"Like the prediction market of whether the dead will return, where you noticed exactly that kind of suspicious activity. Anyway, if you control the Keepers and the legislators you can declare things like that you're going to screen off all of history! I find it hard to believe you couldn't also declare things like that you need to launch a massive secret project almost no one is told about, or remove all works of fiction that might enable someone to learn the gods are real and contact them, or that you need to invent and refine talk-control, or that you need to make a bunch of specific people who are criticizing you decide to freeze themselves.
As far as I can tell, any high-rank Keeper can go to the home of a critic who is particularly troubling to them and in two minutes of conversation convince that person to commit suicide. That is sufficient power to cover up a lot without manipulating prediction markets, even setting aside how you can use it to manipulate prediction markets in a way that's not very obvious."