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Majority illusion occurs in a social network when the majority of the network vertices belong to a certain type but the majority of each vertex's neighbours belong to a different type, therefore creating the wrong perception, i.e., the illusion, that the majority type is different from the actual one. From a system engineering point of view, this motivates the search for algorithms to detect and, where possible, correct this undesirable phenomenon. In this paper we initiate the computational study of majority illusion in social networks, providing NP-hardness and parametrised complexity results for its occurrence and elimination.