If you assume.… [y]ou are, in effect, stipulating that that outcome actually has a lower utility than it’s stated to have.
Thanks, that focuses the argument for me a bit.
So if we assume those curves represent actual utility functions, he seems to be saying that the shape of curve B, relative to A makes A better (because A is bounded in how bad it could be, but unbounded in how good it could be). But since the curves are supposed to quantify betterness, I am attracted to the conclusion that curve B hasn’t been correctly drawn. If B is worse than A, how can their average payoffs be the same?
To put it the other way around, maybe the curves are correct, but in that case, where does the conclusion that B is worse come from? Is there an algebraic formula to choose between two such cases? What if A had a slightly larger decay constant, at what point would A cease to be better?
I’m not saying I’m sure Dawes’ argument is wrong, I just have no intuition at the moment for how it could be right.
I think that the communication goals of the OP were not to tell us something about a hand of cards, but rather to demonstrate that certain forms of misunderstanding are common, and that this maybe tells us something about the way our brains work.
The problem quoted unambiguously precludes the possibility of an ace, yet many of us seem to incorrectly assume that the statement is equivalent to something like, ‘One of the following describes the criterion used to select a hand of cards.....,’ under which, an ace is likely. The interesting question is, why?
In order to see the question as interesting, though, I first have to see the effect as real.