A pump which only pumps once isn't much of a pump.
In order to run the Vegas money pump (three intransitive bets) you need only offer hypothetical alternatives, because the gambler's preferences are inconsistent. You can do this forever. But to run the Allais money pump, you're changing the preferred bet by making one outcome certain. So to do it again, you'd need to reset the scenario by removing the certainty somehow. The gambler would oppose this, so their preferences are consistent.
And I think it might be helpful to phrase it as avoidance of regret, rather than valuing certainty. People have a powerful aversion to the anticipated regret of coming away with nothing from a scenario where they could have gained substantially. There's also interactions here with loss aversion for the lives formulation: dollars gained vs lives lost.
Writing this comment has given me a new appreciation for the difficulties of clearly and concisely explaining things. I've rewritten it a few times and I'm still not happy but I'm posting anyway because of thematically appropriate loss aversion.
A pump which only pumps once isn't much of a pump. In order to run the Vegas money pump (three intransitive bets) you need only offer hypothetical alternatives, because the gambler's preferences are inconsistent. You can do this forever. But to run the Allais money pump, you're changing the preferred bet by making one outcome certain. So to do it again, you'd need to reset the scenario by removing the certainty somehow. The gambler would oppose this, so their preferences are consistent. And I think it might be helpful to phrase it as avoidance of regret, rather than valuing certainty. People have a powerful aversion to the anticipated regret of coming away with nothing from a scenario where they could have gained substantially. There's also interactions here with loss aversion for the lives formulation: dollars gained vs lives lost. Writing this comment has given me a new appreciation for the difficulties of clearly and concisely explaining things. I've rewritten it a few times and I'm still not happy but I'm posting anyway because of thematically appropriate loss aversion.