Vladimir_Nesov comments on [missing post]

[Vladimir_Nesov]

Let’s apply Bayes formula in odds form to this example.$$\frac{P\left(x|D\right)}{P\left(y|D\right)}=\frac{P\left(x\right)}{P\left(y\right)}\times \frac{P\left(D|x\right)}{P\left(D|y\right)}$$ Let $x$ = “Xavier won the lottery”, $y=\neg x$, $D$ = “Yovanni says Xavier won the lottery”. We have $P\left(x\right)/P\left(y\right)\approx 1/1000000$ (for simplicity, let’s assume that Xavier couldn’t be someone who didn’t even enter the lottery), $P\left(D|x\right)\approx 1$. What is $P\left(D|y\right)$? Given that someone other than Xavier won the lottery, what is the probability that Yovanni would claim that it was Xavier in particular who did? While Yovanni might have a reason to single out Xavier, Zenia doesn’t, so from the hypothesis $y$ they would predict that anyone could be wrongly named the winner, which gives picking Xavier one in a million chance (also, the Yovanni within the hypothesis $y$ won’t pay attention to $y$ in particular, so can’t anchor to Xavier based on that). Then, Yovanni must make a mistake or decide to lie, with probability of, say, 1%. In total, we have $P\left(D|y\right)\approx 1/(1000000\cdot 100)$. Putting this in the formula, we get $P\left(x|D\right)/P\left(y|D\right)\approx 100$, so Xavier is probably the winner after all.

(This is the same as Phil’s answer, formulated a little bit differently.)