Microbribery in Group Identification

This paper studies the complexity of two microbribery problems under the model of group identification. In these problems, we are given a subset of distinguished individuals, and the questions are whether these individuals can be made socially qualified or whether they can be made exactly the socially qualified individuals, respectively, by modifying a limited number of entries in the qualificationsprofile. For consent rules, the consensus-start-respecting rule, and the liberal-start-respecting rule, we obtain many NP-hardness results as well as polynomial-time solvability results. We also study the problems in 𝑟-profiles where each individual qualifies exactly 𝑟 individuals.