Scale or Translation Invariant Additive Preferences
A self-contained proof is presented of the fact that any increasing, continuous preferences over contingent payoffs that admit a (possibly state-dependent) additive representation are scale (resp. translation) invariant if and only if they take the form of CRRA (resp. CARA) expected utility, with the probabilities and coefficient of risk aversion uniquely determined as part of the representation. Thus scale or translation invariance allows a significant simplification of the ordinal foundations of subjective expected utility.
Skiadas, Constantinos. 2016. Scale or Translation Invariant Additive Preferences.