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In the Group Identification problem, we are given a set of individuals andare asked to identify a socially qualified subset among them. Each individualin the set has an opinion about who should be considered socially qualified.There are several different rules that can be used to determine the sociallyqualified subset based on these mutual opinions. In a manipulative attack, anoutsider attempts to exploit the way the used rule works, with the goal ofchanging the outcome of the selection process to their liking.  In recent years, the complexity of group control and bribery basedmanipulative attacks in Group Identification has been the subject of intenseresearch. However, the picture is far from complete, and there remain many openquestions related to what exactly makes certain problems hard, or certain rulesimmune to some attacks.  Supplementing previous results, we examine the complexity of groupmicrobribery on so-called protective problem instances; that is, instanceswhere all individuals from the constructive target set are already sociallyqualified initially. In addition, we study a relaxed variant of group controlby deleting individuals for the consent rules, the consensus-start-respectingrule, and the liberal-start-respecting rule. Based on existing literature, wealso formalize three new social rules of the iterative consensus type, and weprovide a comprehensive complexity-theoretic analysis of group control andbribery problems for these rules.

Broadening the Complexity-theoretic Analysis of Manipulative Attacks in Group Identification