# The Savage sure thing principle and Subjective utility representation

I have tried reading and understanding Savage's proof of the subjective utility representation, it is too complicated. Is anyone aware of a shorter/more elegant proof of this? It is not a problem if we assume a finite prices set.

The original is in Savage, L.J. 1954. The Foundations of Statistics. New York: John Wiley and Sons.

A good summary can be found at http://www.econ2.jhu.edu/people/Karni/savageseu.pdf.

The Savage proof is known to be very elaborate, and long. It uses the sure thing principle as its main axiom. I was wondering if there is a more "modern" proof, that is both elegant and shorter. Or a nice challenge would be to try to prove collaboratively using some modern mathematics, like mixture spaces, (I am aware of Anscombe-Aumann).

• Hi! Could you maybe provide a link or reference to the paper in which the original proof is found? – jmbejara Dec 3 '14 at 14:56
• 1) What is the "Almost Sure principle". Did you mean "Sure thing" principle ? 2) The title points to a specific segment of Savage's theory, while in the question you ask of an exposition of the whole. Please clarify. – Alecos Papadopoulos Dec 4 '14 at 11:15
• Yeah. Are you referring to a proof of the "Savage's Theorem" that is mentioned in the paper ("Savagesâ€™ Subjective Expected Utility Model," by Edi Karni) in the link? econ2.jhu.edu/people/Karni/savageseu.pdf – jmbejara Dec 5 '14 at 20:25
• (+1) for the first bounty in Economics.SE (and related to a worthy subject, too). – Alecos Papadopoulos Dec 5 '14 at 23:09
• I don't have access to it, but supposedly there's a brief (read: two chapters) sketch of the proof in Kreps' "Notes on the Theory of Choice". – jayk Dec 6 '14 at 3:03