Fine-grained view on bribery for group identification

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