Henry's response does an excellent job of moving our discussion along. I accept wholesale his explanation about complexity and chaos, so I'll focus on the second half regarding economic theories.
I like Henry's interpretation of Mises, and I can see where he found support for it and I think this is the correct interpretation, but I'd like to note for the record that Mises' statement regarding action necessarily being rational and that the term rational action is pleonistic does not jive with Henry's explanation. Mises is actually asserting that volitional action is necessarily rational. I disagree with him even on that point, but it is a far more defensible position than stating (as Mises does) that all action is rational.
Given this interpretation of Austrian subjectivism, I think there are two approaches through which behavioral criticisms could be viewed. The first would be to assert that even volitional actions can be irrational. The second is to suggest that there may be more economically significant actions than Mises would suppose that are not volitional. I think these two approaches are just different sides of the same coin. I'd like to preface my discussion of these criticisms by agreeing with Henry, that behavioral critique does not render Austrian economics (or neo-classical economics for that matter) invalid, but merely offers a refinement. The assumption of rational preferences and action that characterizes neo-classical economics and Austrian economics is for the most part (as stated in my Round I:Part I response) a good assumption. This assumption is the critical insight on which both theories are based (as well as many political theories) and yields a great deal of useful theory, theories which have validated themselves quite well in actual practice. The behavioral critique is merely an effort to define some possible boundaries for the operation of these theories.
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Coming around then to the criticism, I think the first step is to question the realm of possibility. We don't know precisely how cognitive processes work, and probably won't any time soon. However, we know enough to speculate. Based on current knowledge I think it is valid to speculate that all cognitive processes may not be equal. We know that the brain is a mechanistic device, that neurons fire in networks, that different parts of the brain are engaged for different purposes. We also know from information theory (as was brilliantly illustrated in Henry's chaos discussion) that some calculations are more difficult than others, and that there are many different methods to achieve approximate results and many degrees of precision which can be applied to calculations for approximation. We also know from computer science that many of the tasks of calculation in which the brain engages are phenomenally complex and difficult from an information processing standpoint. Even given equivalent processing power, human programmers would face immense difficulty trying to program something that could accomplish all that the brain does. Taken altogether, I conclude from this that the brain employs many wonderful shortcut algorithms (heuristics) to allow it to perform with the remarkable efficiency that it does.
From here we need to note a few things about heuristics. We know that (by definition) in the act of approximation, some precision is lost. From experience in mathematics and computer science we know that each heuristic has certain limiting characteristics; each heuristic has varying strenths and weaknesses. In some cases one algorithm for compressing an image file will outperform a second algorithm, where a different image file may yield the reverse result. We also know that it's usually (but not always) the case that the more efficiently a heuristic performs, the greater the loss of precision.
At this point we might make a few conclusions and assumptions about brain operation. Due to its use of various heuristics, it is likely that the brain performs more efficiently on some types of calculations than others. Perhaps more importantly, if we are willing to contemplate that the brain may use more than one unique heuristic to solve the same problem in different situations, the brain may yield a varying quality of results to the same question based on which heuristic is applied at a given time. The final step needed to reach the behavioral position is to suppose that external factors may consistently (and non-volitionally--I'll come back to this) trigger the use of one heuristic over another.
There are a lot of assumptions involved here, and I don't ask you to accept them all as true. I would only ask that you consider them as reasonable proposals not obviously contravened by present knowledge about cognitive processes (and I would be entirely happy to hear any criticisms you have on this point). What you are looking at is the central premise of the deductive argument of behavioral theory. It is a theory which Henry rightly states cannot be proven at this point.
The experiments carried out by behavioral psychologists, as Henry notes, do not fully eliminate the possibility of interfering factors (including rational volitional reasons for the actions taken). However, these data are not meant to prove anything, but rather to offer some support, by whatever limited means are available to us, to the premise above. I again disagree with Mises' position that because we cannot know how cognitive processes work nor definitely predict what action they will produce we must treat them as ultimately opaque and (while accepting Mises' own assumptions on cognition) question no further. His assumptions about which actions are volitional and that volitional actions are rational are no less a reach than the assumptions of behavioral theory. As an unknown quantity, cognitive processes remain open to deductive argument and to experimentation such as it is.
