A Bayesian Analysis Framework for Decision Making with Interval Pairwise Comparison Judgments

Abstract

In this research, as a first step toward applying Bayesian inference to subjective expected utility analysis under judgment uncertainty, a Bayesian analysis framework for decision making with interval pairwise comparison judgments is developed on the basis of the analytic hierarchy process. This framework helps to effectively capture the inherent uncertainties associated with interval judgments and integrate prior information, including partially known preferences with observed judgments, to infer posterior preference. The key novelty of this framework lies in its mechanism for incorporating partially known preferences. Moreover, a consistency index is introduced to assess the inconsistency between partially known preferences and observed judgments. Results of illustrative examples and sensitivity analysis demonstrate that the proposed framework is adaptable to various judgmental data and model assumptions, the preference reversal probability is controlled by the inconsistency level and utility gap, and the impact of prior information can be regulated by manipulating its hyperparameters. Funding: This work was supported by the Top Talent Academic Foundation for University Discipline of Anhui Province [Grant gxbjZD2020056] and the National Natural Science Foundation of China [Grants 72171002, 72201004, 72271002, 72301003, and U22A20366]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/deca.2024.0207 .