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
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