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Bayesian Approach

Named after the 18th-century English cleric Thomas Bayes, the Bayesian approach refers to a distinctive framework for decision making. Accepting the dictum that “probability is the guide to life,” the Bayesian approach provides a model for rational choice in which the expected utility of an action is determined in relation to a person's notions of the probabilities and utilities associated with the potential outcomes of the action under consideration. In considering alternative courses of action, the Bayesian principle is to choose an action with the greatest expected utility. The Bayesian approach has been widely influential in the development of rational choice theory and has been used in the study of rational choice in diverse disciplines, including management science and economics. Three elements central to the Bayesian approach include the Bayesian account of belief, rationality, and learning.

Bayesian Belief

There are two key aspects involved in the epistemology of the Bayesian approach toward belief. The first is that beliefs come in varying degrees of strength. According to Bayesians, beliefs are probabilistic in nature rather than all or nothing. Thus, in the Bayesian approach, we can assign probabilistic values, represented by numbers between 0 (no confidence) and 1 (full confidence), to beliefs, based on the degree of strength that persons have in those beliefs. In the Bayesian approach, the strength of a belief corresponds to the level of confidence that a person has in the truth of the proposition expressed by that belief, which, in turn, can be determined by a consideration of what gamble that person would be willing to accept as fair on the truth of that proposition. Most Bayesians now admit that it is unrealistic to think that most persons can assign numerically precise values to the strength of their beliefs. Bayesians, generally, now only hold that we can represent the beliefs of people in terms of some confidence measure, which orders their beliefs on the basis of their comparative confidence in those beliefs.

Second, since the Bayesian approach takes the strength of a belief to represent the actual conviction that a person has in the truth of that belief, Bayesians endorse a subjectivist approach to probability. Since people do often disagree on the degree to which they believe a given proposition, such a subjective view of probability denies that there are objectively correct probability values that attach to individual beliefs. For instance, if Smith believes Proposition p to Degree x, but Jones believes Proposition p to Degree y, there is, according to the Bayesians, no objective fact about which value is closer to the truth. This subjectivism about belief in the Bayesian approach has been the subject of much criticism, since it seems to imply that it is rational for individuals to assign any degree of probability whatsoever to their beliefs. In response, however, Bayesians point toward their account of rational coherence and rational learning as ways of mitigating the force of such a criticism.

Bayesian Rationality

Although the Bayesian approach places no restrictions on people's assignment of probabilities to individual beliefs, it is not the case that any numerical assignment that agents assign to their beliefs is acceptable within Bayesianism. The Bayesian approach requires that the assignments that persons give their beliefs must obey the axioms of the probability calculus. That is, while Bayesians place no restrictions on the assignment of individual probabilities, they do place important restrictions on the assignments that persons can place on their beliefs taken as a set. In this regard, the Bayesian approach can be seen as offering a type of coherence theory of rational belief formation, since it requires that a person's assignment of probabilities be internally consistent.

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