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. We find that a switch to truthful reporting in the DA mechanism offers welfare improvements over the baseline given the belief errors we observe in the data, but that an analyst who assumed families had accurate beliefs would have reached the opposite conclusion.

Many school districts with centralized school choice adopt strategy-proof assignment mechanisms to relieve applicants from needing to strategize based on beliefs about their own admissions chances. This article shows that beliefs about admissions chances shape choice outcomes even when the assignment mechanism is strategy-proof by influencing how applicants search for schools and that “smart matching platforms” that provide live feedback on admissions chances help applicants search more effectively. Motivated by a model in which applicants engage in costly search for schools and overoptimism can lead to undersearch, we use data from a large-scale survey of choice participants in Chile to show that learning about schools is hard, beliefs about admissions chances guide the decision to stop searching, and applicants systematically underestimate nonplacement risk. We use RCT and RD research designs to evaluate scaled live feedback policies in the Chilean and New Haven choice systems. Twenty-two percent of applicants submitting applications where risks of nonplacement are high respond to warnings by adding schools to their lists, reducing nonplacement risk by 58% and increasing test score value added at the schools where they enroll by 0.10 standard deviations. Reducing the burden of school choice requires not just strategy-proofness inside the centralized system but also choice supports for the strategic decisions that inevitably remain outside of it.