Money-Pump Arguments

Money-pump arguments demonstrate that cyclic preferences violate Expected Utility Theory by showing that trading between alternatives can result in a money pump, returning the individual to their starting position with less money.

Format: Paperback / softback
Length: 75 pages
Publication date: 13 October 2022
Publisher: Cambridge University Press

The concept of cyclic preferences, where individuals prefer A to B, B to C, and C to A, contradicts the principles of Expected Utility Theory (EUT). However, money-pump arguments provide a compelling explanation for why these violations of EUT are irrational.

To begin, suppose an individual starts with preference A. According to EUT, they should be willing to trade A for C and then C for B. This is because the individual values A more than B and C more than A, resulting in a linear preference order.

However, the scenario takes an unexpected turn when the individual is offered a trade back to A for a small cost. Despite preferring A to B, the individual pays the small sum to trade from B to A. This seemingly irrational decision is explained by the money-pump argument.

The money-pump argument suggests that the individual has become a money pump. In essence, they are back to the alternative they started with, but with less money. The argument emphasizes that the individual has effectively converted their money from B to A, resulting in a loss.

To defend each of the axioms of EUT using money-pump arguments, consider the following examples:

Consistency Axiom: Suppose the individual prefers A to B, B to C, and C to A. According to the Consistency Axiom, the individual should be willing to trade A for C and then C for B. However, the individual pays a small cost to trade from B to A, which contradicts the Consistency Axiom. The money-pump argument explains that the individual has become a money pump, converting their money from B to A and losing it in the process.

Independence Axiom: The Independence Axiom states that the individual's preferences should be independent of each other. This means that the individual's preferences for A, B, and C should not be influenced by their preferences for other alternatives. However, the individual pays a small cost to trade from B to A, which suggests that their preferences for A and B are dependent on each other. The money-pump argument explains that the individual has become a money pump, converting their money from B to A and creating a dependency between their preferences.

Transitivity Axiom: The Transitivity Axiom states that if the individual prefers A to B and B to C, then they should also prefer A to C. However, the individual pays a small cost to trade from B to A, which contradicts the Transitivity Axiom. The money-pump argument explains that the individual has become a money pump, converting their money from B to A and creating a transitivity violation between their preferences.

By analyzing these examples, it becomes clear that money-pump arguments can be used to defend each of the axioms of EUT against cyclic preferences. The argument emphasizes that individuals who violate EUT by becoming money pumps are irrational because they are effectively converting their money from one alternative to another, resulting in a loss.

This concept is also available as Open Access on Cambridge Core, providing further insights into the rationality of economic decision-making.

Weight: 149g
ISBN-13: 9781108718950