Beyond Strict Preferences: The Value of Indifferences and Cardinal Information in Matching (with Judd Kessler and Clayton Featherstone)
In a Harvard Business School match, we show that eliciting indifferences increases the fraction of 1st-choice assignments by almost 11 percentage points (compared to a counterfactual match in which MBAs are forced to submit strict rankings). Of course, the welfare impact of this improvement depends on the underlying (and unobserved) cardinal preferences. In a teacher-placement match in Chile, we use a novel, incentive-compatible method to elicit cardinal preferences from real teachers. We then compare the standard mechanism used in the field—random serial dictatorship (RSD) with strict preferences—to a version of RSD that allows for indifferences, and to the cardinal welfare max. Relative to RSD with strict preferences, the cardinal welfare max makes each participant almost $1,700 better off on average. Allowing indifference reporting accounts for almost $500 of this.