10.57647/ijm2c.2027.1702.10

Robust Preference Aggregation under Strategic Behavior: A Consensus-Aware Game Cross-Efficiency Framework

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  • Arezoo Khosravirad1,
  • Abdollah Hadi-Vencheh*1,
  • Ali Jamshidi1,
  • Majid Tavassoli Kajani1,
  1. Department of Mathematics, Isf.C., Islamic Azad University, Isfahan, Iran

Received: 24-02-2026

Revised: 11-06-2026

Accepted: 20-06-2026

Published in Issue 03-07-2026

Copyright (c) 2025 Arezoo Khosravirad, Abdollah Hadi-Vencheh, Ali Jamshidi, Majid Tavassoli Kajani (Author)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Khosravirad, A., Hadi-Vencheh, A., Jamshidi, A., & Tavassoli Kajani, M. (2026). Robust Preference Aggregation under Strategic Behavior: A Consensus-Aware Game Cross-Efficiency Framework. International Journal of Mathematical Modelling & Computations. https://doi.org/10.57647/ijm2c.2027.1702.10
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Abstract

The aggregation of heterogeneous preferences in multi-stakeholder environments is often compromised by strategic behavior, scale inconsistencies, and the absence of ground truth for validation. While Data Envelopment Analysis (DEA), specifically the Game Cross-Efficiency model, provides a Nash equilibrium-based mechanism to mitigate weight arbitrariness, existing frameworks suffer from critical ordinal instability and a lack of internal verification mechanisms. This study presents a novel, integrated decision support framework that fortifies the game-theoretic foundations of DEA-based voting through endogenous normalization and exogenous stability assessment. Unlike traditional sequential approaches, the proposed methodology synthesizes three rigorous components: (i) an unmodified DEA game cross-efficiency mechanism to capture peer-evaluated performance; (ii) a Relative Ratio (RR) transformation axiomatically proven to enforce scale invariance and preserve strict dominance without altering the underlying preference structure; and (iii) a composite stability verification protocol utilizing WASPAS and COPRAS algorithms to quantify rank reversals and dominance consistency. Theoretical properties, including affine invariance and monotonicity preservation, are formally established. Furthermore, a novel Composite Stability Index (CSI) is introduced to serve as a proxy for ranking reliability. Application to benchmark voting problems demonstrates that the proposed framework significantly reduces ordinal ambiguity and provides a defensible mathematical basis for detecting unstable rankings. This research contributes to Operations Research by transforming DEA voting from a black-box evaluator into a transparent, verifiable system suitable for high-stakes policy and collective decision-making.

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