The goal of this paper is to analyze the complexity of constructive/destructive bribery and destructive control in the framework of group identification. Group identification applies to situations where a group of individuals determine who among them are socially qualified. We consider consent rules, the consensus-start-respecting rule, and the liberal-start-respecting rule. Each consent rule is characterized by two positive integers s and t, and the socially qualified individuals are determined as follows. If an individual qualifies herself, then she is socially qualified if and only if there are in total at least s individuals qualifying her. Otherwise, she is NOT socially qualified if and only if there are in total at least t individuals disqualifying her. The liberal (resp. consensus)-start-respecting rule determines the socially qualified individuals recursively. In the first step, all individuals qualifying themselves (resp. qualified by all individuals) are socially qualified. Then, the procedure recursively adds individuals who are not socially qualified but are qualified by at least one socially qualified individual into the set of socially qualified individuals until no one can be added this way.

中文翻译：

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贿赂和控制在群体识别中的复杂性

本文的目的是在群体识别的框架下分析建设性/破坏性贿赂和破坏性控制的复杂性。群体识别适用于一群人确定其中谁具有社会资格的情况。我们考虑同意规则，尊重共识开始的规则和尊重自由开始的规则。每个同意规则都以两个正整数s和 t为特征 ，并且具有社会资格的个人如下确定。如果是个人素质要求自己，那么她是社会资格当且仅当总共有至少 小号个人资格赛她。否则，当且仅当总数至少 t个人取消她的参赛资格。自由（尊重共识）开始-尊重规则以递归方式确定了具有社会资格的个人。在第一步中，所有符合条件的个人（由所有个人重新限定）都具有社会资格。然后，该过程将没有社会资格但至少有一个社会资格的人有资格的个人递归添加到社会资格的人的集合中，直到无法以这种方式添加任何人为止。