Evidential Decision Theory
Evidential Decision Theory – EDT - is a branch of decision theory which advises an agent to take actions which, conditional on it happening, maximizes the chances of the desired outcome. As any branch of decision theory, it prescribes taking the action that maximizes utility, that which utility equals or exceeds the utility of every other option. The utility of each action is measured by the expected utility, the averaged by probabilities sum of the utility of each of its possible results. How the actions can influence the probabilities differ between the branches. Causal Decision Theory – CDT - says only through causal process one can influence the chances of the desired outcome . EDT, on the other hand, requires no causal connection, the action only have to be a Bayesian evidence for the desired outcome. Some critics say it recommends auspiciousness over causal efficacy.
CDT uses probabilities of conditionals and contrafactual dependence to calculate the expected utility of an action – which track causal relations -, whereas EDT simply uses conditional probabilities. The probability of a conditional is the probability of the conditional being true, whereas the conditional probability is the probability of the consequent given the antecedent. In most usual cases this two probabilities are the same. However, David Lewis proved  its’ impossible to probabilities of conditionals to always track conditional probabilities. Hence evidential relations aren’t the same as causal relations and CDT and EDT will diverge depending on the problem. In some cases EDT gives a better answers then CDT, such as the Newcomb's problem, whereas in the Smoking lesion problem where CDT seems to give a more reasonable prescription.
- Joyce, J.M. (1999), The foundations of causal decision theory, p. 146
- Lewis, D. (1976), "Probabilities of conditionals and conditional probabilities", The Philosophical Review (Duke University Press) 85 (3): 297–315