Assuming the question was known in advance, the obvious solution is for the people who care more about their grades to pay those who care less to circle A while circling B themselves. If they trust each other, they might even be able to do this after-the-fact.
The universalizing answer would be to choose A 51% of the time.
That’s why you should always have some random bits up your sleeve (memorized).
I remember being surprised that a large number of /r/rational commenters had password systems in case they ever invented time-travel or cloning. Anyone who goes to that effort can presumably also memorize 15 or so random bits if they ever need it, and refresh if used.
Time travel passwords are vulnerable to mindreading. If you want a good time travel password, you have to have an algorithm which the time-travelling version of you can calculate, but which can’t be directly read by a mindreader because if he’s reading it right now, he has no time to calculate it. For instance, I can have a time-travel password of “digits 300-310 of the square root of 3”. A time-travelling version of me would know the password, so can compute it, then can tell me the result and I can check it. A mindreader would have to read my mind before the fact or engage in some time travel himself.
Of course, it’s impossible to have a time-travel password immune to all such tricks (maybe the mindreader did read my mind a week ago), but there’s no reason to allow blatant loopholes.
That one is evil.
Assuming the question was known in advance, the obvious solution is for the people who care more about their grades to pay those who care less to circle A while circling B themselves. If they trust each other, they might even be able to do this after-the-fact.
The universalizing answer would be to choose A 51% of the time.
What was the ratio of As?
Does James Miller let his students take d% dice to his tests?
No, but if a student asked I would be tempted to give her extra credit.
That’s why you should always have some random bits up your sleeve (memorized).
I remember being surprised that a large number of /r/rational commenters had password systems in case they ever invented time-travel or cloning. Anyone who goes to that effort can presumably also memorize 15 or so random bits if they ever need it, and refresh if used.
Time travel passwords are vulnerable to mindreading. If you want a good time travel password, you have to have an algorithm which the time-travelling version of you can calculate, but which can’t be directly read by a mindreader because if he’s reading it right now, he has no time to calculate it. For instance, I can have a time-travel password of “digits 300-310 of the square root of 3”. A time-travelling version of me would know the password, so can compute it, then can tell me the result and I can check it. A mindreader would have to read my mind before the fact or engage in some time travel himself.
Of course, it’s impossible to have a time-travel password immune to all such tricks (maybe the mindreader did read my mind a week ago), but there’s no reason to allow blatant loopholes.
It was several years ago and I don’t remember.