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Manipulation of individual judgments in the quantitative pairwise comparisons method

M. Strada, K. Kułakowski

TL;DR

The paper addresses manipulation of decision outcomes produced by quantitative pairwise comparison methods (AHP) via micro-bribery, formalizing attacker roles and inconsistency constraints. It introduces two heuristic attack algorithms—Row and Matrix—that aim to promote a target alternative by altering as few pairwise judgments as possible while keeping the overall inconsistency below a threshold. Through Monte Carlo experiments, the Matrix algorithm generally achieves higher success rates and lower final inconsistency than the Row algorithm, especially as matrix size grows or the target alternatives are more distant in ranking. The study discusses detection challenges, suggesting that restricting access to experts and monitoring interaction patterns are practical defenses, and highlights the need for future work on algorithmic manipulation detection. The work contributes a concrete framework for assessing manipulation risk in PC-based decision processes and informs defense strategies against micro-bribery attacks.

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.

Manipulation of individual judgments in the quantitative pairwise comparisons method

TL;DR

The paper addresses manipulation of decision outcomes produced by quantitative pairwise comparison methods (AHP) via micro-bribery, formalizing attacker roles and inconsistency constraints. It introduces two heuristic attack algorithms—Row and Matrix—that aim to promote a target alternative by altering as few pairwise judgments as possible while keeping the overall inconsistency below a threshold. Through Monte Carlo experiments, the Matrix algorithm generally achieves higher success rates and lower final inconsistency than the Row algorithm, especially as matrix size grows or the target alternatives are more distant in ranking. The study discusses detection challenges, suggesting that restricting access to experts and monitoring interaction patterns are practical defenses, and highlights the need for future work on algorithmic manipulation detection. The work contributes a concrete framework for assessing manipulation risk in PC-based decision processes and informs defense strategies against micro-bribery attacks.

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.
Paper Structure (13 sections, 35 equations, 7 figures, 3 algorithms)

This paper contains 13 sections, 35 equations, 7 figures, 3 algorithms.

Table of Contents

  1. Introduction
  2. Problem statement
  3. Models of manipulation
  4. From electoral systems to decision-making methods
  5. Algorithms of manipulation
  6. Pairwise comparisons
  7. Decision model
  8. Row algorithm
  9. Matrix algorithm
  10. Construction of two algorithms - a comparison
  11. Monte Carlo experiments
  12. Discussion
  13. Summary

Figures (7)

  • Figure 1: Different types of decision data manipulations
  • Figure 2: Success rate for manipulation algorithms with different size of PC matrices and different preferential distance $\Delta_{pq}$.
  • Figure 3: Success rate for $7\times7$ random PC matrices and different $\varDelta_{pq}$.
  • Figure 4: Number of matrix elements changed using different priority deriving methods: EVM and GMM.
  • Figure 5: Comparison of different inconsistency index gathering methods for $7\times7$ random PC matrices
  • ...and 2 more figures