Pareto Optimal

I. Introduction Let's define decision theory as the study of decisions, specifically their effects on outcomes. There are three main branches of decision theory: descriptive decision theory (how real agents make decisions), prescriptive decision theory (how real agents should make decisions), and normative decision theory (how ideal agents should make outcomes). Since decision theory as a field is too broad to be summarized in one post, I'll primarily focus on normative decision theory and only two-thirds of it. Decisions under ignorance, rational choice theory, bounded rationality, prospect theory, heuristics, and the VNM axioms of rational choice all deserve separate posts. II. Terms and Definitions Before we begin with specific procedures in decision theory, let's start with defining some important terms. We can define a decision as an act or choice an agent has made and an outcome as a result of such decisions. Utility should represent an agent's preference over said outcomes and while may be assigned a cardinal value (such as when the agent is VNM-rational), is still a representation of ordinal preferences. Decisions can be made under certainty, risk, or ignorance. The latter two represent when an agent is uncertain of the outcome corresponding to a decision, however, the former in contrast with the latter allows one to assign subjective probabilities to the outcomes. In this post, only decisions under certainty and risk will be analyzed. III. CDT, EDT, and FDT Finally, we can now discuss three types of decision theory algorithms: Causal Decision theory (CDT), Evidential Decision Theory (EDT), and Functional Decision Theory (FDT). To briefly define each procedure, we can say that CDT recommends choosing decisions that cause the best-expected outcome, EDT recommends choosing which decision "one would prefer to know one would have chosen", and FDT recommends treating a decision as the output of a fixed mathematical function that answers the question,