Oops, turns out I did misremember—Savage does not in fact put the proof in his book. You have to go to Fishburn’s book.
I’ve been reviewing all this recently and yeah—for anyone else who wants to get into this, I’d reccommend getting Fishburn’s book (“Utility Theory for Decision Making”) in addition to Savage’s “Foundations of Statistics”. Because in addition to the above, what I’d also forgotten is that Savage leaves out a bunch of the proofs. It’s really annoying. Thankfully in Fishburn’s treatment he went and actually elaborated all the proofs that Savage thought it OK to skip over...
(Also, stating the obvious, but get the second edition of “Foundations of Statistics”, as it fixes some mistakes. You probably don’t want just Fishburn’s book, it’s fairly hard to read by itself.)
Oops, turns out I did misremember—Savage does not in fact put the proof in his book. You have to go to Fishburn’s book.
I’ve been reviewing all this recently and yeah—for anyone else who wants to get into this, I’d reccommend getting Fishburn’s book (“Utility Theory for Decision Making”) in addition to Savage’s “Foundations of Statistics”. Because in addition to the above, what I’d also forgotten is that Savage leaves out a bunch of the proofs. It’s really annoying. Thankfully in Fishburn’s treatment he went and actually elaborated all the proofs that Savage thought it OK to skip over...
(Also, stating the obvious, but get the second edition of “Foundations of Statistics”, as it fixes some mistakes. You probably don’t want just Fishburn’s book, it’s fairly hard to read by itself.)