[madhadron]

Conceptually you are right: all mathematical models have assumptions, including assumptions about their scope of applicability.

But you are redefining "prior" to refer to all the assumptions of the model, and not its usual meaning as the prior distribution used in Bayes calculations.

[jbay808]

Prior distribution is P(N|I), where I is the background information you have such as "historical interest rates in the USA looked like this", and "communist revolutions occurred 6 times in the 20th century" (made-up number). I is not itself the prior.

For this investing example, it's also the only information we have, unless we're trying to update on something like a central bank announcement. So our probability distribution over N is just the prior distribution.

When you're actually trying to make a decision, and not just solving a problem handed to you in math class, you can't avoid using P(N). You can either say "The minimax procedure requires knowing P(N) as an input, so that it isn't dominated by extremely improbable N", or you can say equivalently that "Minimax doesn't require P(N), but as an assumption of my model I'm ignoring all states of nature N with P(N) < y, then applying minimax regret over the remaining N".

[madhadron]

I think we must be coming from two different communities of practice where the words don't quite line up. All the operational things you are saying I agree with. I just put them under different verbal categories.