Measuring the Welfare Gains from Cardinal-Preference Mechanisms in School Choice

We empirically measure the welfare gains from cardinal-preference over ordinal-preference mechanisms for the school-choice assignment problem. We consider two cardinal mechanisms: a variant of the pseudomarket mechanism of Hylland and Zeckhauser (1979) as well as an envy-free mechanism related to Nguyen, Peivandi and Vohra (2015). We introduce and theoretically analyze a variant of the pseudomarket mechanism that has an equilibrium selection rule as well as a computer algorithm to compute the implied stochastic assignment. We estimate cardinal preferences over schools using data on student submissions of rank ordered lists of schools in Seattle. Using these estimated preferences, we measure the welfare gains from using the cardinal-preference mechanisms instead of the ordinally-efficient probabilistic serial mechanism. We find that the envy-free mechanism captures 58% of the possible gains over the ordinal mechanism using a utilitarian benchmark. The psuedomarket captures 21% of the possible gains over the ordinal mechanism.