Desirable Rankings: A New Method for Ranking Outcomes of a Competitive Process

We consider the problem of aggregating individual preferences over alternatives into a social ranking. A key feature of the problems that we consider---and the one that allows us to obtain positive results, in contrast to negative results such as Arrow's Impossibililty Theorem---is that the alternatives to be ranked are outcomes of a competitive process. Examples include rankings of colleges or academic journals. The foundation of our ranking method is that alternatives that an agent desires---those that they have been rejected by---should be ranked higher than the one they receive. We provide a mechanism to produce a social ranking given any preference profile and outcome assignment, and characterize this ranking as the unique one that satisfies certain desirable axioms. A full version of this paper can be found at: https://arxiv.org/abs/2205.11684.