Function (biology)

Context (archaeology)

Preference learning

Biology

Aggregation problem

Statistics

Social psychology

Archaeology

Computer science

Evolutionary biology

Ranking (information retrieval)

Decision theory

Psychology

Preference

Mathematics

Geography

Axiom

Group decision-making

Econometrics

Revealed preference

Artificial intelligence

Geometry

Mathematical economics

Decision Analysis

Preference–approval structure combines the preference information of both ranking and approval, which extends the ordinal preference model by incorporating two categories of choice alternatives, that is, acceptable (good) and unacceptable (bad), in the preference modeling process. In this study, we present some axioms that imply the existence of a unique distance function of preference–approval structures. Based on theoretical analysis and simulation experiments, we further study a preferences aggregation model in the group decision-making context based on the proposed axiomatic distance function. In this model, the group preference is defined as a preference–approval structure that minimizes the sum of its distances to all preference–approval structures of individuals in the group under consideration. Particularly, we show that the group preference defined by the axiomatic distance–based aggregation model has close relationships with the simple majority rule and Cook and Seiford’s ranking.

Preference–Approval Structures in Group Decision Making: Axiomatic Distance and Aggregation