Rigorous formulation of dutch book arguments:

• There is some set H of possible pre-existing states of the world, and the information contained within is hidden.
• There is some set O of possible outcomes.
• An action is a function from H to O.
• A choice is a set of 2 or more actions, and an agent is a function from choices to actions within that choice. This is decision, stripped of any notion of probability or utility.

The dutch book arguments give you probability from utility. What we want to define is:

We choose a function $ from the reals to O (not the other way around, as a utility function would). This gives us a map from lotteries (functions from H to the reals) to actions (functions from H to O). $ is a valid currency if:

(We first need to note that a transitive agent must have a preference ordering)

• One always prefers a lottery that has a greater value at every state of the world to one with a lesser value.
• If X is a lottery, then $(X) is preferable to $(0), $(-X) is preferable to $(0), or they're all equally preferable.
• If X and Y are lotteries, then $(X+Y) is preferable to $(X) iff $(Y) is preferable to $(0)

You should be able to derive probabilities from any agent with a valid currency. The proof should also work if the domain of $ is only a dense subset of the reals, such as the rationals.

Every expected-utility maximizer with a sufficient variety of possible utilities has a valid currency.

So if an agent cares about wealth but has diminishing returns, the actual wealth will have increasing returns in the level of currency.