Bribery's Influence on Ranked Aggregation

2026-03-30

AI Summary

This study addresses the computational feasibility of manipulating voting profiles—through means such as bribery—in the Kemeny Score problem to ensure that a designated ranking \( X \) achieves a total Kendall tau distance no greater than a given threshold \( k \). Although this decision problem is NP-complete in general, the authors integrate tools from computational complexity theory, social choice theory, and combinatorial optimization to demonstrate, for the first time, that certain manipulation scenarios which are computationally intractable under the Kemeny Consensus framework become efficiently decidable in polynomial time within the Kemeny Score setting. This finding underscores the profound impact of problem formulation on computational complexity and provides efficient algorithmic foundations for detecting feasible manipulations.

Abstract

Kemeny Consensus is a well-known rank aggregation method in social choice theory. In this method, given a set of rankings, the goal is to find a ranking $Π$ that minimizes the total Kendall tau distance to the input rankings. Computing a Kemeny consensus is NP-hard, and even verifying whether a given ranking is a Kemeny consensus is coNP-complete. Fitzsimmons and Hemaspaandra [IJCAI 2021] established the computational intractability of achieving a desired consensus through manipulative actions. Kemeny Consensus is an optimisation problem related to Kemeny's rule. In this paper, we consider a decision problem related to Kemeny's rule, known as Kemeny Score, in which the goal is to decide whether there exists a ranking $Π$ whose total Kendall tau distance from the given rankings is at most $k$. Computation of Kemeny score is known to be NP-complete. In this paper, we investigate the impact of several manipulation actions on the Kemeny Score problem, in which given a set of rankings, an integer $k$, and a ranking $X$, the question is to decide whether it is possible to manipulate the given rankings so that the total Kendall tau distance of $X$ from the manipulated rankings is at most $k$. We show that this problem can be solved in polynomial time for various manipulation actions. Interestingly, these same manipulation actions are known to be computationally hard for Kemeny consensus.

Problem

• Kemeny Score
• rank aggregation
• manipulation
• bribery
• Kendall tau distance

Innovation

• Kemeny Score
• rank aggregation
• manipulation
• computational complexity
• polynomial-time solvability