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A Notion of Hierarchic Social Welfare for Resource Allocations

Abstract:

This paper introduces a novel concept of social welfare that integrates both numerical utility functions and hierarchical relationships among agents. We establish an ordering relation among all possible resource allocations. In the context of binary utility functions, we show that maximal allocations align with those outlined in [1]. Furthermore, we establish that, in the absence of hierarchy, our ordering corresponds to the order induced by a weighted utilitarian social welfare. Finally, we conduct experiments to explore the effects of different degrees of hierarchy strength.