Jim wrote:
My feeling is that C was saying that a jury of 12 would be more accurate in its processing of the facts they were given -- to make a _binary decision_ (guilty/not guilty) -- than would be a jury of 1 or 6, assuming that one of the two verdicts is actually valid. It's like saying "two heads are better than one, while twelve are better than two." Obviously, the "facts" they were given will have been limited and biased by the attorneys and the judge, while their interpretation would be limited by any shared ideology or shared social position that limited and shaped their world-views. Further, discussions about complex theological beliefs such as the Rapture or neoclassical economics seem to go against the assumption of binary decision-making. Strictly speaking, the theorem assumes that the jurors vote independently, rather than discussing matters and voting collectively (which is the way juries I've been on have worked).
Group dynamics are ignored. Given a certain kind of individual psychology, for instance, obviously false beliefs - e.g belief in the possibility of Rapture - can come to be held with greater certainty the greater the number of individuals who share them. Projective idenfication generated phantasies about the motives of excluded others can be reinforced by group psychology (as in paranoid conspiracist theories).
There is an account of intersubjective decision making consistent with the conclusion that the realism of judgments will increase with the number participating in the judgment, but it requires the idea of the individuals as "transcendental subjects," i.e. as subjects able to perceive truly. Each subject is limited in perspective by their location in events (their "perspective") so by increasing the number of subjects who communicate about their perception "enlarged thinking," i.e. thinking less biased by the limitations of individual perspective, is achieved. This is Husserl's idea of transcendental intersubjectivity. The word "transcendental" in this context means the capacity to perceive truly so it makes assumptions about the potential character of human experience (it elaborates experience as experience of internal relations, for example).
This is a sublation of Kant's idea of "enlarged thought" as the "sensus communis." Kant develops this idea in the context of elaborating "production through freedom" as artistic creation. "Freedom" here means "through a will that places reason at the basis of its actions." (Critique of Judgment [Bernard trans.], p. 145) This requires "taste" which Kant defines as "the faculty of judging of that which makes _universally communicable_, without the mediation of a concept, our feeling [of pleasure] in a given representation." (p. 138) This in turn requires a "sensus communis," a capacity for "enlarged thought."
"under the _sensus communis_ we must include the idea of a sense _common to all_, i.e. of a faculty of judgment which, in its reflection, takes account (_a priori_) of the mode of representation of all other men in thought, in order, as it were, to compare its judgment with the collective reason of humanity, and thus to escape the illusion arising from the private conditions that could be so easily taken for objective, which would injuriously affect the judgment. This is done by comparing our judgment with the possible rather than the actual judgments of others, and by putting ourselves in the place of any other man, by abstracting from the limitations which contingently attach to our own judgment." p. 136
In the sublation of this by Hegel, Marx and Husserl, the independence
of the actual judgments of others is subtituted for by communication
with others understood to be other transcendental subjects
("universally developed individuals" in Marx's terminology). Other
aspects are also changed e.g. the limitation of "art" to communication
without concepts is removed. Thus sublated, however, these ideas
reappear in Marx's epistemology and in his aesthetics. They underpin,
for instance, his account of true human production in the Comments on
James Mill.Persons are only potentially "transcendental subjects," however. Such subjectivity is the endpoint of a successful developmental process. Where social relations are incompatible with such development, the rationality and realism of group judgment will be limited by psychopathology.
the way I learned the Arrow/Debreu stuff in grad school (UC-Berkeley, then home of Debreu) was that it showed the assumptions one had to make for competitive equilibrium to exist, and that since the assumptions weren't realistic, the Arrow/Debreu conclusions didn't apply. Any deductive theorem cuts both ways.
Weintraub's account both of the beliefs held by economists with certainty and of the generation of this certainty by the "information" 'The theorem proves that ...' doesn't apply to your grad school days at UC-Berkeley then (. But it wasn't the "utility function" approach itself which was called in question, was it?
What grounds are usually offered to justify restricting the discipline to this starting point? Lack of realism in the aassumptions said by some not to matter, isn't it? Weintraub ignores the rationalization of the starting point in terms of "predictive success" i.e. premises are necessarily unrealistic but this is consistent with truth content defined in terms of predictive success. But the conceptions of predictive success adopted in economics won't withstand rational critique (e.g. Keynes's critique of econometric methods). Certainty of belief in the starting point reached on this basis and with no consideration of, indeed no capacity to understand, the alternative starting points of say Marx and Keynes (Marx is ignored and Keynes is interpreted as a "utility function" theorist) isn't rational. What is its source?
Ted
