Abstract
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.
Original language | English (US) |
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Pages (from-to) | 475-488 |
Number of pages | 14 |
Journal | IIE Transactions (Institute of Industrial Engineers) |
Volume | 48 |
Issue number | 6 |
DOIs | |
State | Published - Jun 2 2016 |
Externally published | Yes |
Keywords
- Axiomatic metrics
- Consensus formation
- Group decision-making
- Incomplete rankings
- Ranking aggregation
ASJC Scopus subject areas
- Industrial and Manufacturing Engineering