Abhimanyu Pallavi Sudhir

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Political Roko's basilisk

Interesting. Did they promise to do so beforehand?

In any case, I'm not surprised the Soviets did something like this, but I guess the point is really "Why isn't this more widespread?" And also: "why does this not happen with goals other than staying in power?" E.g. why has no one tried to pass a bill that says "Roko condition AND we implement this-and-this policy". Because otherwise it seems that the stuff the Soviets did was motivated by something other than Roko's basilisk.

Political Roko's basilisk

But that's not Roko's basilisk. Whether or not you individually vote for the candidate does not affect you as long as the candidate wins.

Against improper priors

The "Dutch books" example is not restricted to improper priors. I don't have time to transform this into the language of your problem, but the basically similar two-envelopes problem can arise from the prior distribution:

f(x) = 1/4*(3/4)^n where x = 2^n (n >=0), 0 if x cannot be written in this form

Considering this as a prior on the amount of money in an envelope, the expectation of the envelope you didn't choose is always 8/7 of the envelope you did choose.

There is no actual mathematical contradiction with this sort of thing -- with prior or improper priors, thanks to the timely appearance of infinities. See here for an explanation:

https://thewindingnumber.blogspot.com/2019/12/two-envelopes-problem-beyond-bayes.html