In a previous article I've demonstrated that you can only avoid money pumps and arbitrage by using the von Neumann-Morgenstern axioms of expected utility. I argued in this post that even if you're not likely to face a money pump on one particular decision, you should still use expected utility (and sometimes expected money), because of the difficulties of combining two decision theories and constantly being on the look-out for which one to apply.

Even if you don't care about (weak) money pumps, expected utility sneaks in under much milder conditions. If you have a quasi-utility function (i.e. you have an underlying utility function, but you also care about the shape of the probability distribution), then this post demonstrates that you should generally stick with expected utility anyway, just by aggregating all your decisions.

So the moral of looking at money pumps, arbitrage and aggregation is that you should use expected utility for nearly all your decisions.

But the moral says exactly what it says, and nothing more.

I prefer the movie Twelve Monkeys to Akira. I prefer Akira to David Attenborough's Life in the Undergrowth. And I prefer David Attenborough's Life in the Undergrowth to Twelve Monkeys.

I have intransitive preferences. But I don't suffer from this intransitivity. Up until the moment I'm confronted by an avatar of the money pump, juggling the three DVD boxes in front of me with a greedy gleam in his eye. He'll arbitrage me to death unless I snap out of my intransitive preferences and banish him by putting my options in order.

Arbitrage, in the broadest sense, means picking up free money - money that is free because of other people's preferences. Money pumps are a form of arbitrage, exploiting the lack of consistency, transitivity or independence in people's preferences. In most cases, arbitrage ultimately destroys itself: people either wise up to the exploitation and get rid of their vulnerabilities, or lose all their money, leaving only players who are not vulnerable to arbitrage. The crash and burn of the Long-Term Capital Management hedge fund was due in part to the diminishing returns of their arbitrage strategies.

Most humans to not react to the possibility of being arbitraged by changing their whole preference systems. Instead they cling to their old preferences as much as possible, while keeping a keen eye out to avoid being taken advantage of. They keep their inconsistent, intransitive, dependent systems but end up behaving consistently, transitively and independently in their most common transactions.

The weaknesses of this approach are manifest. Having one system of preferences but acting as if we had another is a great strain on our poor overloaded brains. To avoid the arbitrage, we need to scan present and future deals with great keenness and insight, always on the lookout for traps. Since transaction costs shield us from most of the negative consequences of imperfect decision theories, we have to be especially vigilant as transaction costs continue to drop, meaning that opportunities to be arbitraged will continue to rise in future. Finally, how we exit the trap of arbitrage depends on how we entered it: if my juggling Avatar had started me on Life in the Undergrowth, I'd have ended up with Twelve Monkeys, and refused the next trade. If he'd started me on Twelve Monkeys, I've had ended up with Akira. These may not have been the options I'd have settled on if I'd taken the time to sort out my preferences ahead of time.