The whole premise of this paper about Buridan's ass principle is wrong. That is to say, its assumption of continuity. A simple strategy of "always go to the right after you haven't made a firm decision after X time" leads to a discontinuous function, violating their assumption. It is trivially possible for strategies to lead to discontinuous decision functions, undermining the whole idea.
The author tries to report that "you aren't sure if you've decided or not after X time", but doesn't go very deeply into it, and clings to the assumption of continuity. In fact, one can always be sure whether they've made a FIRM decision or not by a certain time, in the same way the author has X_t(1) = 1 for all t.
The whole premise of this paper about Buridan's ass principle is wrong. That is to say, its assumption of continuity. A simple strategy of "always go to the right after you haven't made a firm decision after X time" leads to a discontinuous function, violating their assumption. It is trivially possible for strategies to lead to discontinuous decision functions, undermining the whole idea.
The author tries to report that "you aren't sure if you've decided or not after X time", but doesn't go very deeply into it, and clings to the assumption of continuity. In fact, one can always be sure whether they've made a FIRM decision or not by a certain time, in the same way the author has X_t(1) = 1 for all t.