A Bayesian Analysis Framework for Decision Making with Interval Pairwise Comparison Judgments
Why this work is in the frame
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Bibliographic record
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 .
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.009 | 0.026 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.003 |
| Bibliometrics | 0.014 | 0.040 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.003 | 0.001 |
| Open science | 0.004 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it