On neutrality of preferences on acts with respect to use of proxy outcomes

Construing acts as functions on a set of states to the set of lotteries on ultimate outcomes, this partly expository paper cautions that, in non-Savage choice theories, the popular technique of replacing multiattributed ultimate outcomes by equally desirable and crisper proxies may misguide the choice of act, in that preferences between the induced proxy acts may not mirror preferences between their original counterparts. When this pathology cannot occur, preferences and the associated choice theory are said to be neutral as regards proxy substitution. Sufficient conditions for neutrality include Monotone Dominance, Transitivity, and a restricted form of Linearity. The Linearity property can be circumvented by direct assignment of proxy ‘certainty equivalents’ to outcome lotteries rather than to ultimate outcomes; then preferences are said to be semineutral if the corresponding proxy acts mirror preferences between their original counterparts. Relationships of these problem transformations are noted and certain normative choice theories are examined as to neutrality of preference with respect to use of arbitrary proxies.