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).
The first mistake you mention is exactly the mistake I make when I don't convert to odds form as I mentioned here.
If I start with P(Marekliberal)=1/2 and him accusing gives me 1 bit of evidence (he's twice as likely to accuse if he's liberal) then the temptation is to split the uncertainty in half and update incorrectly to P(Marekliberal|accuse|)=3/4 .
Odds form helps - 1:1 becomes 2:1 after 1 bit of evidence so P(Marekliberal|accuse|)=2/3.
More formally:
P(Marekliberal)|accuseP(Marekfascist)|accuse=P(accuse|Marekliberal)P(accuse|Marekfascist).P(Marekliberal)P(Marekfascist)=10.5.0.50.5=21
1jaek
You can improve your tex formatting by putting your text in \text{}
1jaek
You're definitely right about the 2/3rds. I guess I wrote this up too quickly.
I'm not sure if I agree with your next point. It seems like I have the equality, P(marek fascist|marek passed a fascist policy)=P(marek saw a liberal policy)+P(marek saw 3 fascists)∗P(marek fascist) Using the fact that the events are disjoint. Maybe I'm missing an easy application of Bayes though?
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 10... (read more)