Decision making using similarity to a reference distribution.

This article introduces a novel methodology for discriminant analysis (DA) and multicriteria decision analysis (MCDA) that requires specifying only one reference or "ideal" group rather than multiple groups. Central to this approach is the overlap index, defined as the probability that a random observation from a candidate group could have originated from the reference group’s distribution, providing a measure of compatibility rather than exact group membership. The paper details the theoretical foundation, estimation, and computational methods for the overlap index, including Monte-Carlo integration for multivariate normal distributions and adaptations for Bernoulli variables. Practical applications are demonstrated through examples involving iris species classification, surgeon performance appraisal, and football player position suitability, illustrating the method’s managerial relevance and robustness despite model assumptions. The methodology simplifies decision analysis by requiring only the ideal group’s characteristics, offering confidence intervals and bias correction, and aims to enhance explainability in decision-making contexts.