rank dependent expected utility is another alternative formulation of utility.

Order X as x1<=x2<=...<=xn

v(x)=Sum(i=1,n,u(xi)w(p1,...,pi))

Where w(p1,...,pi)=g(Sum(j=1,i,pj))-g(Sum(j=1,i-1,pj))

with g(0)=0 g(1)=1 g monotonic and g(p0)=0