Tetlock told an amusing story of his debiasing experiment that backfired, in his book I reviewed earlier. He attempted to get participants to explicitly consider a wide range of alternative scenarios in making a forecast, to try to overcome a common bias of focusing too soon in analysis. But his single-minded “hedgehogs” refused to take the scenarios seriously since they thought they already knew exactly what was going to happen; their scores didn’t change. And his open-minded “foxes” wasted so much time delightedly exploring the intricacies of the new scenarios that they lost track of the bigger picture and ended up doing worse in the exercises.

In general there seems to be something of an unstated assumption that just teaching people Bayesian decision theory would be uselessly abstract; I don’t know if this is due to earlier failed experiments, or perhaps reflects experimenters’ judgment that the theory is too complex for average subjects to grasp.

How strong is the empirical evidence that an understanding of the cognitive problems that can result in decision making errors, such understanding the sources and effects of the many forms of bias, improves an individual’s decision making significantly? Or, instead of improving metacognition, does the evidence show that more benefit comes from improving the process itself? Or both?

Is this different for group decision making as opposed to invidividual decision making? In other words, what provides the decisions with the least error – design and execution of the process or training the individual members? Would everyone, from individual consumers to national politicians actually make significantly different choices if they better understood what aspect of this?

A related question. Does a sound understanding of the human learning process, such as it is, improve a learner’s performance significantly? Or should the focus remain on the design of the instruction process itself that in turn drives and controls the learner’s behavior much of the time?

Finally, there are still computational objections to even intuitionism — interpreted computationally, intuitionistic logic limits you to computable functions, but a strongly finitist view might be that “computable” is still too generous, since no one can actually compute a function that takes (say) hyper-exponential space. While I have a good deal of sympathy for this point of view, I think that the logics here are still to immature to try and base a decision theory on.

Finally, I suggest Bayesian beliefs as a normative standard of reference, not as an exact procedure. So it would be a problem if I could not show you Bayesian arguments that our initial inclinations of beliefs about epistemic criteria are full of error. But it is not problematic that I did not exactly calculate Bayesian probabilities when I formed those beliefs. In fact, we have many kinds of data suggesting l(to a Bayesian) large errors in our beliefs about what kinds of beliefs are reasonable. Is this really in any doubt?

This works perfectly sensibly as a probability theory too. The main change is that instead of building probability theory over a boolean algebra (ie, a model of classical logic), you build it up over a Heyting algebra (ie, a model of constructive logic). The constructive failure of the law of the excluded middle becomes the rule that P(X) + P(not X) <= 1. Now, you can do decision and game theory in a standard way over this nonstandard probability theory, though I haven’t analyzed any theorems to see how they decompose constructively. (I need to graduate….)

This choice about the appropriate standard of rationality will be motivated by your opinions about the proper foundations of mathematics (eg, constructive or classical). This, in turn, means that you cannot choose the foundations rationally, because how you rationally update your beliefs depends on your beliefs about the foundations.

There are three main points I would make. First, I would suggest that Bayesianism is ill suited to justifying why we should believe the second premiss, since what we need is an argument for why beliefs are relevantly like noisy data. You have offered some reasons along that line, and my point is that you have engaged in standard non-deductive reasoning rather than offered a calculation of its probability. If this point is correct then the conclusion must be false and all we can talk about are which circumstances are those in which Bayesianism is the right guide. But that is not what you want. Secondly, the second premiss looks like a contingent claim, so the conclusion is too strong and could only apply when beliefs are in fact relevantly like noisy data. Finally, the conclusion has to be amplified in terms of justified belief being a matter of belief formed in accordance with Bayesian principles, but what are they and what exactly would that mean for how our beliefs ought to be? As a matter of fact we do not reason by calculating probabilities except when we are reasoning with *full* beliefs about probabilistic propositions. But your Bayesian wishes to apply these principles to our beliefs in general, including a priori beliefs such as philosophical doctrines (I see that Paul has brought up the class of a priori beliefs that are moral beliefs in his querying the use of Bayesianism). The way you have applied this is by formulating general principles of reasoning by reflecting on the outcomes of the mathematical results, e.g. ‘take account of disagreement’. But that, by being only supplemental, is to acknowledge the priority of the standard modes of non-deductive reasoning.