P(accuse)=37.5% because if I am liberal I only accuse Sam if he is fascist (50% of the time) and if I am fascist I accuse only when I am bold and Sam is liberal (25% of the time).
Imagine 100 games are played. Sam gets accused in 37.5 games. Marek is liberal in 25 of those games.
I had a belief that Marek was Fascist with probability about 50% but I should have already updated to ~88% that he was a fascist as opposed to an unlucky liberal (100% of the time he didn't draw 3 fascist articles he buried a liberal and is a fascist and half the rest of the time he's a fascist by my prior).
Using Bayes' theorem and 23% as the probability of drawing 3 fascist policies, I got 81.3% (and not 88%) as the accurate probability that Marek is fascist.
Another thing to consider is that fascists sometimes intentionally pass a liberal policy to confuse others. This is especially true of Hitler who wants to appear liberal so that he can later be elected chancellor.
I agree with the qualitative analysis and the conclusion but I got different answers when I did the same calculations.
I think the correct probability here is 2/3, not 75%.
P(accuse)=37.5% because if I am liberal I only accuse Sam if he is fascist (50% of the time) and if I am fascist I accuse only when I am bold and Sam is liberal (25% of the time).
Imagine 100 games are played. Sam gets accused in 37.5 games. Marek is liberal in 25 of those games.
Using Bayes' theorem and 23% as the probability of drawing 3 fascist policies, I got 81.3% (and not 88%) as the accurate probability that Marek is fascist.