This paper studies how welfare outcomes in centralized school choice depend on the assignment mechanism when participants are not fully informed. Using a survey of school choice
participants in a strategic setting, we show that beliefs about admissions chances differ from
rational expectations values and predict choice behavior. To quantify the welfare costs of belief
errors, we estimate a model of school choice that incorporates subjective beliefs. We evaluate
the equilibrium effects of switching to a strategy-proof deferred acceptance algorithm, and of
improving households' belief accuracy. Allowing for belief errors reverses the welfare comparison
to favor the deferred acceptance algorithm.