Rules of behavior and expected utility theory. Compatibility versus dependence

Conclusions

We have seen that many decision rules which are intuitively and/or empirically supported and compatible with MEU, are compatible with it but not dependent on it.

There are of course rules of behavior which are implied in MEU and also depend on it like this:

If the hope of winning any of the prizes in a lottery motivates you to buy a ticket, and if you win half the amount of the highest prize, you should play double or nothing with your prize.

Suppose you would prefer a one in a million chance of winning $2 million to a two in a million chance of winning $1 million, but your first choice is not available so you buy a ticket for $1 million. If you win, you should play 50–50 double or nothing with your prize. Generalize: put x in the place of $1 million and p in the place of 1/1 000000, and test yourself against this principle (Pf = preferred to): (p, 2x)Pf(2p, x) ⇒ (0.5, 2x)Pf(1, x).

See Friedmann and Savage (1968).

In the real world lotteries are multiprize, i.e., composite games of elements like these. The same applies: If you would not have preferred the highest prize exchanged for a higher probability of some lower prize, then winning a lower prize would put you in the market for some simple bet like above. If you stand up to this test, you are a unique person because, as we know, such bets are not made.

While in the process of finishing the final draft, I got hold of (Samuelson, 1983). He expresses grave doubts as to what he calls the dogma of Expected Utility maximizing. In a somewhat apologetic way, he preserves some formulations deriving behavior from EUM because, as he states in a general way, they do not depend on that particular “dogma”. More specifically: many models incompatible with EUM imply risk aversion, which would result also from maximizing the expectation of a concave utility function,

In view of the authoritarian disposition of some of the strongest defenders of EUM and of Samuelson's (well deserved) authority and his leading role in the school of EUM theory, his open expression of doubt may well mark the beginning of the last chapter in the history of the rise and fall of the most powerful school that has so far been active in 20th century decision theory.