Decision Making using Similarity to a Reference Distribution

Baker, Rose D; McHale, Ian G

Abstract

In discriminant analysis and some methods of multicriteria decision analysis (MCDA) we often wish to assign a ‘candidate’ to one of two or more groups, e.g. ‘satisfactory’ or ‘unsatisfactory’. This requires specifying the characteristics of both groups. However, often we are only able or willing to specify the characteristics of one group, the reference or ‘ideal’ group. We propose a method for proceeding in this case, using the overlap index. This is shown to be the probability that a random variable could have come from a reference distribution. This article motivates and introduces the index, describes its estimation and computation, and illustrates its use with examples from discriminant analysis and MCDA. Two of these examples, one of choosing soccer players and another of appraising surgeons, involve managerial decisions. The novelty here is the introduction of ‘1-group discriminant analysis’ based on the overlap index, the application to MCDA, and the methodology for the computation of the overlap index.

Citation

Baker, R. D., & McHale, I. G. (2025). Decision Making using Similarity to a Reference Distribution. IMA Journal of Management Mathematics, 36(1), 67-82. https://doi.org/10.1093/imaman/dpae026

• Journal Article Type: Article
• Acceptance Date: Oct 8, 2024
• Online Publication Date: Oct 12, 2024
• Publication Date: 2025-01
• Deposit Date: Jan 22, 2025
• Journal: IMA Journal of Management Mathematics
• Print ISSN: 1471-678X
• Publisher: Oxford University Press
• Peer Reviewed: Peer Reviewed
• Volume: 36
• Issue: 1
• Pages: 67-82
• DOI: https://doi.org/10.1093/imaman/dpae026