Yes, you’re missing something, but it’s not what you think.
Actual humans do not conform to the VNM axioms. You correctly point out one serious problem with axiom 1 (completeness); there are also serious problems with axiom 3 (continuity) and axiom 4 (independence). (It also happens to be an empirical fact that many humans violate axiom 2 (transitivity), but there’s much less reason to believe that such violations are anything but irrational, by any reasonable standard of rationality.)
Oskar Morgenstern himself regarded the VNM theorem as an interesting mathematical result with little practical application in the real world, much less application to actual humans. This is also my own view, and that of others I’ve spoken to. It is, in any case, not at all obvious that conformance to the axioms is mandatory for any rational agent (as is sometimes claimed).
The assumption which I advise you to discard is that the VNM theorem is either descriptive of real (or realistic) agents, or that it’s prescriptive for “rational” agents. It is neither; rather, it’s a precise mathematical result, and no more. Anything more we make of it requires importing additional assumptions, which the theorem certainly does not dictate.
Downvoting, because it is prescriptive, and the comment doesn’t even bother to argue why it wouldn’t be. VNM utility generalizes both the Dutch Book arguments and deterministic utility, and similar arguments apply.
My comment was intended to be informative, not to offer a proof of anything. The idea that one has to argue for everything one says in all comments is, frankly, bizarre. (If you disagree, fair enough, you can challenge my statement and ask for support, etc., but “you didn’t argue for [thing X which you said]” is a very strange objection in this case.)
Dutch Book arguments
If you’re familiar with Dutch Book arguments, then no doubt you’re also familiar with all the reasons why Dutch Book arguments fail to apply in the real world except in certain specific circumstances, and with the non-trivial assumptions that are required in order for the arguments to carry forth.
deterministic utility
I’m not sure I get this reference. Mind giving a link, at least to point to the sort of thing you have in mind?
Yes, you’re missing something, but it’s not what you think.
Actual humans do not conform to the VNM axioms. You correctly point out one serious problem with axiom 1 (completeness); there are also serious problems with axiom 3 (continuity) and axiom 4 (independence). (It also happens to be an empirical fact that many humans violate axiom 2 (transitivity), but there’s much less reason to believe that such violations are anything but irrational, by any reasonable standard of rationality.)
Oskar Morgenstern himself regarded the VNM theorem as an interesting mathematical result with little practical application in the real world, much less application to actual humans. This is also my own view, and that of others I’ve spoken to. It is, in any case, not at all obvious that conformance to the axioms is mandatory for any rational agent (as is sometimes claimed).
The assumption which I advise you to discard is that the VNM theorem is either descriptive of real (or realistic) agents, or that it’s prescriptive for “rational” agents. It is neither; rather, it’s a precise mathematical result, and no more. Anything more we make of it requires importing additional assumptions, which the theorem certainly does not dictate.
Downvoting, because it is prescriptive, and the comment doesn’t even bother to argue why it wouldn’t be. VNM utility generalizes both the Dutch Book arguments and deterministic utility, and similar arguments apply.
Why would it be?
My comment was intended to be informative, not to offer a proof of anything. The idea that one has to argue for everything one says in all comments is, frankly, bizarre. (If you disagree, fair enough, you can challenge my statement and ask for support, etc., but “you didn’t argue for [thing X which you said]” is a very strange objection in this case.)
If you’re familiar with Dutch Book arguments, then no doubt you’re also familiar with all the reasons why Dutch Book arguments fail to apply in the real world except in certain specific circumstances, and with the non-trivial assumptions that are required in order for the arguments to carry forth.
I’m not sure I get this reference. Mind giving a link, at least to point to the sort of thing you have in mind?