The weighted expected utility is another alternate formulation of utility
Let X={x1,p1;,..,;xn,pn}
v(x)=Sum(i=1,n,piw(xi)u(xi))/Sum(i=1,n,piw(xi)))
where w(xi)=concievability of xi. inconcievable xi => w(xi)=0
The axioms required to formulate this are:
* weak order
* continuity
* FSD
* independence: x~y=> forall a in (0,1] s.t. ax+(1-a)z~by+(1-b)z forall z
* betweenness