A novel robust strategic manipulation model with tolerance and risk aversion behaviour
本文首次提出一个同时考虑决策者容忍行为、风险规避行为和补偿成本不确定性的鲁棒策略操纵模型，通过均值-方差理论和鲁棒优化方法，帮助管理者更有效地防御多准则决策中的策略操纵。
In the strategic manipulation process of multiple criteria decision-making (MCDM), participants often exhibit tolerance and risk aversion behaviours. These behaviours can cause actual decisions to deviate from the solution recommendations derived using existing strategic manipulation models. Concurrently, uncertainties inherent in MCDM, such as human assessment biases, are frequently inevitable. To address these research gaps, this article for the first time proposes a robust strategic manipulation model that simultaneously integrates tolerance behaviour, risk aversion behaviour, and uncertainty in compensation costs within a unified framework. Firstly, a cost-free threshold is formally defined by considering the manager’s tolerance level and its impact on the weight adjustments required to achieve strategic manipulation. Manipulation within this range requires no compensation costs from the decision maker (DM). Then, leveraging mean-variance theory, a strategic manipulation model with tolerance and risk aversion behaviour is developed. It captures the DM’s risk aversion and uses a risk coefficient to regulate the achievement of strategic manipulation objectives. Furthermore, addressing the human assessment biases concerning the mean and covariance of compensation costs in uncertain environments via robust optimisation approach, a novel robust strategic manipulation model with tolerance and risk aversion behaviour is proposed. This model is equivalently transformed into a series of computationally efficient mixed 0–1 linear programming models. Finally, the proposed strategic manipulation models are demonstrated using extensive synthetic and real-world datasets. The results indicate that: First, incorporating participants’ tolerance and risk aversion behaviours necessitates higher compensation costs from the DM, thereby enhancing the model’s defence against strategic manipulation. Second, the ordered weighted averaging operator (OWA) demonstrates superior performance in defending against strategic manipulation in MCDM problems compared to the weighted averaging operator (WA), improving model robustness. Third, the model considering both mean and covariance assessment biases simultaneously achieves optimal performance in defending against manipulation. However, this does not allow DM to arbitrarily manipulate the ranking of any alternative. Finally, variations in the mean and covariance of compensation costs exert only a minimal impact on the DM’s ability to manipulate alternative rankings, indicating they lack significant potential for defending against strategic manipulation.