I feel like the following game-theoretic model might be illustrative. Suppose that you have N people ordered by radicalness. These people will repeatedly vote on the proposition of killing the most radical among them (with a simple majority needed to succeed). Assume that each person's preferences are such that they would prefer to have people who are more radical than they are killed but not at the cost of being killed themselves.

This is a game of perfect information and is not hard to analyze. The result is that people will be killed until a power of 2 are left at which point the more radical half of those remaining will all vote to spare the remaining person (because if this person was killed, the same logic dictates that all of them would also end of dieing). This shows how a Schelling point can be established with no communication.