Money pump

See also: Dutch book

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 well known 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. See the Stanford Encyclopedia of Philosophy article "Preferences"[1] for a discussion of intransitive preferences and their relation to the Money Pump argument.

The Money Pump argument was invented to show that rational behavior requires transitive preferences. It argues that people can be made to act as money pumps if they have intransitive preferences. Suppose Mr X prefers A to B, B to C, and C to A. In each of these three cases, X is willing to pay $1 (or for the sake of argument, $0.0000…0001; it doesn't really matter) to have his preferred choice. Then he can be made to act as a money pump. Give him C, and then offer him B if he pays a dollar. When he takes B, offer him A for a $1. When he takes A, offer him C for a $1. At the end of this procedure, X is exactly where he was before, but $2 has been "pumped" out of him. Alternatively, he will keep cycling through these choices and paying $1 for each choice, effectively becoming a money pump. This does not seem like rational behavior.

There are many counter-arguments which can be made to this. One of the simplest was made by Cubitt.[2] 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 incommensurabilty[3] 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 (that is, fails to have subjective probabilities), 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.

References

  1. ↑ Hansson, Sven Ove; Grüne-Yanoff, Till (2012). Edward N. Zalta, ed. "Preferences". The Stanford Encyclopedia of Philosophy (Winter 2012 ed.). Stanford University. sec. 1.3 Transitivity. ISSN 1095-5054.
  2. ↑ Cubit, Robin; Sugden, Robert (2001). "On Money Pumps". Games and Economic Behavior. Amsterdam: Elsevier. 37 (1 (October)): 121–160. ISSN 0899-8256.
  3. ↑ Andreou, Chrisoula (2012). Edward N. Zalta, ed. "Dynamic Choice". The Stanford Encyclopedia of Philosophy (Fall 2012 ed.). Stanford University. sec. 1.1 Incommensurable Alternatives. ISSN 1095-5054.

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