Affiliation was introduced by Milgrom and Weber (1982) through the
positive dependence intuition, that is, high value of one bidder’s estimate
makes high values of the others’ estimates more likely. However, positive
dependence has many alternative definitions; we show that affiliation is one

of the most restrictive among them. This poses the question whether affili-
ation’s main implications (equilibrium existence and the revenue ranking of

auctions) remain valid for other formalizations of positive dependence. We

show that both implications can indeed be generalized in the context of pri-
vate values, and give counterexamples for further generalizations.

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