Consider the case of 2 blue eyed people, Ben and Betty. Everybody knows there is at least one blue eyed person. But does everybody know that? That is, does ever

Consider the case of 2 blue eyed people, Ben and Betty. Everybody knows there is at least one blue eyed person. But does everybody know that? That is, does everybody know that (everybody knows there is one blue eyed person)? From Ben's perspective, Betty might be the only blue-eyed person, so Ben does not know if Betty knows there is at least one blue eyed person. This is important because Ben needs to correlate Betty's actions with her knowledge; he can't do that if he doesn't know what her knowledge is. After the traveler's announcement, Ben knows that Betty knows there is at least one blue eyed person. This is the new information. And with three people, we add another layer: Ben does not know if Betty knows that Bobby has blue eyes. And so on. The visitor's announcement is special because it is infinitely layered. Everyone knows one person has blue eyes, and everyone knows that everyone knows, and so on, ad infinitum. This is called common knowledge: https://en.wikipedia.org/wiki/Common_knowledge_(logic) https://en.wikipedia.org/wiki/Common_knowledge_(logic)). Though to be fair, this isn't explicitly stated: the traveler "addresses the entire tribe" but it's critical that everyone in the tribe knows this is common knowledge. Merely addressing the entire tribe is not enough: if the traveler's announcement was in the form of a BCC mass mailing, there would be no new information and so no suicides.