Savage's model is built from the following tools. * S= states of the world * X= set of consequences * A=2^S = algebra * F=set of all acts f:S->X * "=>" a binary relation on f There are a set of 7 axioms: * P1 * P2 * P3 * P4 * P5 * P6 * P7 Step 1: Proposition: P1-5 => "=>*" is a qualitative probability Proposition: P1-6 => "=>*" is a qualitative probability and satisfies partition axiom 2. corollary: P1-6 => there exists p, a probability charge on (S,A) s.t. * forall B,C in A B"=>*"C <=> p(B)=>p(C) * forall B in A forall rin [0,1] there exists C subset of B s.t. p(B)=rP(A) with P unique. Step 2: get the result for finite acts. Let Pf = distribution on a finite X induced by f. Proposition: P1-6 /\ f,g in Fs s.t. Pf=Pg => f~g Step 3: representation. Proposition: given P1-6, "=>" on Ps satisfies J1,J2,J3 => there exists U:X->R s.t. p"=>"q <=> Sum(P(x)u(x))=>Sum(q(x)u(x)) step 4: Extend result to t~ by defining integral. Theorem: "=>" satisfies P1-P7 <=> there exists P a probability charge on (S,A) which is convex randed /\ there exists u:X->R bounded and nonconstant s.t. f"=>"g <=> Integral(u(f(s))dP(s))=>Integral(u(g(s))dP(s))