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A Consensus Leximin Rule

In this paper we propose to widen both the domain and range of Arrovian social choice to allow for a more general and transparent model. The domain will be enlarged towards pro...les of extended orderings, while we allow the range to contain quasi-orderings, and thus possibly incomplete social relations. By adapting some standard axioms towards our framework, we can derive a generalization of the leximin rule the consensus leximin rule as the unique rule satisfying a set of reasonable axioms.