Oh, nice! It seems more irrational to me to violate this “sure thing” principle than the axioms in your post, or at least, this comment makes it clear that you can get Dutch booked and money pumped if you do so. You have a Dutch book, since the strategy forces you to commit to switching to a lottery that’s stochastically dominated by a lottery available at the start that you previously held (assuming X0 has identically 0 payoff). There’s also a money pump here, since Omega can offer you a new St. Petersburg lottery after you see the outcome of your previous lottery and charge you an arbitrarily large finite amount to switch.
Still, this kind of behaviour seems hard to exploit in practice, because someone needs to be able to offer you a finite unbounded lottery with infinite expected value (or something similar, if we aren’t using expected values).
Oh, nice! It seems more irrational to me to violate this “sure thing” principle than the axioms in your post, or at least, this comment makes it clear that you can get Dutch booked and money pumped if you do so. You have a Dutch book, since the strategy forces you to commit to switching to a lottery that’s stochastically dominated by a lottery available at the start that you previously held (assuming X0 has identically 0 payoff). There’s also a money pump here, since Omega can offer you a new St. Petersburg lottery after you see the outcome of your previous lottery and charge you an arbitrarily large finite amount to switch.
Still, this kind of behaviour seems hard to exploit in practice, because someone needs to be able to offer you a finite unbounded lottery with infinite expected value (or something similar, if we aren’t using expected values).