Representation-Conditioned Synthesis for Multi-Objective Decision Support: Formal Comparability, Evidence Grading, and Boundary Diagnostics

Abstract

Multi-objective decision support is fragmented by a representation mismatch: Pareto-set methods, outranking relations, and scalarization-based methods emit different mathematical objects, yet review articles often compare them as if they were directly commensurable. We present a representation-conditioned synthesis framework that formalizes within-family comparability, separates cross-family evidence grading from raw metric aggregation, and makes theorem-level assumptions explicit. The manuscript contributes two proved formal results and one boundary analysis linked to executed validation artifacts: (i) an impossibility result showing that no family-blind scalar embedding can preserve bidirectional order fidelity when Pareto incomparability is present, (ii) a constructive existence result showing that typed contradiction-loss minimization attains zero loss under finite-acyclic and separability assumptions, and (iii) a local bridge-stability characterization for preference perturbations that is valid only inside a margin-Lipschitz regime. Executed evidence supports these claims with typed violation mean 0.0083 versus family-blind violation mean 0.2863, typed zero-loss feasibility in 405/540 runs under satisfied assumptions, and a sign-flip increase from 0.0723 inside the stability regime to 0.2108 outside it. The resulting survey protocol yields defensible method-selection guidance without asserting unsupported universal rankings across non-equivalent method families.