The Money Pump Argument by Stuart Yasgur.
The Money Pump and the Justification of the Transitivity Condition
Stuart Yasgur
Rationality is said to require that agents have transitive preferences. The justification of the transitivity condition, as it will be referred to here, is widely thought to be provided by the money pump argument, though there is less consensus about the exact form of this justification.
An excerpt of a larger paper that examines the main justifications of the transitivity condition, this paper focuses on the consequentialist justification. It is important to note that since this paper focuses on the justification of the transitivity condition, it will differ significantly from papers which attempt to characterize the decisions within the money pump itself.
To begin, I will present a basic version of the transitivity condition and a statement of the money pump argument. There are a number of variations of the transitivity requirement, but here we can avoid complications and deal with a weak version, though the arguments in the paper apply equally to stronger versions:
Take the expression x>y to mean that the agent prefers x to y and the expression x > y to mean that the agent prefers x to y or is indifferent between the two. Given this, we can define transitivity as follows: an agent’s preferences are taken to be transitive if, for all triples of alternatives (x, y, z), x > y and y > z imply x > z. Correspondingly an agent’s preferences are taken to be intransitive if for a triple of alternatives (x, y, z), x > y, y > z, and z > x.
Generic version of the money pump argument:
An agent prefers x to y, y to z, and z to x. The agent also prefers more money to less. The agent is offered the opportunity to switch from z to y for a small amount of money, and he accepts. He is then offered the opportunity to switch from y to x for a small amount of money, and he accepts. And, he is offered the opportunity to switch from x to z for a small amount of money, which he accepts.
There is also an extended version of the money pump that is quite common, in which the cycle is repeated until the agent looses all of his money. Though it is easy to slip between the two, the potential justificatory force of each differs, so here they will be dealt with separately. Unless otherwise mentioned, I will be focusing on the basic version.
There are a few things to notice about the money pump argument. First, the agent has intransitive preferences. Second, the agent always moves from a less preferred option to a more preferred option. Third, in terms of his own preferences, the agent is unambiguously worse off at the end of the cycle than he was at the beginning of the cycle. I.e., in terms of his preferences over x, y, and z, the agent is no better off and no worse off, but in terms of his preference for more money rather than less he is worse off.
It should also be clear that the money pump is not an argument. It is an example, but examples on their own are not arguments. To establish that the money pump example justifies the transitivity condition, we must understand the force of the example, and this is where views begin to diverge.
Arguably, the consequentialist justification of the transitivity condition is the most plausible. As was already mentioned, the agent in the money pump is made unambiguously worse off, and it is thought to be these consequences themselves that justify the claim that transitivity is a requirement of rationality.
Consequentialist justifications of requirements of rationality take the following form:
· P1: If X leads an agent to suffer negative consequences, then X is irrational.
· P2: X leads an agent to suffer negative consequences, in suitable circumstances.
· C: Therefore X is irrational.
Much can be said to make arguments of this form more specific, but the general version should suffice to make the point at hand. The first thing to note is that the money pump offers a case in which P2 holds, and if P1 holds, then the conclusion follows. Next, notice that if we take X to be ‘false beliefs’, then P2 would also hold. If P1 holds, then it would follow that having false beliefs is irrational. Having false beliefs is not irrational, therefore P1 does not hold; and therefore the money pump does not offer a consequentialist justification for considering intransitive preferences irrational.
Further, because of the gap between preferences and the consequences of choices based on them, there does not seem to be a way to refine P1 so that it would apply to intransitive preferences but not false beliefs.[1]
Conclusion:
In the longer version of this paper I argue that despite its currency in the literature the money pump does not justify the transitivity condition. However, my own view is that the transitivity condition, suitably qualified, is a genuine requirement of rationality that can be justified based on a broader understanding of the relationship between rationality and value. Rather by discussing the money pump’s limited justificatory force I hope to bring into focus the need to reexamine the justification of one of the basic conditions of preference theory; and I am particularly interested in people’s thoughts about possible consequentialist justifications.
[1] Consider the following example:
· P1`: If X leads an agent to suffer negative consequences even when he is ideal in every other way, then X is irrational.
· P2`: X leads an agent to suffer negative consequences in suitable circumstances, even when he is ideal in every other way.
· C: Therefore X is irrational.
Since P2` still holds for false beliefs, P1` should as well. But it does not.
