Create a subrule to rule 2.11 Doomsday Cult, called “Misinformation”:

As a weekly action, a Cultist may send a PM to the Leader containing the name of a single Survivor and whether or not they want that survivor to appear as a cultist or a non-cultist. When the leader makes that week’s Investigation Results post per rule 2.11.3 Locating the Cult, he must also include the name of the mentioned survivor(s), and state whether they are a cultist or not, taking into account the potentially incorrect information due to Misinformation. It should not be possible for another Survivor to be able to discern between the correct and incorrect results.
If there are more Misinformation results than genuine results, the Leader must randomly select Misinformation results, and discard them. He must also do this if there are the same number of each type of result, unless there are only 1 of each (I.E. The results post must have less misinformation than fact, unless there is only one of each).
If a Survivor was genuinely investigated, then the Leader must not post any Misinformation about that survivor for the week they were investigated.

Remove the following text from Locating the Cult: “; one of those notations (chosen at random by the Leader) must be correct, and for each of the others the Leader must make it correct with a 60% chance, and incorrect with a 40% chance”.