Mark Tuttle points to an article from 1955, “Fair Bets and Predictive Probabilities,” by John Kemeny. Tuttle writes:

I assume that this paper is near and dear to your heart. At the time, during the “Bayesian” wars, I’m guessing it was novel, relatively.

Per the conclusion of your recent post, Gambling is fun but it can ruin addicts, are you “wary” of this paper, in 1955 at least . . . ?

My response: I’ve never read this particular article before, but to my eyes in 2022, it seems like piles and piles of math, to prove something that I already know is true!

Now, I know what you’re gonna say: it’s only obvious to me now because this dude went to the trouble of proving it, back in 1955. For me to criticize this article for being obvious and overkill would be like hating on Beethoven’s Fifth for being nothing but one musical cliche after another.

But I don’t think so. I think it’s more of a language thing, or a style thing. I think the Neumann/Morgenstern utility theorem is both beautiful and important; I enjoyed Luce and Raiffa; and I like a lot of other decision theory literature. I still think the theorems in this Kemeny paper are trivial, and I’m not a fan of the way the article is written. But, again, that’s a style thing. If you could bring Kemeny back to life today and force him to read the collected works of me, I daresay he’d be disgusted that I wrote ten thousand blog posts and managed to say so little. Why not focus a bit, he’d say, and just publish some theorems??? And maybe he’d be right, who’s to say.

Here’s another way of looking at it: Modern-day statistics research has tons of computing for each bit of statistical insight. It’s just the way things go: if you have an idea, you evaluate it on a lot of examples. Back in the day, they didn’t have cheap computing cycles so they did lots of math.