Which Differences Matter? Controlled Tests of Rule Transfer, Joint Reliability, and Information Use in Decision Models

Tianyou Lai, Wentao Yue, Zhiwei Zuo, Qilei Li

Decision models map stated rules and observed states to discrete answers. Aggregate accuracy leaves unresolved which rule and information changes guide those answers. We connect controlled input changes to transfer, joint reliability, and directed information use through executable arithmetic rules. Semantic rule separation and crossed rule and state tests make transfer and joint success separately measurable. We compare equivalent wordings, calibrate joint correctness through marginal-preserving reassociation, and alter tables to define alternative answer targets. Adaptation gains increase with nearest-source answer agreement; fully conflicting quartets yield small pooled gains and different gain signs across source splits. Equivalent rewrites have opposing task-level effects, linking transfer gains to rule presentation. Joint-score departures depend on which rule and state associations the reference preserves. A decision service changes answers more across equivalent wordings than across identical-text repeats and usually follows the answer targets implied by altered table values or mappings.