Desirable Rankings
Gaurab Aryal, Thayer Morrill, Peter Troyan
TL;DR
This paper develops desirable rankings, a method to aggregate agent preferences into a social ranking when agents are matched to alternatives. By filtering out idiosyncratic components via shadow matchings and two axioms (AoD and justification), it constructs the IRUS algorithm to produce unique desirable rankings relative to a given shadow matching. In the limit, with a utility decomposition $U_{i,c}=\alpha\theta_c+(1-\alpha)\eta_{i,c}$ and large markets, the resulting percentile ranks converge to the true quality order $\theta_c$, while ranking tiers become vanishingly small. The Chilean medical programs application demonstrates practical viability with minimal data (ROLs and initial matches), and comparisons to revealed preference and Borda rankings show clear advantages in stability and fidelity to true quality.
Abstract
We study the problem of aggregating individual preferences over alternatives into a collective ranking. A distinctive feature of our setting is that agents are matched to alternatives. Applications include rankings of colleges or academic journals. The foundation of our approach is that alternatives agents desire -- that is, those they rank above their match -- should also be ranked higher socially. We introduce axioms to formalize this idea and call rankings that satisfy them desirable. We develop an algorithm to construct desirable rankings and prove that, as the market becomes large, desirable rankings converge to the true underlying ranking of the alternatives by quality. We support this convergence result through simulations and demonstrate the practical usefulness of our approach by ranking Chilean medical programs with data from their centralized admission system. Finally, we compare performance and show that our approach outperforms two benchmarks: revealed preference rankings and Borda counts.