What do large language model panels add to multi-criteria decisions? Order-invariant q-rung dual hesitant preference aggregation and a hybrid supercapacitor case study

Large language models (LLMs) increasingly replace human experts in multi-criteria decision analysis, but their contribution to decisions computable from published data is rarely examined. This is studied with q-rung dual hesitant fuzzy preference relations elicited from five LLMs of five developers. The standard group relation, built with the weighted geometric operator and a reciprocity rebuild, depends on the order of the criteria; a q-power-mean aggregation with row-sum priority weights is proved to be order invariant, to preserve the q-rung constraint and to keep every weight positive, and without consensus adjustments the results depend on each hesitant set only through the means of the q-th powers of its degrees. In a hybrid supercapacitor selection problem built from verified full-cell data, the standard construction yields up to 26 rankings over the criterion orderings, the proposed construction one; the elicited judgments, however, shift with the order of the prompt (four permutation tests, p ≤ 0.009). Single central judgments per entry reproduce the hesitant-set rankings. With the decision table in the prompt, all 18 direct-data configurations reproduce the LLM-pipeline ranking; without it, the LLM performance judgments diverge from the evidence and change the ranking. Under ranking by multi-objective optimization by ratio analysis plus the full multiplicative form, resampling of models and sessions places the lithium-ion capacitor first in 0.748 (standard) and 1.000 (fixed-bound variant) of the draws; with literature source rows also resampled and the rebuilt table as performance matrix, the shares are 0.533 and 0.504. The LLM judgments are not validated against human experts.