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Axiomatic aggregation of incomplete rankings

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Version 2 2016-02-18, 23:24
Version 1 2015-11-26, 00:00
journal contribution
posted on 2016-02-18, 23:24 authored by Erick Moreno-Centeno, Adolfo R. Escobedo

In many different applications of group decision-making, individual ranking agents or judges are able to rank only a small subset of all available candidates. However, as we argue in this article, the aggregation of these incomplete ordinal rankings into a group consensus has not been adequately addressed. We propose an axiomatic method to aggregate a set of incomplete rankings into a consensus ranking; the method is a generalization of an existing approach to aggregate complete rankings. More specifically, we introduce a set of natural axioms that must be satisfied by a distance between two incomplete rankings; prove the uniqueness and existence of a distance satisfying such axioms; formulate the aggregation of incomplete rankings as an optimization problem; propose and test a specific algorithm to solve a variation of this problem where the consensus ranking does not contain ties; and show that the consensus ranking obtained by our axiomatic approach is more intuitive than the consensus ranking obtained by other approaches.