I propose a new mechanism" design approach to the problem of ranking standard auctions with two heterogeneous bidders. A key feature of the approach is that it may be possible to rank two auctions even if neither dominates the other for all combinations of types. The approach simplifies the analysis and unifies results in the existing literature. Roughly speaking, the first-price auction is more profitable than the second-price auction when the strong bidder's distribution is flatter and more disperse than the weak bidder's distribution. Applications include auctions with one-sided externalities. Moreover, contrary to previous work, reserve prices are easily handled. Finally, the method can be extended to some environments with many bidders.
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