In your example with m*, what if we have a random variable that takes values equal to 1/n, for integer n? Then maybe we measure whether n is even. Wouldn’t the probability of this would depend on m* as well as k?
For the case of a Dutch book, the problem is that wagers do not satisfy countable additivity. Maybe we could identify some subset of wagers that do and use this in a proof?
You make a lot of interesting points.
In your example with m*, what if we have a random variable that takes values equal to 1/n, for integer n? Then maybe we measure whether n is even. Wouldn’t the probability of this would depend on m* as well as k?
For the case of a Dutch book, the problem is that wagers do not satisfy countable additivity. Maybe we could identify some subset of wagers that do and use this in a proof?