This paper examines the implications for social welfare functions of restricting the domain of individual preferences to type-one preferences. Type-one preferences assume that each person has a most preferred alternative in a euclidean space and that alternatives are ranked according to their...

This note uses Farkas's Lemma to prove new results on the implementability of general, asymmetric auctions, and to provide simpler proofs of known results for symmetric auctions. The tradeoff is that type spaces are taken to be finite.