Year: 2026
Type: article
Abstract: We provide an axiomatic foundation for two indices intended to quantify dynamic discrepancy between alternative decision criteria under the canonical invariance principle of decision theory and social choice: welfare representations are meaningful only up to positive affine transformations. The first index, the Preference-Class Gap (PPG), measures representation-level mismatch between two instantaneous welfareprimitives on a common compact admissible domain, by computing the uniform-norm distance from one primitive to the positive-affine equivalence class generated by the other, with a scale-free normalization ensuring well-posedness under near degenerate benchmark scales. The second index, the Pathwise Distortion Index (PDI), measures outcome-level discrepancy along realized optimal trajectories: it aggregates the benchmark-evaluated welfare wedge induced by the alternative criterion and normalizes it in benchmark units, with a strictly positive floor regularization required for stability when baseline magnitudes become small. For each index we propose transparent axioms and prove representation theorems: up to a monotone transform, PPG is uniquely characterized by the uniform-norm distance to a positive-affine class, and PDI is uniquely characterized by a floor-regularized normalized cumulative wedge along realized paths. We also establish a sharp logical separation: representation-level proximity and pathwise distortion are not equivalent objects. Small preference-class gaps can be dynamically amplified by constraints and feedback, while large primitive mismatches may be irrelevant on realized paths. These results provide a measurement-theoretic basis for a general Dynamic Discrepancy Theory of regime comparison in dynamic decision problems.
Source: Operations Research Forum
Author: Takashi Matsuhisa
Institution: Karelian Research Centre
Language: English
Subfield: General Decision Sciences
Field: Decision Sciences
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W7136089515