Biologists have proposed a variety of explanations for extravagant sexual displays, and controversies over explanations define the history of sexual selection research. Recently, Richard Prum has defended Darwin’s idea that the evolution of sexual displays is driven by arbitrary and nonadaptive preferences of potential mates. Prum argues that this explanation should be the null model for sexual selection research. I show that if we adopted Prum’s proposal, the inferences we could be justified in making are more modest than he claims. I also discuss problems with estimating model parameters that at present prevent his proposal from being useful in practice.