Multiobjective Optimization-Based Subjective Probability Distribution Aggregation: A Survey
Zhen-Song Chen, Han Wang, Zheng Ma, Yi Yang, Zhengze Zhu, Francisco Chiclana, Witold Pedrycz, Miroslaw Jan Skibniewski · IEEE Transactions on Systems Man and Cybernetics Systems · 2026
Subjective probability distribution aggregation (SPDA) refers to the process of combining multiple expert judgments into a single representative distribution and has become essential for decision-making under deep uncertainty. Despite its importance, a systematic review of multiobjective optimization-driven approaches to SPDA remains lacking. To address this gap, we trace the paradigm evolution from classical axiomatic and Bayesian approaches to contemporary optimization-driven frameworks, revealing a progression from single-objective consensus maximization through biobjective consensus-confidence models to comprehensive multiobjective formulations incorporating fairness and social welfare. We conduct a systematic literature review and establish a unified taxonomy that classifies methods by structural objectives and behavioral tradeoffs. Bibliometric analysis reveals a marked shift toward socially informed aggregation, with fairness concern and group dynamics emerging as dominant themes. We systematically examine applications across risk engineering, economics and finance, climate science, and policy planning, demonstrating that method selection must align with domain-specific uncertainty structures. In addition, key research challenges are identified, and a forward-looking roadmap is outlined to guide future investigations. This synthesis consolidates existing advances and provides both theoretical foundations and practical guidance for developing next-generation SPDA methods that balance statistical performance with social acceptability in complex decision environments.