Abstract
In this article, I examine the consequences of Mamou’s recent solution to the so-called problem of reindividuation. The problem is first proposed by John Broome as an argument against the Humean view of rationality and subjective decision theory. Essentially, Broome argues that the reindividuation of outcomes must be constrained in some way if the axioms of rationality are not to be vacuous, but the constraints on individuation cannot be consistent with the Humean view of rationality. Mamou offers an elegant Humean solution to this problem. We do not need such rules for reindividuation since the subjective decision theory operates under the assumption of maximal relevance of description, and only under that assumption do the axioms tell anything. Thus the problem of reindividuation dissolves in a quite natural and simple way. However, I argue that if we connect this solution to the topic of justification for the requirements of rationality, problems arise. I examine the influence of the solution on the common argument for the axioms of decision theory, the so-called money-pump arguments. These arguments are a staple in the justification of the axioms of subjective decision theory. I argue that they are in collision with Mamou’s solution. This collision brings us to the dilemma: either accept Broome’s conclusions or lose the money-pump arguments as an effective tool for justification of the axioms. I conclude that neither of the options is really good for the defenders of the Humean view of rationality.
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Notes
Broome raised a similar possibility about money-pump arguments but with a different conclusion and intention. We will consider Broome’s points and conclusions in detail in subsection 4.1.
For example, Broome’s reasoning regarding why there are only these two options to stop reindividuation is as follows. Consider our agent faced with the choice of fruits. Her claim to rationality is twofold: (a) for her, the outcome BA is not a single outcome but two outcomes, BA&P and BA&Imp; (b) between these two outcomes, BA&P and BA&Imp, she is not indifferent but strongly prefers BA&P to BA&Imp. If either of these conditions is not fulfilled, the agent has intransitive preferences. According to Broome, if we want to stop reindividuation, we can either argue that the agent is incorrect in differentiating two outcomes when there is, in fact, only one outcome (i.e., use the principle of individuation), or we can argue that the agent is correct in differentiating between two outcomes but is rationally obligated to be indifferent between them (i.e., use the requirement of indifference). Successfully stopping reindividuation, according to Broome, depends on external facts, which is ultimately all that is important to him. Broome was ambiguous about whether the reindividuation in the example he provided should, in fact, be stopped (cf. Broome 1991, pp. 100–103; Broome 1993, pp. 55–58). For instance, in one place, he says, talking about the agent from his example: “Is this enough to show that Maurice is rational? I do not know, but I do know what it depends on.” (Broome 1993, p. 56). At another place, he says, talking about the example: “We need a principle for individuating outcomes that wards off this danger.” (Broome 1991, p. 102).
We should emphasize the term “normative”. The problem of reindividuation can indirectly concern descriptive theories, but the problem is presented as a problem for normative theories. Mamou responds to the problem as such, not mentioning descriptive theories. Finally, the issue we raise in this article is not related to the descriptive theories, for the simple reason that money-pump arguments are not arguments for descriptively interpreted axioms.
See Fishburn (1981) for a great review of many major normative representation theorems. His review is a bit dated and it does not deal with more modern axiomatizations such as Joyce’s (1999) axiomatization of causal decision theory, but it is nevertheless the best bang for the buck among the reviews.
While his arguments are made from the point of view of those two theories, the arguments are easily extendable to other approaches such as classic examples of Ramsey’s (1926), von Neumann, J., and Morgenstern’s (1944) axiomatizations, or more modern theory such as Joyce’s causal decision theory (1999).
The name is probably not the greatest one for the view for two reasons. First, it is far from elegant. Second, it is not true that there are no criteria for the validity of descriptions since Mamou mentions some fairly liberal guidelines that stay within the Humean framework. But since we differentiate this view from Broome’s Non-Humean view that explicitly adds additional criteria (for descriptions or preferences), I choose this name. On the part of elegance, I cannot think of anything better so I just hope that this will suffice.
The stipulation or the claim on the intuitive plausibility are not really arguments for the axioms, since they consist of (often quite vague) claims on the characteristics of the axioms.
Even earlier and perhaps even more famously, a similar idea of showing that agents are exploitable if they violate the axioms of probability is used in the Dutch Book arguments by de Finetti (1937). The Dutch Book arguments, though related to the topic of rational choice via the concept of subjective probability, are different from money-pump arguments since they are not directly concerned with the agent’s preferences.
It is not essential to use money in the arguments. One can substitute “money” with “utility” or anything that represents utility. But using money is standard as it gives the clearest picture of exploitability that agents face.
We should emphasize that these are the main options, since there are more options to get out of the problem, but far less conventional. We can, for example, reject the view that transitivity is the requirement of rationality. But this seems like a very radical road to take, since it would negate one of the most common axioms of the decision theory.
As mentioned when discussing Broome’s solution to the problem of reindividuation in Sect. 2, it should be noted that it is irrelevant for us that Broome was somewhat ambiguous as to whether the principle or the requirement should be applied in this case concretely. His analysis shows that if we want to stop the reindividuation, we must apply the principle or the requirement, as highlighted in footnote 4. Since one option for moderate Humeanism here is to stop reindividuation, we must apply Broome’s principle and requirement.
It should also be noted that this subsection is not an attempt at criticizing Broome’s overall position, but an attempt to extrapolate a possible criticism from Broome’s words. Broome himself offers rules for reindividuation, i.e., he gladly takes a non-Humean position. He is also not that much interested in money-pump arguments, saying that if he were to justify the axioms he would “make no use of Dutch books or money pumps” (Broome 1991, p. 119, note 20).
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This work was supported by Ministry of Education, Science and Technological Development of Republic of Serbia within funding of research at Belgrade University, Faculty of Philosophy, (Grant number 451-03-68/2022-14/ 200163).
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Filipović, N. The Problem of Reindividuation and Money-Pump Arguments: Analysis of Mamou’s Solution. Topoi (2023). https://doi.org/10.1007/s11245-023-09983-6
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DOI: https://doi.org/10.1007/s11245-023-09983-6