Ted Winslow <egwinslow at rogers.com> wrote: andie nachgeborenen wrote:
> No, Arrow's social choice theory is decidedly not game theory.
I didn't say it was.
I was pointing to a possible psychological relation based on the Arrow's relation to the socialist calculation debate. That relation is spelled out in Mirowski's Machine Dreams. I don't have the book handy, but there is a review of it at (interestingly enough) that reproduces the relevant part of the book (as well as other stuff re the relation, including the institutional relation, between Arrow/Debreu "general equilibrium theory" and "game theory").
"According to Mirowski, an even more famous economist found himself gripped by the need to respond to Mises and Hayek. Kenneth Arrow’s impossibility theorem 'was also a direct product of Cowles’s participation in the socialist calculation controversy, although few have seen fit to situate it within that context' (p. 302). "Mises and Hayek said that a socialist economy could not function. Arrow turned the tables on them by claiming that a democratic system of majority rule could not generate a consistent set of social preferences. Only 'dictatorial or imposed regimes' could achieve complete logical consistency. 'For anyone steeped in the socialist calculation controversies of the 1930s, it is hard to see it [Arrow’s theorem] as anything other than a reprise of the Cowles theme that the Walrasian market is a computer sans commitment to any computational architecture or algorithmic specification; the novel departure came with the assertion that democratic voting is an inferior type of computer for calculating the welfare optima already putatively identified by the Walrasian computer' (pp. 303–04)."
Another illustration of the same psychology is provided by the following idea of "truth".
"mathematical (economic) models are rigorous (and 'true' in the only useful scientific sense of the word) if they are built on a cogent axiom base - like von Neumann and Morgenstern, and Debreu." (Roy Weintraub, How Economics Became a Mathematical Science, p. 100)
"The Arrow-Debreu model was a major accomplishment; it presented an economy composed of individual, self-interested agents - both utility-maximizing households and profit-maximizing firms - pursuing their own self-interest and whose actions produced an equilibrium in which all choices were potentially reconcile. Put briefly, the pursuit of individual self-interest could lead not to social chaos but to a coordinated social order. But how did a piece of work in mathematical economics actually settle an economic question? How did it come to pass that a particular paper, in a journal at that time read by very few economists, came to be accepted as having established a foundational truth about market economics? These are not questions economists typically ask. 'The theorem proves that ...' is enough information to persuade economists that knowledge associated with the theorem is secure knowledge. Professional economists are confident about the result and the implications of the equilibrium proof, and no one needs to attend to the means of its construction: the validity of the equilibrium proof in incontrovertible. Economists-in-training must learn that the existence of a competitive equilibrium has been proved. All economists can make use of the proof of that result without subjecting it to incessant challenge and reassessment." "Scientists take some components of their research as given; intellectual paralysis awaits the scientist who seeks to reopen every foundational issue every day. For most economists the competitive equilibrium proof is a tool to use with little regard to how the tool was constructed. Those who study science use the idea of a 'black box' for settled results that are locked up and impenetrable, and thus closed to current investigation. For every science, black boxes are both healthy and necessary." (pp. 183-4)
Ted
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