A Unified Model of Induction
Date du début: 1 déc. 2011,
Date de fin: 30 nov. 2016
In a recent paper with Larry Samuelson and David Schmeidler, we have proposed a model of inductive learning that unifies Bayesian, case-based, and rule-based learning. The model allows one to study the dynamics of induction, and, in particular, it showed that under fairly reasonable conditions, a reasoner who does not know the process she is facing is likely to converge to put more weight on case-based reasoning viz. a viz. Bayesian reasoning. The present proposal aims to generalize and extend this project in several directions. First, we intend to develop a decision theory under uncertainty that would accompany it, thereby unifying several existing decision theories and studying the dynamics of their relative importance in determining people's mode of decision making under uncertainty. Second, we intend to extend the present model, which is akin to representation of information by a capacity, to a multiple-capacity model, bringing together ideas from the multiple-prior model with the capacity model, and examining the implications of such a model to decision making. Third, we wish to study the origin of counterfactuals and their usage, based on a variant of the basic model, and to study their implications to game theoretic analysis. Fourth, we plan to study the dynamics of case-based vs. rule-based reasoning, as determined endogenously by the accumulation of data, and to extend our empirical similarity approach to this set-up.
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