Ordinal Ranking with Intensity of Preference

Abstract

In conventional ordinal ranking models the voter/ranker supplies an ordered set of preferences on a collection of objects without specifying any form of intensity of preference. For example, an executive committee of ten members is required to assign five candidates to five positions. The nature of the positions is such that position one requires the highest qualified candidate (relative to a given attribute), position two the second qualified person and so on. Each one of the members in the committee is required, therefore, to supply a ranking of the five candidates and from each individual preference the committee must come up with an aggregate or consensus ranking which dictates the assignments of the candidates to the jobs. In many situations, however, it is desirable to permit the individual to express some measure of intensity of preference. For example, suppose that six committee members agreed that candidate number one is slightly better than candidate number two, but four of them evaluated candidate number two as being much better than candidate number one. The question now is whether this situation is identical to the case where the six members evaluate candidate one as much better than candidate two and four members evaluate candidate two as slightly better than candidate one. The ordinal ranking model will not distinguish between the above two cases while it is clear that when taking account of the intensity of preference, the committee should end up with two different consensus rankings. This paper develops a model for aggregating ordinal rankings in which the voter is allowed to express such intensity of preferences, and a method to derive the consensus ranking is proposed.

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