The finite states argument feels kind of wrong. You're usually interested in the general behavior for n people, and the number of states is exponential in n, wh

The finite states argument feels kind of wrong. You're usually interested in the general behavior for n people, and the number of states is exponential in n, which means that you need time exponential in n to repeat yourself. What you're seeing here is the early behavior of the system. Your arguments is a bit like saying every computer is actually a finite state machine, because of the finite memory it's going to repeat itself eventually. The argument is fundamentally flawed because you inflated one part of the question (time of running the question) while keeping the more significant part (number of particiants) fixed.