Formulas are derived which estimate the accuracy of conjoint analysis in predicting preferences in a validation sample. This accuracy turns out to depend on (among other things) which model of preference is used (e.g., whether interactions are added, whether partworth or linear functions are used). I first show a paradoxical result that simpler models often yield higher predictive accuracy, even when a more complex model is the true one. The reason for this is that the additional parameters of the complex model are estimated with larger variance, which tends to overwhelm the benefits of using the true model. I then shift my criterion from predicting an individual's preferences, to predicting market share, which is of most interest to managers. Under this criterion my conclusions reverse, and I show that a true model (even when complex) is much more likely to yield higher predictive accuracy than a simpler incorrect model. This reverses some previous conclusions in marketing, and confirms that finding the correct model of consumer preference is important in improving prediction. Results from four previous empirical papers are correctly predicted by these formulas, as well as results from additional Monte Carlo studies.