[1] Consider the following example:
· P1`: If X leads an agent to suffer negative consequences even when he is ideal in every other way, then X is irrational.
· P2`: X leads an agent to suffer negative consequences in suitable circumstances, even when he is ideal in every other way.
· C: Therefore X is irrational.
Since P2` still holds for false beliefs, P1` should as well. But it does not.
Stuart Yasgur
Rationality is said to require that agents have transitive preferences. The justification of the transitivity condition, as it will be referred to here, is widely thought to be provided by the money pump argument, though there is less consensus about the exact form of this justification.
An excerpt of a larger paper that examines the main justifications of the transitivity condition, this paper focuses on the consequentialist justification. It is important to note that since this paper focuses on the justification of the transitivity condition, it will differ significantly from papers which attempt to characterize the decisions within the money pump itself.
To begin, I will present a basic version of the transitivity condition and a statement of the money pump argument. There are a number of variations of the transitivity requirement, but here we can avoid complications and deal with a weak version, though the arguments in the paper apply equally to stronger versions:
Take the expression x>y to mean that the agent prefers x to y and the expression x > y to mean that the agent prefers x to y or is indifferent between the two. Given this, we can define transitivity as follows: an agent’s preferences are taken to be transitive if, for all triples of alternatives (x, y, z), x > y and y > z imply x > z. Correspondingly an agent’s preferences are taken to be intransitive if for a triple of alternatives (x, y, z), x > y, y > z, and z > x.
Generic version of the money pump argument:
An agent prefers x to y, y to z, and z to x. The agent also prefers more money to less. The agent is offered the opportunity to switch from z to y for a small amount of money, and he accepts. He is then offered the opportunity to switch from y to x for a small amount of money, and he accepts. And, he is offered the opportunity to switch from x to z for a small amount of money, which he accepts.
There is also an extended version of the money pump that is quite common, in which the cycle is repeated until the agent looses all of his money. Though it is easy to slip between the two, the potential justificatory force of each differs, so here they will be dealt with separately. Unless otherwise mentioned, I will be focusing on the basic version.
There are a few things to notice about the money pump argument. First, the agent has intransitive preferences. Second, the agent always moves from a less preferred option to a more preferred option. Third, in terms of his own preferences, the agent is unambiguously worse off at the end of the cycle than he was at the beginning of the cycle. I.e., in terms of his preferences over x, y, and z, the agent is no better off and no worse off, but in terms of his preference for more money rather than less he is worse off.
It should also be clear that the money pump is not an argument. It is an example, but examples on their own are not arguments. To establish that the money pump example justifies the transitivity condition, we must understand the force of the example, and this is where views begin to diverge.
Arguably, the consequentialist justification of the transitivity condition is the most plausible. As was already mentioned, the agent in the money pump is made unambiguously worse off, and it is thought to be these consequences themselves that justify the claim that transitivity is a requirement of rationality.
Consequentialist justifications of requirements of rationality take the following form:
· P1: If X leads an agent to suffer negative consequences, then X is irrational.
· P2: X leads an agent to suffer negative consequences, in suitable circumstances.
· C: Therefore X is irrational.
Much can be said to make arguments of this form more specific, but the general version should suffice to make the point at hand. The first thing to note is that the money pump offers a case in which P2 holds, and if P1 holds, then the conclusion follows. Next, notice that if we take X to be ‘false beliefs’, then P2 would also hold. If P1 holds, then it would follow that having false beliefs is irrational. Having false beliefs is not irrational, therefore P1 does not hold; and therefore the money pump does not offer a consequentialist justification for considering intransitive preferences irrational.
Further, because of the gap between preferences and the consequences of choices based on them, there does not seem to be a way to refine P1 so that it would apply to intransitive preferences but not false beliefs.[1]
Conclusion:
In the longer version of this paper I argue that despite its currency in the literature the money pump does not justify the transitivity condition. However, my own view is that the transitivity condition, suitably qualified, is a genuine requirement of rationality that can be justified based on a broader understanding of the relationship between rationality and value. Rather by discussing the money pump’s limited justificatory force I hope to bring into focus the need to reexamine the justification of one of the basic conditions of preference theory; and I am particularly interested in people’s thoughts about possible consequentialist justifications.
[1] Consider the following example:
· P1`: If X leads an agent to suffer negative consequences even when he is ideal in every other way, then X is irrational.
