[Note for bibliographic reference: Melberg, Hans O. (1998), Decision making and infinite regress, www.oocities.org/hmelberg/papers/981220.htm]  

Decision making and infinite regress
More complicated than I thought is was!

by Hans O. Melberg




Introduction
Two months ago I wrote a short observation on the problem on infinite regress. Since then my thinking has progressed for two reasons. I found an article that was very relevant (Holly Smith (1991): "Deciding how to decide: Is there a regress problem?") and my own thought became more organized as I tried to structure the problem. In short, I discovered that there were many infinite regress problems and that we need to disaggregate the concept of information before we can get a better understanding of the arguments. In this paper, I will first describe what I used to think the infinite regress problem was. The second part will present Smith's arguments. Third, I want to try to create a frame in which the different infinite regress problems can be discussed.

Initial thoughts
I first read about the infinite regress problem in Elster's review of a book by Nelson and Winter (Elster 1983). I then accepted the argument as valid and important. In short, it seemed true that before we made a decision we had to make a decision on how much information to collect. But, before we can make a decision on how much information to collect we also need to collect information about how much information we should collect to make that decision and so on. This is a problem in two ways. First, it produces an infinite regress. Second, it may be impossible to get reliable information even when you decide to spend time seeking the information. I believed this was important because it demonstrated that rational choice theory had to be complemented by psychological theories in order to explain behaviour. The infinite regress problem made it impossible to make a rational decision in some situations. If rational behaviour was logically impossible, then behaviour in those circumstances could not be explained as the outcome of rational choice.

After reading the same argument repeated by Elster in different works (such as in his introduction to the book Rational Choice from 1986), I began to question the infinite regress argument. My first thought was that if the value of information decreased in a "well behaved" manner, then there would be no infinite regress problem in the limit.

Having given the issue slightly more though, I wrote the observation "Is it logically possible to make a rational decision?" (at www.oocities.org/hmelberg/papers/981017.htm). I intended to develop the argument above (about a possible solution in the limit), but while doing so I discovered that different authors used the term "infinite regress" about different problems. I then found the mentioned article by Holly Smith ("Deciding how to decide: Is there a regress problem?"), which further convinced me that the term was used about different problems. Let me give some examples before I try to impose some order.

Smith's arguments
Smith starts by distinguishing between deliberation and research. "Information-gathering includes a wide variety of processes, which I shall divide into two rough categories, deliberation and research. By 'deliberation, I shall mean all those processes aimed at revealing to the agent, for purposes of making a decision, information that she already implicitly possesses. ... Research, on the other hand, involves acquiring information not already implicitly contained in the agent's 'mental store.'" (Smith 1991, 194-195).

He then limits his subject with the following argument: "Since most theorists have focused on the problem as it concerns deliberation rather than research, I shall confine my attention to the former" (Smith 1991, 196). While it is perfectly acceptable to limit your subject, Smith's justification is questionable. Is it really true that "most theorists" have focused on deliberation as opposed to research? Smith quotes Jon Elster as an example of a theorists in the field, but he fails to note that Elster's focus is precisely the opposite of Smith: Elster discusses the problem of deciding how much information you should collect i.e. the problem of infinite regress in search and not deliberation. There is, however, no need to make this a major point since it is not important to the main arguments that follow.

Smith also introduces a second distinction, that is between deferral and non-deferral cases. Moreover, he writes that "In this paper I shall consider nondeferral cases only" (Smith 1991, 198). At this point we might become slightly more suspicious. Does he really disprove the infinite regress problem, or is he simply limiting the subject in a way that defines the problem away?

The suspicion is further increased when he introduces a third distinction, this time between two concepts of rationality. First, he writes that "... it is rational to choose an action if and only if it is prescribed by the highest decision guide that one is capable of using to make one's decision" (Smith 1991, 198). The second conception of rationality, is introduced as follows: "It is often thought that what it is rational to choose depends, not on the action satisfying the relevant decision guide, but rather on the agent's justifiably believing that it does" (Smith 1991, 199. This is labeled "Justified-belief decision guides"). This time, however, he does not use the distinction to focus on only one since he claims that his arguments against the infinite regress problem applies to both cases. Now, I cannot claim to fully understand everything he writes, but I believe that this is a point that deserves further scrutiny.

Smith then discards one interpretation of the infinite regress problem as obviously wrong since infinite postponement cannot take place in the real world because the agent (if human) will die eventually (p. 197). Instead he interprets "the genuine threat from the regress problem" as follows: "Universal irrationality: the regress problem entails that there is no action which is rational to perform" (p. 197). He claims two arguments are used to support this "First ... since there is always some superior act that it would have been more rational to perform, namely acquiring information about the act in question" (p. 197). "Second, ... to avoid an infinite regress, agents must make some initial decision without reference to relevant decision-guiding principles. Since such an unguided decision is irrational, so are all the subsequent decisions and actions that flow from it" (p. 197).

Before going on to present his counterarguments to the two arguments above, I would like to note the following. The rational formation of beliefs requires us to search and deliberate until the (expected) marginal costs of doing so are equal to the (expected) marginal benefits (including process costs and benefits). In other words, there is an optimal level. How is this line of reasoning affected by our mortality? True, it implies that we cannot postpone a decision forever, but then again we do not know exactly for how long we can postpone it or for how long it would be optimal to collect information. We do not know when we will die or the costs/benefits of unknown information.

