Random Matching and Aggregate Uncertainty

Random matching is often used in economic models as a means of introducing uncertainty in sequential decision problems. We show that random matching schemes that satisfy standard conditions on proportionality are not unique. Two examples show that in a simple growth model, radically di¤erent optimal behavior can result from distinct matching schemes satisfying identical proportionality conditions. That is, non-uniqueness has interesting economic implications since it a¤ects the reward and the transi- tion structures. We propose information entropy as a natural method for selecting unique matching structures for these models. Next, we give conditions on the reward and transition structures of sequential decision models under which the models are not a¤ected by non-uniqueness of the matching scheme.

Some Lesson About the Law From Self-Referential Problems in Mathematics

We first describe briefly mathematician Kurt Gödel\u27s brilliant Incompleteness Theorem of 1931, and explore some of its general implications. We then attempt to draw a parallel between axiomatic systems of number theory (or of logic in general) and systems of law, and defend the analogy against anticipated objections. Finally, we reach two types of conclusions. First, failure to distinguish between language and metalanguage in mathematical self-referential problems leads to fallacies that are highly analogous to certain legal fallacies. Second, and perhaps more significantly, Gödel\u27s theorem strongly suggests that it is impossible to create a legal system that is complete in the sense that there is a derivable rule for every fact situation. It follows that criticisms of constitutional systems for failure to determine every answer are unfair: they demand more than any legal system can give. At best they are antilegal in the sense that rejection of such constitutional systems on such a ground would require the rejection of all constitutional systems

Random Matching and Aggregate Uncertainty

Random matching is often used in economic models as a means of introducing uncertainty in sequential decision problems. We show that random matching schemes that satisfy standard conditions on proportionality are not unique. Two examples show that in a simple growth model, radically di¤erent optimal behavior can result from distinct matching schemes satisfying identical proportionality conditions. That is, non-uniqueness has interesting economic implications since it a¤ects the reward and the transi- tion structures. We propose information entropy as a natural method for selecting unique matching structures for these models. Next, we give conditions on the reward and transition structures of sequential decision models under which the models are not a¤ected by non-uniqueness of the matching scheme

Some Lesson About the Law From Self-Referential Problems in Mathematics

We first describe briefly mathematician Kurt Gödel\u27s brilliant Incompleteness Theorem of 1931, and explore some of its general implications. We then attempt to draw a parallel between axiomatic systems of number theory (or of logic in general) and systems of law, and defend the analogy against anticipated objections. Finally, we reach two types of conclusions. First, failure to distinguish between language and metalanguage in mathematical self-referential problems leads to fallacies that are highly analogous to certain legal fallacies. Second, and perhaps more significantly, Gödel\u27s theorem strongly suggests that it is impossible to create a legal system that is complete in the sense that there is a derivable rule for every fact situation. It follows that criticisms of constitutional systems for failure to determine every answer are unfair: they demand more than any legal system can give. At best they are antilegal in the sense that rejection of such constitutional systems on such a ground would require the rejection of all constitutional systems