vector of property rights, referred to as the reference vector, specifies how much water each agent is entitled to. The key concept in this study is an allocation's distance-to-reference vector. At an allocation, this vector specifies, for each agent, the amount of money that needs to be subtracted from the bundle the agent receives in order for the agent to be indifferent between the reference vector and the allocation. First, we characterize a social ordering, called the reference-welfare equivalent Lorenz ordering, which prefers an allocation to another if the distance-to-reference vector of the former is more equal than the distance-to-reference vector of the latter. Second, we show that maximizing the reference-welfare equivalent Lorenz ordering over the set of acceptable allocations (defined in the sense of the core) leads to a unique allocation which meets the three key objectives of international river management: efficiency, fairness and stability. Moreover, we show that this allocation coincides with the egalitarian solution of Dutta and Ray (Econometrica, 1989) and the downstream incremental solution of Ambec and Sprumont (Journal of Economic Theory, 2002) for particular conceptions of property rights.
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