Show a problem where non-monotonously decreasing f(N) escapes some issue. You really can choose what ever f(N) you want (subject to it summing to 1) but in the pascal’s mugging if your f(N) is sufficiently stupid (e.g. is zero everywhere except for 1 at n=3^^^3), you’ll pay the money. Non-monotonously decreasing f(N) leads to cases where claiming 1 extra person raises your probability that the claim is true. Of course, an agent can be made to act this way; an agent can be made which would pay; nobody’s proving that an agent can’t exist which would pay.
One can hypothesise a case, whereby there is some simple way of simulating the people, which produces exactly (some number of people), and then the agent that gets this claim, would be inclined to believe because the false claimant wouldn’t know the number, and then the agent would have to pay any demand. (number acting as password). That, however, is not a part of pascal’s mugging. One can also come up with universe where it is, in fact, best to pay.
Show a problem where non-monotonously decreasing f(N) escapes some issue. You really can choose what ever f(N) you want (subject to it summing to 1) but in the pascal’s mugging if your f(N) is sufficiently stupid (e.g. is zero everywhere except for 1 at n=3^^^3), you’ll pay the money. Non-monotonously decreasing f(N) leads to cases where claiming 1 extra person raises your probability that the claim is true. Of course, an agent can be made to act this way; an agent can be made which would pay; nobody’s proving that an agent can’t exist which would pay.
One can hypothesise a case, whereby there is some simple way of simulating the people, which produces exactly (some number of people), and then the agent that gets this claim, would be inclined to believe because the false claimant wouldn’t know the number, and then the agent would have to pay any demand. (number acting as password). That, however, is not a part of pascal’s mugging. One can also come up with universe where it is, in fact, best to pay.