A belief operator derived from preferences is presented. It generalizes ‘belief with probability1’ to incomplete preferences and satisfies minimal requirements for belief operators under weak conditions.

Orthodox decision theory gives no advice to agents who hold two goods to be incommensurate in value because such agents will have incomplete preferences. According to standard treatments, rationality requires complete preferences, so such agents are irrational. Experience shows, however, that...

This chapter provides a critical review of the theories of decision making under risk and under uncertainty and the notion of choice-based subjective probabilities. It includes formal statements and discussions of the various models, including their analytical frameworks, the corresponding...