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

Last time we saw that the set of probability assignments is convex. Today we’re going to show that convex sets have a special sort of “obtuse” relationship with outsiders. Given a point outside a convex set, there is always a point in the set that forms a right-or-obtuse angle with it. Recall our 2D diagram from the first post. The convex set of interest here is the diagonal line segment from $(0,1)$ to $(1,0)$:... Read more

In this and the next two posts we’ll establish the central theorem of the accuracy framework. We’ll show that the laws of probability are specially suited to the pursuit of accuracy, measured in Brier distance. We showed this for cases with two possible outcomes, like a coin toss, way back in the first post of this series. A simple, two-dimensional diagram was all we really needed for that argument. To see how the same idea extends to any number of dimensions, we need to generalize the key ingredients of that reasoning to $n$ dimensions.... Read more

Starting in July, philosophy’s two most prestigious journals won’t reject submitted papers anymore. Instead they’ll “grade” every submission, assigning a rating on the familiar letter-grade scale (A+, A, A-, B+, B, B-, etc.). They will, in effect, become ratings agencies. They’ll still publish papers. Those rated A- or higher can be published in the journal, if the authors want. Or they can seek another venue, if they think they can do better.... Read more

Last time we took Brier distance beyond two dimensions. We showed that it’s “proper” in any finite number of dimensions. Today we’ll show that Euclidean distance is “improper” in any finite number dimensions. When I first sat down to write this post, I had in mind a straightforward generalization of our previous result for Euclidean distance in two dimensions. And I figured it would be easy to prove. Not so.... Read more

We’ve all been there. One referee is positive, the other negative, and the editor decides to reject the submission. I’ve heard it said editors tend to be conservative given the recommendations of their referees. And that jibes with my experience as an author. So is there anything to it—is “editorial gravity” a real thing? And if it is, how strong is its pull? Is there some magic function editors use to compute their decision based on the referees’ recommendations?... Read more

We looked at author gender in a previous post, today let’s consider referees. Does their gender have any predictive value? Once again our discussion only covers men and women because we don’t have the data to support a deeper analysis.1 Using data from Ergo, we’ll consider the following questions: Requests. How are requests to referee distributed between men and women? Are men more likely to be invited, for example?... Read more

Spare a thought for Reviewer 2, that much-maligned shade of academe. There’s even a hashtag dedicated to the joke: A rare glimpse of reviewer 2, seen here in their natural habitat pic.twitter.com/lpT1BVhDCX — Aidan McGlynn (@AidanMcGlynn) January 15, 2017 But is it just a joke? Order could easily matter here. Referees invited later weren’t the editor’s first choice, after all. Maybe they’re less competent, less likely to appreciate your brilliant insights as an author.... Read more

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