Fine-Grained View on Bribery for Group Identification

TL;DR

This paper explores the computational complexity of bribery in group identification, analyzing how changing agents' qualifications affects social qualification outcomes under various rules and costs.

Contribution

It provides a comprehensive parameterized complexity analysis of bribery problems in group identification, including new cost models and combined bribery goals.

Findings

Complexity landscape varies with different social rules and parameters.

New models for bribery costs and combined goals are introduced.

Results include polynomial-time and NP-hard cases depending on settings.

Abstract

Given a set of agents qualifying or disqualifying each other, group identification is the task of identifying a socially qualified subgroup of agents. Social qualification depends on the specific rule used to aggregate individual qualifications. The classical bribery problem in this context asks how many agents need to change their qualifications in order to change the outcome in a certain way. Complementing previous results showing polynomial-time solvability or NP-hardness of bribery for various social rules in the constructive (aiming at making specific agents socially qualified) or destructive (aiming at making specific agents socially disqualified) setting, we provide a comprehensive picture of the parameterized computational complexity landscape. Conceptually, we also consider a more fine-grained concept of bribery cost, where we ask how many single qualifications need to be changed, nonunit prices for different bribery actions, and a more general bribery goal that combines the constructive and destructive setting.