Recursive Rational Choice.
STANFORD UNIV CA INST FOR MATHEMATICAL STUDIES IN THE SOCIAL SCIENCES
Pagination or Media Count:
It is the purpose of the present study to indicate the means by which Kramers results may be generalized to considerations of stronger computing devices than the finite state automata considered in Kramers approach, and to domains of alternatives having the cardinality of the continuum. The means we employ in the approach makes use of the theory of recursive functions in the context of Churchs Thesis. The result, which we consider as a preliminary result to a more general research program, shows that a choice function that is rational in the sense of Richter not necessarily regular when defined on a restricted family of subsets of a continuum of alternatives, when recursively represented by a partial predicate on equivalence classes of approximations by rational numbers, is recursively unsolvable. By way of Churchs Thesis, therefore, such a function cannot be realized by means of a very general class of effectively computable procedures. An additional consequence that can be derived from the result of recursive unsolvability of rational choice in this setting is the placement of a minimal bound on the amount of computational complexity entailed by effective realizations of rational choice.
- Sociology and Law
- Numerical Mathematics