Graded and Hysteretic Vetoes in Outranking: An Axiomatic Characterisation with Application to Energy Planning

Multicriteria decision problems in energy planning couple mandatory feasibility requirements with compensatory trade-offs, a structure that fully compensatory aggregation handles poorly and that the recently proposed Phase-Equilibrium Outranking Method (PEOM) addresses through a graded veto band embedded in a scoring architecture. A formal and computational audit identifies three defects in that architecture. First, the net-flow stage of PEOM is a strictly increasing transformation of its composite score, so no exploitation of score differences by an increasing kernel can generate outranking content. Second, the published case-study scores cannot be reproduced from the printed formulas. Third, the published ranking violates near-dominance. We propose R-PEOM, a reconstruction in which the band acts as a level-based graded discordance on an ELECTRE-type pairwise credibility index defined on raw evaluation scales, admitting incomparability, and whose credibility structure is provably invariant under modification of the alternative set. A characterisation theorem establishes that, under four behavioural axioms, the multiplicative credibility σ(a,b) = C(a,b)·F(a) is the unique admissible form up to reparameterisation of the band curvatures. Preference parameters are inferred from holistic statements through compatible-set sampling in the spirit of robust ordinal regression, and a stochastic acceptability layer quantifies robustness. A hysteretic veto with distinct exit and re-entry thresholds extends the model to monitored systems, with a proven no-chattering guarantee. Across two published energy case studies, R-PEOM eliminates the infeasible option, restores the near-dominant wind site to first rank with 88.5% rank-one acceptability, confirms green liquid hydrogen as the preferred pathway, and reduces noise-induced feasibility flicker by up to 97%. Note. This is the author's version of a manuscript currently under review. The audit in Section 2 concerns the article by Yerlikaya et al. (Scientific Reports, https://doi.org/10.1038/s41598-026-59606-4) as published in early access on 1 July 2026, which is the version of record at the time of writing. This work rests solely on that published version.