Comparisons across individuals MWG Proposition 6.C 2: Given two utility function uI( and u2(, the following statements are equivalent (1rA(x,u2>rA(r, un for every X (2) there exists an increasing concave function y(such that u2(=y(u( i.e. u2 ( is a concave transformation of (3c(F,u2)<c(F,un for any FO (4)T(, u2)> T ,E,un for any x and s (5)whenever u2(.) finds a lottery F(at least as good as a riskless outcome, x, then ui( also finds that lottery at least as good as the riskless outcomeComparisons across individuals MWG Proposition 6.C.2: Given two utility function u1. and u2., the following statements are equivalent: (1) rAx,u2  rAx, u1 for every x (2) there exists an increasing concave function . such that u2.  u1., i.e. u2. is a concave transformation of u1. (3) cF,u2  cF,u1 for any F(.) (4) x, ,u2  x, , u1 for any x and  (5) whenever u2. finds a lottery F(.) at least as good as a riskless outcome, x, then u1. also finds that lottery at least as good as the riskless outcome