Alternative in Decision theory

 

Alternatives

A highly controversial issue is whether one can replace the use of probability in decision theory by other alternatives.

Probability theory

Advocates for the use of probability theory point to:

• the work of Richard thelked cox for justification of the probability axioms,
• the Dutch book paradoxes of Brunio de fenetti as illustrative of the theoretical difficulties that can arise from departures from the probability axioms, and
• the complete class theorems, which show that all admisible decision rules are equivalent to the Bayesian decision rule for some utility function and some prior distribution (or for the limit of a sequence of prior distributions). Thus, for every decision rule, either the rule may be reformulated as a Bayesien procedure (or a limit of a sequence of such), or there is a rule that is sometimes better and never worse.

Alternatives to probability theory

The proponents of fuzzy logic, possibility theory, quantum cognitation, Dempster-shafer theory, and info-gap decision theory maintain that probability is only one of many alternatives and point to many examples where non-standard alternatives have been implemented with apparent success; notably, probabilistic decision theory is sensitive to assumptions about the probabilities of various events, while non-probabilistic rules such as minimax are robust in that they do not make such assumptions.