Ryan Richt writes:
I wondered if you have a quick moment to dig up an old post of your own that I cannot find by searching. I read an entry where you discussed if there really was a difference between a prior of 1/2 meaning that we have no knowledge of a coin flip, or meaning we are exactly certain that it’s generative distribution is 1/2.
I’m only 24 and just got my masters last year, but I now have my own summer interns (who of course I encourage to read ET Jaynes and see the bayesian light) and one of them basically asked that question today.
My reply: The two original blog entries are here and here. Here’s my published article. And here‘s a link discussing actual wrestlers and boxers. (Apparently the wrestler would win.)
My own way of understanding the distinction between coin tosses and "boxer vs. wrestler" situations relies on de Finetti's theorem. Admittedly there's no exchangeable set of realizations in the boxer vs. wrestler setup, but the integral representation makes the distinction between coin tosses and "uncertain" probabilities very clear. Other commenters to the previous posts have made similar points, but I don't think anyone has brought up de Finetti's theorem yet.
Jaynes discusses this near the end of the published version of PT:LOS; it's not in the online pre-publication version.