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Sniffnoy comments on Terminology suggestion: Say "degrees utility" instead of "utils" to prompt affine thinking - Less Wrong
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Yes, but "we want to use calculus to solve this" isn't a very natural constraint on the set of orderings. :) It's a "we want to make the math easier" constraint, not a "we have reason to believe that any rational agent should act this way" constraint.
Not that it's necessarily inappropriate in the example you give -- it probably makes sense there. Just a bit surprising that UDT would restrict itself in such a way.
In the UDT case, the set of outcomes is finite (well, or at least the set of equivalence classes of outcomes under the preference relation is finite) and the utility functions don't have any particular properties, so every possible preference relation the model can treat at all can be represented by a utility function!
(I should note that this is not UDT as such we're talking about here, but one particular formal way of implementing some of the ideas of UDT.)
Oh, OK then!