by Hans O. Melberg

Assume that you have to decide how much information to collect before you make an important decision, for instance a major business investment. Is it possible to make a rational decision on how much information to collect?

The question is important because many economic theories assume that a rational decision is possible, for instance theories of investment. But if no rational decision is available the actual decision that was made cannot be explained as the outcome of a rational choice. Three implications follow. First, some of the theories that rely on rational choice agents are incomplete and possible incorrect as explanations - such as the mentioned theories of investment. Second, we should seek to examine exactly how these decisions are made (If they are not - and cannot be - rational, then how do individuals make up their mind?). Third, the reliance on rational choice assumptions may still be justified if the aim is to predict (as opposed to explain) behaviour since natural selection may imply that people behave "as if" they were rational.

I shall discuss these three implications in turn, but first of all the question must be answered: Is it possible to make a rational decision on how much information to collect?

The economists Roy Radner believes the answer is "yes." As he writes:

Against Radner, we may quote the social scientist Jon Elster, who writes that:

In sum, there seems to be a real disagreement, but short quotations are not enough to determine who is right. To do so, we need to examine the details of the arguments.

Radner argues that the so-called Wald paradigm solves the problem of costly observations. He gives two examples. First, imagine that you are supposed to decide whether a shipment of artillery shells is of acceptable quality. In order to determine this, you need to fire a sample of shells to see if they work. Wald showed that under certain assumptions the optimal procedure was not to take a fixed sample, but to use a sequential procedure. That is, one would decide whether to fire one more shell based on the result from the firing of previous shells. The second example, is how to best test a new drug in a clinical trial. Once again it is possible to find an optimal number of trials using the sequential procedure described above. In short, in some situations it is possible to decide how much information to collect before we draw a conclusion.

Elster's argument seems to be that in some situations we simply do not know the precise marginal value of gathering more information. A detective might have discovered a new piece of information if he had spent one more hour on the case, but there is no way he could know in advance that doing so would result in a very valuable piece of information. However, Elster is careful to point out that the argument does not apply equally to all situations; Sometimes the gap between the lower and upper bound is narrow and it is possible to form relatively reliable estimates:

Or, in short:

It seems to me that Elster's argument is more general and correct. Radner's two examples do not amount to a general argument that it is possible to collect an optimal amount of information. In fact, he picks examples from what Elster calls "highly stereotyped situations" and he ignores the cases in which it is difficult or impossible to conduct experiments or use the past as a reliable guide to future events. The problem is not that Radner is unaware of the distinction; when discussing the problems created by computation and communication he argues that "it will be useful ... to distinguish decisions that are relatively routine, or periodic, from those that are relatively unique or 'one time only' ..." (Radner 1996, 1364). Yet, he fails to apply this distinction when it comes to the problem of collecting information. [If one want to speculate why, it is evident from the article that his interest is to prove the "inevitability of decentralized decision-making" (Radner 1996, p. 1366). This led him to focus on the factors that created this inevitability and ignore other problems.]

It is easy to argue for the theoretical possibility that sometimes it is impossible to make a rational choice. However, the real empirical question is whether this problem occurs frequently enough in important decisions to be worth studying closer. I believe the answer is yes and I want to use investment as an example.

The simple theory of investment says that one should choose that project which has the highest expected, discounted, net present utility. Expected because you need to make assumptions about the probability of sales and costs in the future; Discounted present utility because one dollar in ten years is worth less than one dollar today; Net because you must balance the costs and the benefits; Utility and not value since the utility of a sum (A) is usually not the same as the utility of half A + the utility of half A. The point in the current context, is not that this is a very complex calculation (which it is), but that it may be difficult to find a rational basis for deciding how much information to seek before you make up your mind. How is it possible to form rational expectations about interest rates the next twenty years? What kind and how much information would be optimal to decide the issue? Moreover, the chain is not stronger than its weakest link. Or, in other words, even if it is possible to decide on an optimal amount of information for many of the issues, the whole process breaks down if it is impossible in one aspect.

One might argue that the issue could be determined by looking at previous investment decisions (your own and other people), how much information that was collected then and the end-profit of the project. However, this seems too crude. Some decisions and environments require more information than others do. To solve this one might try to collect the level of information that proved to be the most profitable for projects similar to the one you are considering. However, this raises the question of by what criteria we may judge one situation to be similar to another. It also raises the question of whether this is an area in which it is possible to learn from the past at all in this way. In any case, I do not think it is possible to find a unique and rational solution to the problem of information-gathering using this device. We lack a "rational" way of defining "similar" situations and sometimes there may be no "similar" situations to learn from. This leads me to conclude that the problem information-gathering having no uniquely rational solution is real and not insignificant in economics.

