More Data, Worse Decisions? Preference Reversals in Neural Networks under Gram Incompatibility

2026-07-28

AI Summary

This work addresses the reliability degradation of neural networks trained on pooled multi-source data, where models may violate decision preferences commonly supported across sources. Drawing on the combination axioms from case-based decision theory, the study analyzes how geometric variations in the inverse Gram matrix within fixed-representation neural networks affect preference preservation. It introduces a Gram mismatch metric, a scale-invariant regularization scheme, and a three-stage decision reversal auditing framework. This approach is the first to translate combinatorial reliability into a measurable and controllable operational mechanism, effectively identifying stable versus reversal-prone regions in load-bidding, healthcare, and financial proxy tasks. The method significantly mitigates harmful preference reversals while enabling joint optimization of accuracy and decision consistency.

Abstract

Neural networks increasingly combine data across populations, time periods, and operating conditions to improve generalization. This raises a reliability question: whether a model refitted on pooled data preserves an action ordering supported by both sources. Case-Based Decision Theory (CBDT) formalizes this requirement through its composition axiom, which requires source-supported preferences to survive their union. We study when this property holds for fixed-representation neural networks with ordinary least squares (OLS) output heads. First, we show that pooled refitting recomputes the inverse-Gram geometry used to weight source evidence, which can reverse shared preferences, and derive exact and approximate preservation conditions. Next, we introduce a scale-invariant Gram mismatch measure for prioritizing candidate pools and geometry-oriented regularization for shaping source geometry during training. Finally, we develop a three-stage audit that traces strict pairwise reversals through decision changes to task-defined utility loss. Experiments spanning a load-based bidding proxy and medical and financial decision proxies reveal stable and reversal-prone pooling regimes: the load audit identifies a measurable nonzero class of source-consensus-relative harmful decisions under the proxy utility, while cross-domain audits show that comparable mismatch can correspond to sharply different preservation rates. Geometry-oriented objectives occupy distinct descriptive accuracy-consistency-geometry-harm operating points. Together, the framework makes compositional reliability measurable and operational through screening, analytic certification, geometry-oriented training, and decision-consequence auditing.

Problem

• preference reversal
• Gram incompatibility
• compositional reliability
• neural networks
• data pooling

Innovation

• Gram incompatibility
• preference reversal
• geometry-oriented regularization
• compositional reliability
• decision auditing