· P2`: X leads an agent to suffer negative consequences in suitable circumstances, even when he is ideal in every other way.
· C: Therefore X is irrational.
Since P2` still holds for false beliefs, P1` should as well. But it does not.
[1] Consider the following example:
· P1`: If X leads an agent to suffer negative consequences even when he is ideal in every other way, then X is irrational.
· P2`: X leads an agent to suffer negative consequences in suitable circumstances, even when he is ideal in every other way.
· C: Therefore X is irrational.
Since P2` still holds for false beliefs, P1` should as well. But it does not.
Labels: decision theory, dutch book, epistemology., justification, Money pump, transitivity, utility
posted by bloggin the Question at 7:39 PM
6 Comments:
This comment has been removed by a blog administrator.
Thanks for your post Stuart,
You rely heavily on the assumption that false beliefs aren't irrational. But surely someone who is ideally rational should do their utmost to guard against false beliefs, and for this reason, false beliefs ARE irrational. There is a sense in which it is "ok" to make mistakes, if you are in an unfortunate epistemic situation. But this can apply equally to intransitive preferences.
Suppose I prefer John to Joan, and prefer Joan to James. I don't realise that John is in fact Mr Peterson, who I only correspond with by email, and I prefer James to Mr Peterson. I claim that this would be an "innocent" intransitive preference because it is not knowingly intransitive. It is not "irrational", it is just a case of misidentification. However were I to discover that Peterson was John, I should, under pain of irrationality, adjust my preferences accordingly.
The same is true of false beliefs. If I believe that the beans this man is selling me have magical properties and reason that I should sell my cow to buy them, I am not being irrational, if my belief is "innocent". However, if I have other reasons to believe that the belief that the beans have magical properties is false, or even probably false, then my action would be irrational.
In general "X" in P1 has to be an action, and to act on false beliefs IS irrational, provided than you have good reason to believe that they are false.
PS. Sorry R, I removed your comment because I didn't think it relevant to this post.
You're quite right to point out that my argument makes much of the possibility that an agent can rationally have false beliefs. But I am not committed to the view that all false beliefs are rational. I have a minimal account of rationality, but as long as you admit the possibility that an agent can rationally have false beliefs that should be enough for present purposes.
In contrast, if you hold that all false beliefs are irrational, then our dispute is likely terminological. If that’s the case, I can offer some reasons for why we should adopt a more modest understanding of ‘irrationality’.
The label 'irrational' is applied to failings of many different kinds. While we may conclude from this that ‘irrational’ is an umbrella term, I don’t think it is particularly fruitful to do so because of the variety of failings involved.
Having false beliefs is quite different from not having the beliefs an ideal reasoner would have. An agent can fail in both of these ways or either of them, quite independently. Further an agent can have an irrational belief though not fail in either of these ways.
Applying the label ‘irrational’ to all of these failings obscures the pertinent differences. As a result, I suggest we adopt a modest understanding of irrationality that renders these differences transparent.
This is quite a brief treatment of these issues, but I look forward to hearing your thoughts.
Best,
Stuart
Hi Stuart,
I am trying to get into a tiny chink in your armor. Of course you do not need ALL false belief to be rational. But it is very plausible as you say that some false belief are rational, namely JUSTIFIED false beliefs. I grant that a rational agent does on occasion have false beliefs. Rational agents are FALLIBLE. It is a jump to say that IDEALLY rational agents are fallible, this seems to be self contradictory.
My question is, can there be an intelligible perspective from which the same belief is justified AND false? For a belief to be justified is relative to a body of knowledge. If that body of knowledge includes the fact that the belief is false, then the belief is not justified. In this sense false beliefs are never justified.
On the other hand, from a perspective where a belief IS justified, it cannot be described as false, whether it is true or false is left open, both truth values are possible. But depending on the strength of the justification, it is presumed that a justified belief is more likely to be true than an unjustified one. This is part of the MEANING of justified.
So we have the proposition that justified beliefs are more likely to lead to good consequences than unjustified ones.
Choices that lead to bad consequences through bad luck must be excluded from P1 or natural disasters come out as irrational as well as other unintentional bad luck.
So my ammendment to P1 is
P1J: If X is such that X is likely from the agents perspective to lead to bad consequences for the agent, then X is irrational.
Intransitive preferences, false beliefs and unjustified beliefs all come out as irrational on this ammendment, whereas justified belief come out as rational even though they are fallible.
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