In economic theory, the money pump argument is a thought experiment intended to show that rational behavior requires transitive preferences: If one prefers A to B and B to C, then one should not prefer C to A. Standard economic theory assumes that preferences are transitive. However, many people have argued that intransitive preferences are quite common, and often observed in real world settings. A cognitive bias is called the focusing effect: people focus on one characteristic which stands out in order to make decisions In choosing potential mates, candidate A is more beautiful/handsome than candidate B. B is wealthier then C. C is far better attuned on a personal level than A – the hearts meet. Then choices could be intransitive because instead of evaluating the whole package, people focus on one characteristic which distinguishes between two candidates to make decisions.
Example
The original example of the Money Pump was published by Davidson, McKinsey and Suppes in 1955. It was based on gambling games. In their example, there are two "tickets", each of which entitles the bearer to play a gambling game once. Any money paid to obtain the ticket does not count towards the stake for the game. An example of the type of tickets available are:
Ticket A gives a chance to play a game where you stake $1 for a 50:50 chance of winning $5.
Ticket B gives a chance to play a game where you stake $1 for a 1:20 chance of winning $100.
McKinsey and Suppes found that most players would rate the ticket with the higher chance of winning as more desirable, but the ticket with the higher prize as more valuable, thus representing intransitive preferences. This would theoretically allow a "money pump" to operate as follows:
The operator offers the customer a chance to buy ticket B at a fairly negotiated price, P.
The operator then offers the customer ticket A in exchange for ticket B, on the grounds that they desire it more.
The operator then offers to buy ticket A back for a fairly negotiated price, P'. Since A is considered less valuable than B, P' should be less than P. But after all these transactions, all that has happened is that dollars have been transferred from the customer to the operator in exchange for ultimately nothing.
Reactions
There are many counter-arguments which can be made to this. One of the simplest was made by Cubitt. His paper shows that the argument rests on some very strong assumptions and is tautological: to say that X acts as a money pump is no different from saying that X has intransitive preferences, and does not add anything to evidence for or against the existence of intransitive preferences. A second argument is more fundamental, and this rests on the possibility of incomparability. This differentiates between choice and preference. Forced to choose between A and B, I may choose A, yet the two may really not be comparable choices, thus we cannot conclude that I must have preferred A to B. See section on incommensurability in article on "Dynamic Choices" in the Stanford Encyclopedia of Philosophy for a more detailed discussion. If choices are not comparable, then again the money pump argument fails. A more complex and sophisticated version of this argument occurs in the context of subjective probability, where it is known as the Dutch book argument. There it is shown that rational behavior involves making choices over bets in such a way that they correspond to subjective probabilities. If someone fails to satisfy this condition, then his preferences over lotteries will be intransitive and he can be made to act as a money pump. Thus the argument is used to justify the existence of subjective probabilities as a requirement for rational behavior. Again there are many possible counter-arguments.
