Also, I think isomorphism should also be complete, not just partially true, you can’t map yourself to only one model, you need to map yourself to all models out there. If you have two clones, you need to map yourself to both, you should not consider (true but partial) isomorphism that maps only to one clone.
e.g.
There are two independent predictors who predict what would you pick in Rock Paper Scissors, each puts money on some symbol and debt notes on symbol it beats, of the same amount of money. When you pick a symbol you get the money from symbol it beats, but have to pay the debt from your chosen symbol.
(basically additive Rock Paper Scissors against multiple opponents at the same time)
Additionally, first predictor P1 is (4/10, 3⁄10, 3⁄10), and second predictor P2 is (6/10, 2⁄10, 2⁄10), on win-draw-loss. They place $10 bet each. What amount of money you would have to be paid to play this game?
Isomorphism that maps you only to the model of P1 gets you more expected value than isomorphism that maps you to P2′s model or both models.
Also, I think isomorphism should also be complete, not just partially true, you can’t map yourself to only one model, you need to map yourself to all models out there. If you have two clones, you need to map yourself to both, you should not consider (true but partial) isomorphism that maps only to one clone.
e.g.
There are two independent predictors who predict what would you pick in Rock Paper Scissors, each puts money on some symbol and debt notes on symbol it beats, of the same amount of money. When you pick a symbol you get the money from symbol it beats, but have to pay the debt from your chosen symbol.
(basically additive Rock Paper Scissors against multiple opponents at the same time)
Additionally, first predictor P1 is (4/10, 3⁄10, 3⁄10), and second predictor P2 is (6/10, 2⁄10, 2⁄10), on win-draw-loss. They place $10 bet each. What amount of money you would have to be paid to play this game?
Isomorphism that maps you only to the model of P1 gets you more expected value than isomorphism that maps you to P2′s model or both models.
Phi(P1) > Phi(P2) > Phi(P1, P2)
Misleadingly.
You’re right. I focused too much on the pragmatic aspect, and didn’t include all the formalisms. I’ll have to redo this properly.
Thanks!