What about natural selection and "as if" arguments?
To rescue the rational choice argument, one might try to argue that non-optimal decision-makers will fail and those who happen to hit the correct trade-off will prosper. For instance, Friedman (1953) makes this kind of argument on behalf of rational choice analysis. On the surface this may appear plausible, but a closer look reveals problems. The problem is this: It is likely that the correct level of information gathering (or the correct rules for doing so) changes over time. If the speed of the selection mechanism (and/or the mutation mechanisms) is slow relative to the changes in the environment it is not true that natural selection makes sure that the population consists largely of people behaving "as-if" they were rational. The issue is clearly empirical: How fast does the economy change the optimal information gathering level (or rule) and how speedy is the selection mechanism (bankruptcy). It is at least not obvious that the selection mechanism is quick enough relative to the environmental changes to justify the "as-if" analysis. [For more on this, see R. Nelson and S. Winter (1982) An Evolutionary Theory of Economic Change and Jon Elster's review of the book in London Review of Books vol. 5 (1983) no. 9, pp. 5-7].

To determine the optimal level of information gathering, we need to collect information on how much information to collect. This, in turn, requires us to collect information on how much information we should collect in order to determine the correct information gathering level. This chain goes on infinitely and this infinite regress has made some people argue that no rational solution is possible. For instance, in the mentioned review of Nelson and Winter, Elster claims that :

Theoretically, I wonder if the argument about infinite regress is watertight since the regress may have a solution in the limit if the value of activity at one level decreases from the previous level. Moreover, the use of the term "rational" may need some further discussion in this context: If it simply means the best possible decision-making procedure, then the demonstration that one procedure is impossible discredits that procedure, not rationality.

The argument against natural selection is also open to attack since there might be higher level factors that are adaptive even in changing economic environments. For instance, the ability to learn and be flexible might be beneficial in fast changing environments. Hence, the fact that environments are fast changing do not necessarily implies that natural selection argument fails.

Let me elaborate on the point that there may be a solution to the infinite regress problem in the limit. The argument must be that the value of collecting information about how much information to collect must be lower than the value of gathering information directly relevant to the problem (or maybe the argument should be couched in marginal terms? That is, at each level we reach the marginal costs = marginal benefit of information at a lower information level). If this is true, one would eventually reach a point at which it was not profitable to collect any information. The "optimal" amount of information about how much information to gather about how much information to gather about how much information to gather (and so on) might be zero. Logically this seems possible. One might, however, ask whether it is plausible. For instance, "learning how to learn" might initially have a high payoff compared to "learning." But, if there are few reliable techniques for learning how to learn then the payoff may be lower. Similar arguments may apply to information: the value of direct information may be higher than the value of gathering information about how much information to gather if there are few reliable devices for doing so. In any case, this is an empirical argument. Now, if it is true that we reach a point in the chain in which the value is zero, the rational action would be to base the decision on the facts you know (without spending time gathering more information).

When I started this observation I intended to explain why it sometimes was logically impossible to make a rational choice on the issue of how much information to collect before making a decision, and that the "as-if" justification for rational choice analysis was dubious. While writing, I discovered that the problem in fact turned on empirical issues. On the first, we need to know whether the process of gathering information on how much information to gather has a limit solution. On the second, we need to know whether the speed of the selection mechanisms relative to the speed of environmental changes that lead to changes in the optimal rules. Both are empirical issues.

Of course, for all practical reasons I doubt whether it is practically possible to solve these questions. Moreover, I have only discussed a small problem in rational choice theory (information collection). There are also numerous others - empirical and logical. For instance, another potential logical flaw is the problem of the false counterfactual in backward induction. But this is not the topic of this paper.

Finally, I should add that when we admit that information gathering is costly, we might also find that "imitation" is profitable. Instead of gathering all the relevant information, I simply base my decision on the signals or actions that I receive from other people in the same market. There is no point gathering information about which stock to buy if the stock market is perfectly efficient. Yet, the stock market cannot be efficient if nobody gathers information. One possible stable solution to this, is that some agents collect while others simply immitate the behaviour of those who do. A possible consequence is that some markets may become volatile since the behaviour of a few "leaders" will be immitated by the many that find it profitable to be uninformed.

Elster, Jon (1983), The Crisis in Economic Theory (Review of Nelson and Winter (1982) and J. Roemer (1982), London Review of Books 5 (9):5-7.

Elster, Jon (1985), 'The nature and scope of rational-choice explanations' in Ernest LePore and Brian P. McLaughlin (1985), eds., Actions and Events: Perspectives on the philosophy of Donald Davidson, Oxford: Blackwell, pp. 60-72.

Friedman, Milton (1953), The method of positive economics. In: Essays in positive economics.

Melberg, Hans Olav (1990), Verstehen of Correlation (more on natural selection), Papers by Hans O. Melberg. www.oocities.org/hmelberg/papers/940423.htm

Nelson, Richard and Sidney Winter (1982), An Evolutionary Theory of Economic Change, Harvard University Press.

Radner, Roy (1996) "Bounded rationality, indeterminacy, and the theory of the firm", Economic Journal 106 (September), pp.1360-1372.