Circular Preferences Don't Lead To Getting Money Pumped

The bad thing about circular preferences is that they make the number you assign to how good an option is ("utility"-ish thing) not be a function). If you have some quantity of X, normally we'd expect that to determine a unique utility. But that only works because utility is a function! If your decision-maker is based off of some "utility"-ish number that isn't single-valued, you could have different utilities correspond to the very same quantity of X.

Your post basically says "getting money pumped would require us to have higher utility even if we just had a lower-probability version of something nice we already had - and since any thinking being knows that utility is a function, they will avoid this silly case once they notice it."

Well, no. If they have circular preferences, they won't be held back by how utility is actually supposed to be a function. They will make the trades, and really truly have a higher number stored under "utility" than they did before they made the trades. You build a robot that has a high utility if it drives off a cliff, and the robot doesn't go "wait, this sounds like a bad idea. Maybe I should take up needlepoint instead." It drives off the cliff. You build a decision-making system with circular preferences, and it drives of a cliff too.

I had what feels like an insight about this type of money pump scenario in general, so I'll run it by everyone.

If X is a painful experience, like a stubbed toe. Y is a second painful experience, like a caffeine headache, and Z is a third painful experience, like a sore muscle, then trading repeatedly in the manner listed above seems entirely correct, since you would essentially be repeatedly trading to eventually almost no pain whatsoever. So the circularity of the trades themselves do not appear to be a problem (as opposed to the circularity of the preferences). As another example of this, if someone is offering 2 bagels for 1 apple, someone else if offering 2 candies for 1 bagel, and someone else is offering 2 apples for 1 candy, and you get utility from apples, bagels, and candies, then you have a great arbitrage situation.

In this case, your preferences are wrong, but they are coherently wrong. If you flip the sign bit, (what you think is good is actually bad and vice versa) for instance, you'll go back to perfectly reasonable, so you can say "If I look three steps ahead, in this scenario I would be better off doing what I would intuitively prefer NOT to do at each step."

This also appears to work whether you flip the sign bit on X's value (Actually you SHOULD discard X because it hurts) or the trade order (Actually, you should make all of those trades in the reverse order then you would think.) but presumably not both, because then you would be voluntarily trading to what you currently think is infinite disutility, which brings up a weird point. Reversing your preferences and reversing how you ACT on those preferences shouldn't do anything to change your behavior, but in this case if you attempt to evaluate the results of doing it in this case, it appears to be infinite disutility. That's probably extremely clear evidence you need to change your value system.

Am I onto something, or am I missing the point?

Edit: Clarified a point about circularity.

My understanding is that real humans routinely have cyclic preferences -- particularly when comparing complicated objects like apartments or automobiles, where there are many different attributes and we ignore small differences. I can't find a reference for this in a few minutes of googling, however.

I suspect in practice transaction costs are high enough that the money pump doesn't arise in most cases where we have intransitive preferences. Once people have made their decision by some arbitrary means, they will stick to it.

Having circular preferences is incoherent, and being vulnerable to a money pump is a consequence of that.

I knew that if I had 0.95Y I would trade it for (0.95^2)Z, which I would trade for (0.95^3)X, then actually I'd be trading 1X for (0.95^3)X, which I'm obviously not going to do.

This means that you won't, in fact, trade your X for .95Y. That in turn means that you do not actually value X at .9Y, and so the initially stated exchange rates are meaningless (or rather, they don't reflect your true preferences).

Your strategy requires you to refuse all trades at exchange rates below the money-pumpable threshold, and you'll end up only making trades at exchange rates that are non-circular.

the ability to trade X for Y at an exchange rate of 0.95Y for 1X, and Y for Z at an exchange rate of 0.95Z for 1Y, and Z for X at an exchange rate of 0.95X for 1Z

The above set of exchange rates is problematic. Thinking of X, Y & Z as currency units, you have Y > X, Z > Y, and X > Z - not possible. You would be unlikely to encounter this set of exchange rates.

Suppose I randomly give you X, Y, or Z, and offer you a single trade for the one you prefer to it, but you have to pay a penny. In each case, the trade benefits you, so you'd make the trade. You end up with exactly the same probability distribution, but one penny poorer.