I would like to contribute to this, since I take exception to Gul and Pesendorfer’s paper on quite different grounds that no one seems to mention. That in a moment, but first I want to offer a half-defense. This is, of course, strictly wrong:

“Neuroscientific evidence cannot refute economic models because the latter make no assumptions and draw no conclusions about the physiology of the brain.”

It is wrong because of computability and complexity. Mappings can’t be computed instantaneously or by magic. If we simply want to score debating points, we are done. But scoring debating points is for sophomores in debate club.

I think that, in their own innocent-of-cognitive-science way, Gul and Pesendorfer are trying to articulate what David Marr articulated so well. From the “Marrian” perspective, formal neoclassical economic theory is “computational theory:” An attempt to guess at what is computed and why. It is like addition, or the mathematics of stereopsis. Nonlinear optimization, addition and stereopsis can all be handled by a great number of alternative algorithm/representation combinations, and those in turn can all be realized in a large number of physical types of hardware. So, there is some sense in skepticism about looking at hardware, if you are really more interested in what is computed and why. At best, knowing the hardware could put some limits on the kinds of algorithms that are running on the hardware. But, there would (for most big parallel machines) be a huge number of algorithms that could in turn approximate a bewilderingly large number of mathematical mappings with all kinds of error characteristics. Under these circumstances, can you really blame someone for being skeptical about looking at hardware?

Marr’s question is basically this. Suppose visiting alien A is given a hand calculator and opens it up and studies its circuits, while visiting alien B is shown the calculator and told it approximates an operation that is commutative, reflexive, associative, etc., with some known biases. Which alien now has more interesting knowledge about the calculator? It depends on what interests you. If you are interested in building adding machines, maybe you want to be alien A. If on the other hand, you are a social scientist interested in the significance the hand calculator has in this culture, you probably want to be alien B.

The really, real problem with Gul and Pesendorfer, in my own opinion, is that it erases the notion of algorithmic bias in computing mappings. Put differently, it must rule out competence/performance gaps. Indeed, the whole notion of performance as something that can be anything other than maximal gets erased by Gul and Pesendorfer’s worldview. The paper really should have been called “The case for machine-free, algorithm-free economics.”

To the extent algorithms exist in Gul and Pesendorfer’s world, they all perfectly compute all mappings that are relevant to human economic situations. There are no performance failures. If there is something metaphysically ridiculous about their view, surely this must be it; in Gul and Pesendorfer’s metaphysical universe, Alan Turing, Donald Knuth, etc. never said anything of fundamental importance.

I would like to contribute to this, since I take exception to Gul and Pesendorfer’s paper on quite different grounds that no one seems to mention. That in a moment, but first I want to offer a half-defense. This is, of course, strictly wrong:

“Neuroscientific evidence cannot refute economic models because the latter make no assumptions and draw no conclusions about the physiology of the brain.”

It is wrong because of computability and complexity. Mappings can’t be computed instantaneously or by magic. If we simply want to score debating points, we are done. But scoring debating points is for sophomores in debate club.

I think that, in their own innocent-of-cognitive-science way, Gul and Pesendorfer are trying to articulate what David Marr articulated so well. From the “Marrian” perspective, formal neoclassical economic theory is “computational theory:” An attempt to guess at what is computed and why. It is like addition, or the mathematics of stereopsis. Nonlinear optimization, addition and stereopsis can all be handled by a great number of alternative algorithm/representation combinations, and those in turn can all be realized in a large number of physical types of hardware. So, there is some sense in skepticism about looking at hardware, if you are really more interested in what is computed and why. At best, knowing the hardware could put some limits on the kinds of algorithms that are running on the hardware. But, there would (for most big parallel machines) be a huge number of algorithms that could in turn approximate a bewilderingly large number of mathematical mappings with all kinds of error characteristics. Under these circumstances, can you really blame someone for being skeptical about looking at hardware?

Marr’s question is basically this. Suppose visiting alien A is given a hand calculator and opens it up and studies its circuits, while visiting alien B is shown the calculator and told it approximates an operation that is commutative, reflexive, associative, etc., with some known biases. Which alien now has more interesting knowledge about the calculator? It depends on what interests you. If you are interested in building adding machines, maybe you want to be alien A. If on the other hand, you are a social scientist interested in the significance the hand calculator has in this culture, you probably want to be alien B.

The really, real problem with Gul and Pesendorfer, in my own opinion, is that it erases the notion of algorithmic bias in computing mappings. Put differently, it must rule out competence/performance gaps. Indeed, the whole notion of performance as something that can be anything other than maximal gets erased by Gul and Pesendorfer’s worldview. The paper really should have been called “The case for machine-free, algorithm-free economics.”

To the extent algorithms exist in Gul and Pesendorfer’s world, they all perfectly compute all mappings that are relevant to human economic situations. There are no performance failures. If there is something metaphysically ridiculous about their view, surely this must be it; in Gul and Pesendorfer’s metaphysical universe, Alan Turing, Donald Knuth, etc. never said anything of fundamental importance.

If you really want a comprehensive look at these questions I would recommend Ross (2005)[http://mitpress.mit.edu/catalog/item/default.asp?ttype=2&tid=10526] but my problem is less the content of the Gul&Pesendorfer paper than what others are trying to use it for – as a way of keeping out important behavioural criticisms of formal models, and a basis for arguing that cognitive science is not relevant to the field of decision theory. I don’t think the arguments in the paper can actually be used to support such claims.

If you really want a comprehensive look at these questions I would recommend Ross (2005)[http://mitpress.mit.edu/catalog/item/default.asp?ttype=2&tid=10526] but my problem is less the content of the Gul&Pesendorfer paper than what others are trying to use it for – as a way of keeping out important behavioural criticisms of formal models, and a basis for arguing that cognitive science is not relevant to the field of decision theory. I don’t think the arguments in the paper can actually be used to support such claims.