“…Then for all health improvements ( w, x ) and ( y, z ) in H × H , for all positive integers m and n , and for all policies c 1 = 〈( w 1 , x 1 ), ... , ( w m , x m ), 0 m+1 , ... , 0 m+n 〉 and c 2 = 〈0 1 , ... , 0 m , ( y m+1 , z m+1 ), ... , ( y m+n , z m+n )〉 in C for which c 1 ≥ c 2 , the statements (i) and (ii) are equivalent:
The preference relation, ≥, satisfies Marginality (Definition 1) and Anonymity (Definition 2).
There exists a positive real function U on H × H such that c 1 ≥ c 2 if and only if .
With Theorem 4.1 the utility function over health state improvements takes an additive form (
Fishburn, 1965; Keeney & Raiffa, 1993). The additive form can accommodate some concerns about inequality (
Atkinson, 1970), but not all (
Bleichrodt, Crainich & Eeckhoudt, 2008). We next characterize a person tradeoff for which preference for health state improvements is represented by health state value differences, i.e.…”