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Second-price auctions are designed to induce people to reveal their private preferences for a good. Laboratory evidence suggests that while these auctions do a reasonable job on aggregate, they fall short at the individual level, especially for bidders who are off-margin of the market-clearing price. Herein we introduce and explore whether a random nth-price auction can engage all bidders to bid sincerely. Our results first show that the random nth-price auction can induce sincere bidding in theory and practice. We then compare the random nth-price to the second-price auction. We find that the second-price auction works better on-margin, and the random nth-price auction works better off-margin.