Nice—I hadn’t gotten so far as analyzing the other tiebreak policy.
“Prior information” in this kind of problem includes a bunch of rather unlikely assumptions, such as that every player is maximally rational and that the rules of the game reward picking the true choice of urn.
Unfortunately there is no reason to prefer one tiebreak policy over the other. Does it make the problem more determinate if we assume the game scores per Bayesian Truth Serum, that is, you get more points for a contrarian choice that happens to be right ?
Since the total evidence you can get from examining all previous guesses (assuming conventional strategy and rewards as before) gives you only a 4⁄5 accuracy, and you can get 2⁄3 by ignoring all previous guesses and looking only at your own draw: Yes, rewarding correct contrarians at least 20% more than correct majoritarians would provide enough incentive to break the information cascade. Only until you’ve accumulated enough extra information to make the majoritarian answer confident enough to overcome the difference between rewards, of course, but it would still equilibrate at a higher accuracy.
Nice—I hadn’t gotten so far as analyzing the other tiebreak policy.
“Prior information” in this kind of problem includes a bunch of rather unlikely assumptions, such as that every player is maximally rational and that the rules of the game reward picking the true choice of urn.
Unfortunately there is no reason to prefer one tiebreak policy over the other. Does it make the problem more determinate if we assume the game scores per Bayesian Truth Serum, that is, you get more points for a contrarian choice that happens to be right ?
Since the total evidence you can get from examining all previous guesses (assuming conventional strategy and rewards as before) gives you only a 4⁄5 accuracy, and you can get 2⁄3 by ignoring all previous guesses and looking only at your own draw: Yes, rewarding correct contrarians at least 20% more than correct majoritarians would provide enough incentive to break the information cascade. Only until you’ve accumulated enough extra information to make the majoritarian answer confident enough to overcome the difference between rewards, of course, but it would still equilibrate at a higher accuracy.