Against the first argument for the significance of the regress problem, Smith uses the example of a physician who has to choose between two different types of chemotherapy (A or B). This argument is dismissed since there is "no reason to suppose in advance" that "the benefits of deliberation always outweigh the costs" (p. 206). This is true, and it is in line with what I argued in my observation, but it does not tell us exactly how long we should deliberate. Moreover, it seems to me that the definition that we have a non-deferral case strongly contributes to the conclusion. The assumptions also play a crucial when he argues that it is "highly unlikely" to find conditions in which there is "greater utility from higher levels of deliberation" (p. 208). But, if we instead focus on search behaviour (which he has assumed away), it seems at least a little more plausible that information about how much information to collect could outweigh the net benefit of one more unit of "direct" information. An analogy could be that spending time on learning how to learn is probably beneficial up to some level before we actually spend time learning what we want to learn. (I should note that I need to think more about these issues and my I do not want to sound too sure about this).

The second argument, that all decisions ultimately can be traced back to an initial decision that was not (and/or could not be) made based on cost/benefit calculations, is dismissed using the following example. Suppose the physician once spontaneously (i.e. without being guided by a decision rule or cost/benefit considerations) read an article about decision theory which influences his decision to do an act. Does this mean that the decision is irrational? Smith answers: "As far as I can see, the answer is no"; "The fact that an arbitrary choice prior to a given decision provided information that influenced that decision has no tendency to show that the decision itself is arbitrary or irrational." (p. 210) I am unsure about this answer. True, given that we have already read an article, then it would be rational to utilize the information even if the decision to read the article was not rational. But, the question is not really whether it is rational to use all information you have (however it was acquired). It is how much information (or deliberation) to collect and whether we can make a rational decision about this. Consider the following example: How much information should you collect about a used car before presenting your bid? If the person decides to collect no information (or no deliberation), I think it is intuitive to say that the bid itself is not rational.

After dealing with the infinite regress problem in simple decision problems (as he calls them), he goes on to make the same arguments when rationality is interpreted as "justified-belief decision guides." The argument is essentially the same in the sense that it is (at least sometimes) possible to escape the infinite regress problem when rationality is defined as justified belief decision guides. He goes into some deep philosophical arguments which I cannot claim to fully understand, but it nevertheless sounds counterintuitive to argue that "the agent's justification on believing something does not depend in any way on what kind of deliberation preceded or generated that belief" (p. 213). In any case, since my knowledge of "foundationalism" and "coherentism" is limited I shall not spend more time on his "zipping forward" problem.

The beginnings of a frame
This is still rather loose, but consider first the following structure. There are at least three kinds of infinite regress problems. First, we have to decide how to decide (and this may lead to an infinite regress). Assuming we have decided how to decide (for instance that we should maximize expected utility), we have to find the optimal level of information and deliberation before the decision rule can be used. Once again, it is possible that this leads to an infinite regress. Finally, we might ask about the optimal use of a given set of information. Now, I do NOT want to argue that these problems are separate. For instance, deciding how to decide requires us to collect information (which leads to the second problem). I nevertheless tend to think that even if we could collect an optimal level of information, one might still have an infinite regress problem in deciding how to decide. (Even if we assume that the optimal level of information is known at every stage, this does not automatically ensure that there is a final end-point.)

Let's try an example. An example of an infinite regress problem that occurs in the third category, may be the infinite regress that sometimes occur when my action depends on my belief of what you will do and vice versa. (My previous observation "Backward Induction, the false counterfactual and terrorism" may be an example that fits here. See www.oocities.org/hmelberg/papers/960321b.htm). Elster's concern about the infinite regress when collecting information about how much information to collect fits the second category of infinite regress problems. Finally, Smith's concern is of the first category.

I am, however, very uncertain whether the frame above is detailed enough. Let me present a list important distinctions when discussing the problem of infinite regress.

Rationality = ?
- Thin vs. Broad
- Justified/reasonable process vs. end-result that conforms to certain axioms

Rationality of ...
- General acts (like deciding how to decide)
- Isolated acts
- Belief-formation for given information
- Information-collection
(Should we use the same definition of rationality for all stages?)

Situations
- Parametric vs, Strategic
- Ergodic vs. Nonergodic
- Fast changing vs. Slow
- Deferral vs. Nondeferral

Types of information
(See "The information required for perfect prediction" at www.oocities.org/hmelberg/papers/960313.htm for more on this)
At the very least we should distinguish between:
* Beliefs about:
- how things are (factual beliefs),
- how things are related (causal beliefs) and
- beliefs about beliefs (strategic beliefs, e.g. of the type "what does he believe that I believe").

Information processing
H. Smith divides this into two categories:
- deliberation and
- search.

R. Radner (1986) presents four distinctions related to information:
- 1. the gathering of information;
- 2. the storage of information;
- 3. the manipulation of information.
- 4. the transmission of information.

Using these distinctions, we could identify a large number of possible places for the infinite regress problem to occur. For instance, Smith claims to concentrate on the regress problem in the context of deciding how to decide, focusing on deliberation (not search) and non-deferral cases. But, the infinite regress problem could show up in a different way if we focused on the context of search and finding the optimal level of information to collect. In sum, using the distinctions above there is a large number of possibilities for different types of infinite regress problems to manifest themselves. This is illustrated in the table below. The end of each branch could give rise to different infinite regress problems.

Possible infinite regress problems

Rationality:
		broad,process			thin, end-state 


		/	\				/	\
 Activity:
	Deliberation	search			deliberation	search


	/	\	/	\		/	\	/	\
parametric strategic parametric strategic parametric strategic parametric strategic
(Eenvironment) 
(and more ...)