From my perspective, I find the assumptions made by behavioralists to be emminently reasonable. They very much conform to my own intuitions about cognitive processes and my knowledge of data processing and heuristic algorithms and my observations of human behavior. I find that behavioral experiments, although they vary in quality (and I agree that the VCR one is particularly weak), do offer at least some support for behavioral theory. The results of many of them are difficult to interpret as anything but the application of a weak heuristic in a decision which, in other circumstances, humans are capable of applying a stonger one.
To determine, finally, how behavioral theory plays with Austrian subjectivism requires behavioral heuristics to be placed within the context of actions, volition, and rationality. This may be a discussion about cognitive processes, but I see it as rather more a matter of semantics. The key cognitive insight (and a largely subjective one at that) is that we don't generally think in terms of heuristics. I had been planning on making an argument of this, but arriving here I realize that this argument would probably equal in length the rest of this post and I'm not up for that at the moment. Feel free to challenge this premise and I will flesh it out at a future date. For now, suffice it to say that the immense amount of effort invested by cognitive scientists, behavioralists, and computer scientists to uncover the heuristics utilized by the brain speaks volumes about our conscious awareness of the heuristics applied on our behalf. While we do experience a conscious phenomenon of weighing decisions before us, resulting in volitional action, the selection of heuristics and the application of them in the weighing process appears to be entirely subconscious.
The rest of the analysis descends into a semantic morass. In undergrad I took a 500-level philosophy course that dedicated an entire semester to a single question: What is agency (i.e. how do we define a person's actions)? Based on my experiences therein I'll offer the following conclusion to the above conundrum: Nobody has the first fricking clue what any of this means. At some point in the discussion the level of detail is such that we have no remaining useful intuitions about the basic terms (action, volition, intent, etc.) and they become maleable and in some senses interchangeable. But I'll try...
First, going back to my initial theory of rational as "consistent with or based on reason," I conclude that the variation in outcomes caused by the application of various heuristics are irrational. The output of the more precise heuristic here represents a rational action. By contrast the output of the subpar heuristic is simply not consistent with or based on reason. It is rather the product of, in essence, a cognitive defect. There is a sense in which you could say even the better heuristic is irrational, since it also is frequently an approximation, and it is only by comparison to the subpar heuristic that it appears rational. In other words, there is a danger here that I am calling any nonoptimal (in some ultimate sense) decision irrational. That is not my intent. I think there is something noteworthy about the supposition that a) the human mind can apply heuristics of varying quality to the same problem and b) external stimuli can consistently alter which heuristic is applied. I do not assert that the reasoning relied on needs necessarily to be optimal to be rational, but only that the subpar heuristic is inconsistent with that individual's own ability to reason through the problem (applying their own subjective values and objectives in the process), and that the subpar heuristic is applied not due to a rational choice (i.e. I don't have time to think this through), but as the result of the nonvolitional impact of seemingly irrelevant external circumstances. It is this quality that makes it irrational.
Next, in these cases the action is volitional in any meaningful sense, and yet the decision is framed by heuristic analysis which is subconscious and involuntary. What does that mean? One could say that this infection of nonvolitional framing which resulted in an irrational act caused the act to be effectively nonvolitional. This would fit with Mises' view of action (being nonvolitional, it is no longer assumed to be rational), although the scope of behavioral impact on economic actions would remove from his theories many actions that I think he would have thought covered by them. The alternative, which seems rather more straightforward to me, is to consider this a volitional action, but an irrational one, hence my basic conflict with Mises' assumption.
In either case the results would be the same. In the former, we've just removed a lot of economically significant actions from Mises' theory. In the latter Mises' theory would need to be amended to cover only rational volitional actions and the same thing occurs. In either case we now have a whole class of actions for which we need to reformulate existing economic theories.
Whew. Well, that shoots my afternoon. :)