Money pumps, diachronic and synchronic.

Author:Levy, Yair

WHY HAVE ACYCLIC PREFERENCES? A common reply invokes the threat of being turned into a money pump. If one prefers a over b, b over c, but c over a, one may be manipulated into paying for a series of trades, only to be left with one's initial object of choice. This influential argument for acyclicity of preferences appeared first in Davidson, McKinsey and Suppes (1955). In their example, Mr. S. has the following cyclic set of preferences: Faced with choices among the positions of full professor with a salary of $5,000 (a); associate professor at $5,500 (b); and assistant professor at $6,000 (c), Mr. S. prefers a over b, b over c and c over a. The cyclic set renders Mr. S. vulnerable to manipulation:

The department head, advised of Mr. S's preferences, says, "I see you prefer b to c, so I will let you have the associate professorship--for a small consideration. The difference must be worth something to you." Mr. S. agrees to slip the department head $25 to get the preferred alternative. Now the department head says, "Since you prefer a to b, I'm prepared--if you will pay me a little for my trouble--to let you have the full professorship." Mr. S. hands over another $25 and starts to walk away, well satisfied, we may suppose. "Hold on," says the department head, "I just realized you'd rather have c than a. And I can arrange that-- provided ..." (1) A common reaction to the money-pump argument raises the possibility of devising ways to circumvent the threat of exploitation. For example, having traded c for b and then b for a, Mr. S. may "get the drift" and refuse any further transactions with the greedy department head (Schick 1986); alternatively, he may resolve in advance to avoid any trades that will result in his being exploited (McClennen 1990: 13).

Recently, a new version of Money Pump has surfaced, which promises to improve on the original when it comes to overcoming these standard objections. Thus Johan Gustafsson (2013) dismisses the above objections as "irrelevant"; their seeming force comes from targeting a conspicuous but dispensable feature of the argument, while leaving its important core untouched. The threat of being fleeced for money is a mere dramatic device that serves to illustrate the deeper lesson of Money Pump: the irrationality of cyclic preferences. Remove the money pumper from the scene and you remove a vivid, dramatic illustration of why cyclic preferences are rationally flawed; but you have not upset the thrust of the argument. Gustafsson demonstrates this point by formulating a synchronic analogue of the diachronic money pump. His synchronic version dispenses with the threat of exploitation, and hence undercuts the standard objections. Instead of the sequence of pairwise choices that figures in the original diachronic argument, Mr. S. is imagined to face just a single choice from the complete three-term set {a, b, c}. With no trades offered to swap one object for another, Mr. S. is not vulnerable to manipulation by the department head, and consequently has no use for precautionary measures of the kind suggested by Schick and McClennen. But his irrationality remains manifest. His cyclic preferences render him unable to make a choice with which he will be satisfied; whatever he chooses, there will be some alternative that he prefers.

The synchronic version of Money Pump demonstrates the dialectical dispensability of the threat of exploitation. The irrationality of Mr. S. consists in a defective structure of preferences that cannot perform its role of effecting a stable choice. It is because of this irrational defect that Mr. S. is vulnerable to exploitation in the original money pump: No matter which option he manages to secure, he would always be willing to pay to...

To continue reading