There are ontological assumptions built into the question. It is assumed that “utility” is f(money owned), for some increasing function f, and that an “action” is a single monetary transaction.
Someone trying to maximise their long-term growth of wealth has no such function f. The material circumstances that their utility (if they have one) is a function of is not their current bankroll. Neither are their actions single transactions, but long-term policies. That they have no “utility function” in the terms originally posed is not evidence of irrationality, but evidence that if they do have any sort of utility function, its domain is not that envisaged in the statement of the paradox. So also their repertoire of “actions”.
Maximising long-term growth leads in ideal circumstances to Kelly betting, and in non-ideal (i.e. real) circumstances to something more conservative. Zvi recommends 25 to 50% of the Kelly bet.
This, it seems to me, dissolves the paradox. We need not say that “loss aversion … makes no sense for the platonic ideal betting.”. Nor need we reject considering the ideal, scam-free situation (even while always considering one’s counterparties’ probity and reliability when acting in the real world). Nor need we feel compelled by a clever argument to turn down vast but only 50% certain possibilities. We need only bet no more than half of our bankroll on them.
There are ontological assumptions built into the question. It is assumed that “utility” is f(money owned), for some increasing function f, and that an “action” is a single monetary transaction.
Someone trying to maximise their long-term growth of wealth has no such function f. The material circumstances that their utility (if they have one) is a function of is not their current bankroll. Neither are their actions single transactions, but long-term policies. That they have no “utility function” in the terms originally posed is not evidence of irrationality, but evidence that if they do have any sort of utility function, its domain is not that envisaged in the statement of the paradox. So also their repertoire of “actions”.
Maximising long-term growth leads in ideal circumstances to Kelly betting, and in non-ideal (i.e. real) circumstances to something more conservative. Zvi recommends 25 to 50% of the Kelly bet.
This, it seems to me, dissolves the paradox. We need not say that “loss aversion … makes no sense for the platonic ideal betting.”. Nor need we reject considering the ideal, scam-free situation (even while always considering one’s counterparties’ probity and reliability when acting in the real world). Nor need we feel compelled by a clever argument to turn down vast but only 50% certain possibilities. We need only bet no more than half of our bankroll on them.