Problem
Research questions and friction points this paper is trying to address.
Aggregating individual preferences into social rankings
Ranking alternatives from competitive processes outcomes
Establishing axioms for desirable ranking consistency
Desirable Rankings: A New Method for Ranking Outcomes of a Competitive Process
🤖 AI Summary
This paper addresses the problem of social ranking under competitive allocation outcomes—such as university admissions or journal submissions—where individual preferences are unobserved. We propose an axiomatic method that infers preference intensity from rejection destinations. Our key innovation is the introduction of the *desirability axiom*: any rejected alternative must be ranked above the agent’s actual assignment. Building upon this, we uniquely characterize a social ranking satisfying desirability, consistency, neutrality, and continuity—thereby circumventing Arrow’s impossibility theorem within competitive settings. The resulting ranking is computationally tractable, uniquely determined, and interpretable. We provide an explicit constructive algorithm and rigorously prove its equivalence to the stated axioms. The method has been empirically applied to university and academic journal rankings, demonstrating both theoretical soundness and practical feasibility.
📝 Abstract
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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Aggregating preferences into social rankings
Using competitive outcomes for positive results
Algorithm constructs unique desirable rankings
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