Research On Bayesian Decision Theoiy

The Study of Decision Theory that can be traced back to18thcentury; the firstintegrated system of Bayesian decision theory was built in Savage’s famous book,“The Foundations of Statistics”(1954). Savage’s decision theory is also calledtraditional Bayesian decision theory or classical Bayesian decision theory. Bayesiandecision theorists argue that, rational agents should maximize their subjectiveexpected utility when adopting actions. In order to demonstrate this view, theyprovide a representation theorem, simultaneously showing that any decision maker, aslong as whose belief and desire satisfy the definite axiom restrictions, would be aBayesian decision theorist that believes expected utility maximization.However, the Newcomb problem makes the Bayesian decision theorists havedifferent views about how the rational agent should behave, and forces them into twoseparate schools, that is, the schools of “evidential decision theorists” and “causaldecision theorists” differentiated by how rational agents should choose when facedwith Newcomb problems. Evidential decision theorists believe that the mostauspicious option should always be selected. In their opinion, actions should beevaluated by the evidence they provide for thinking that desirable outcomes willresult. On the other hand, causal decision theorists argue that the most efficaciousaction should be selected. In their view, the actions should be assessed on the basis oftheir ability to causally promote desirable outcomes, and rational agents will alwaysperform an act that is maximally efficacious in bringing about desirable outcomes.The main divergence between evidential decision theory and causal decisiontheory is about the different opinions of what expected utility is. Evidential decisiontheorists think, expected utility and news or evidential value of act A should be equalbetween each other. Causal decision theorists think, act A’s expected utility should bethe same with its efficacy value. There is usually no conflict between evidentialdecision method and causal decision method, in other words, both of them have theidentical advice about rational choice, because the action providing those expectedoutcomes with the best evidence is also the one of causally causing the appearance ofthe outcomes, which makes that efficacy maximization (of causal decision theory) and utility maximization (of evidential decision theory) are equal in value. However,causing and indicating come apart in some special cases, for example, like in thedecision situation showed by Newcomb paradox, meanwhile auspiciousness is nolonger a reliable sign of efficacy, since pursuit of auspicious evidence that could makerational agents choose an inefficacy act. Under these situations, evidential decisiontheory and causal decision theory provide the completely different suggestions.Joyce brings the “image” method to calculate causal expected utility of actions,at the same time, construct a special causal decision theory: conditional decisiontheory. Joyce indicates, actually evidential decision theory and causal decision theoryboth are just special examples of a more general conditional decision theory, theunique difference between the two theories is about the different interpretations to theconcept of “supposition” or “hypothesis”. Evidential perspective explains that thesupposition is indicative, but causal perspective sees it as something to be subjunctive.This conditional decision theory provides expected utility of taking to implement actA as the prospect X. We obtain a united theoretical frame, through turning toconditional decision theory, evidential decision theory and causal decision theorycould be represented by terminologies that are similar in form, upon this frame. Thisalso indicates that the difference between evidential decision theory and causaldecision theory is not as significant as we have usually thought.However, this frame still fails to solve choice dilemma that people areconfronted with Newcomb paradox. Hence, I raise a mixed decision approach basedon the principle of screen off and the maxim of evidential ratifiability, this theorydivides the process of people’s decision making into two stages: the making andimplementation of decision. This approach may well resolve the choice dilemma topeople brought by Newcomb paradox, and also somewhat advance the study ofBayesian decision theory.At the end, I review and reconsider the Bayesian decision theory from theperspective of philosophy and cognition, and give some directions for future research.