This mixes in an expected value and a (-log) probability concept. Was that intentional? I know, I probably shouldnât ask. And I guess Patrick sort of started it.

I edited my first post responding to yours because I originally referred to something similar to Patrick: the Dutch book argument, which says you should construct your subjective probabilities so that they satisfy the probability axioms. Under than constraint, I think it is a consequence that in a series of hands of a game of chance, you should align your probabilities (and bets) to the overall probabilities of each hand.

But if there is just one trial, then that argument would not apply. Thatâs where the principal principle comes in.

Still, if we use âsurpriseâ to refer to a personal feeling, you can certainly violate that by your personal feeling of surprise. I think you are saying that your personal feeling of surprise is a step function, not something continuous as is -log p.

But then using âsurpriseâ in that way for Shannonâs work is the same as using âinformationâ in its colloquial sense in the context of that work. Thatâs why surprisal is a better term. Like âentropyâ, its not so easy to anthropomorphize.

Too bad von Nuemann didnât think of that word. too. You might of thought he would have. After, he was a calculating machine!.