Abstract
We impose a lattice-theoretic structure on a class of social welfare functions, which properly include Arrowian social welfare functions, by ordering their families of decisive sets by set inclusion. We show that this lattice is compactly generated and characterize the completely meet irreducible elements of this lattice. Certain completely meet irreducible elements correspond to Arrowian social welfare functions. Those social welfare functions corresponding to the other completely meet irreducible families of decisive sets are approximate solutions to the problem of social choice as posed by Arrow.
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