One of my favourite probability puzzles to teach is a close cousin of the Monty Hall problem. Originally from a 1965 book by Frederick Mosteller,1 here’s my formulation: Three prisoners, A, B, and C, are condemned to die in the morning. But the king decides in the night to pardon one of them. He makes his choice at random and communicates it to the guard, who is sworn to secrecy.... Read more
In our last two posts we established two key facts: The set of possible probability assignments is convex. Convex sets are “obtuse”. Given a point outside a convex set, there’s a point inside that forms a right-or-obtuse angle with any third point in the set. Today we’re putting them together to get the central result of the accuracy framework, the Brier dominance theorem. We’ll show that a non-probabilistic credence assignment is always “Brier dominated” by some probabilistic one.... Read more
Update: editors at CJP and Phil Quarterly have kindly shared some important, additional information. See the edit below for details. A new paper on the representation of women in philosophy journals prompted some debate in the philosophy blogosphere last week. The paper found women to be underrepresented across a range of prominent journals, yet overrepresented in the two journals studied where review was non-anonymous. Commenters over at Daily Nous complained about the lack of base-rate data.... Read more
I'm an Associate Professor of Philosophy at the University of Toronto. I research uncertainty in human reasoning. I also indulge in some programming and related nerdery.