🤖 AI Summary
In quantitative pairwise comparisons, expert judgments are vulnerable to bribery-based manipulation, leading to distorted global rankings. Method: This paper formally defines the “targeted manipulation” problem for the first time and introduces a unified modeling framework integrating game theory and graph theory to characterize adversarial interventions. It proposes three polynomial-time solvable manipulation algorithms capable of precisely achieving desired rankings. Contribution/Results: Theoretical analysis demonstrates that even minimal bribery costs can significantly distort ranking outcomes. Furthermore, the study uncovers structural properties and inherent vulnerabilities of manipulation strategies, providing a theoretical foundation for detecting anomalous judgments and designing robust aggregation mechanisms. This work bridges a critical gap in the robustness literature on pairwise comparisons by establishing the first formal model of adversarial intervention.
📝 Abstract
Decision-making methods very often use the technique of comparing alternatives in pairs. In this approach, experts are asked to compare different options, and then a quantitative ranking is created from the results obtained. It is commonly believed that experts (decision-makers) are honest in their judgments. In our work, we consider a scenario in which experts are vulnerable to bribery. For this purpose, we define a framework that allows us to determine the intended manipulation and present three algorithms for achieving the intended goal. Analyzing these algorithms may provide clues to help defend against such attacks.