Foundations of Bayesian Theory: Extensions and Applications

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Since the beginning of the 20th century social scientists were interested in the possibility of quantifying individual beliefs about the likely realization of various events with probabilities. In addition to the obvious philosophical interest this inquiry was intended to provide a behavioral foundations of Bayesian statistics and of subjective expected utility theory that is often used to model decision-making under uncertainty in economics. The failure of exiting theories to attain the aforementioned goal motivated the development of a new approach described in my work on the foundations of Bayesian theory. The objective of this project is to extend the scope and to examine some applications of this approach. The research involves the application of mathematical analysis at two levels: For the envisioned extensions the method is axiomatic and the expected results are representation theorems, namely, the expression of individual preferences and beliefs, respectively, by utility functions and probability measures. The applications involve mathematical modeling of unemployment insurance with moral hazard and its analysis. The objective is to compare the exiting results on optimal unemployment insurance, recognizing that these results may be based on probabilities that may not represent the unemployed beliefs about the likely success of their job-search activities, to the optimal unemployment insurance program under the new theory. The project will also address the issue of elicitation of probabilities that express individual beliefs.This research will highlight the theoretical and empirical importance of correctly assessing individual beliefs for the purpose of designing incentive contracts and public policies in which incentive issues are essential. It will also extend the behavioral basis of the Bayesian methods used in statistical analysis.