Axioms for a Class of Algorithms of Sequential Decision Making

We axiomatically characterise a class of algorithms for making sequential decisions in situations of complete ignorance. These algorithms assume that a decision maker (DM) (human or or a software agent) has exogenously defined utilities for prizes and she uses the empirical distribution of prizes to calculate the “expected utility” of each action maximising this expected utility at each stage of the decision making process. We show that this class of algorithms is defined by three simple axioms that highlight the independence of the given actions, the bounded rationality of the agent, and the principle of insufficient reason at margin.