Causal Decision Theory
Causal Decision Theory – CDT - is a branch of decision theory which advises an agent to take actions that maximizes the causal consequences of desired outcomes . 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 results. How the actions can influence the probabilities differ between the branches. Contrary to Evidential Decision Theory – EDT - CDT focuses on the causal relations between one’s actions and its outcomes, instead of focusing on which actions provide evidences for desired outcomes. According to CDT a rational agent should track the available causal relations linking his actions to the desired outcome and take the action which will better enhance the chances of the desired outcome.
The core aspect of CDT is mathematically represented by the fact it uses probabilities of conditionals in place of conditional probabilities . A conditional probability of B given A - P(A|B) -, simply implies the Bayesian probability of the event B happening given we known A happened, it’s used in EDT. The probability of conditionals – P(A > B) - refers to the probability that the conditional A implies B is true, the probability of the contrafactual ‘If A, then B’ be the case. Since contrafactual analysis is the key tool used to speak about causality, probability of conditionals are said to mirror causal relations. In most cases these two probabilities track each other, and CDT and EDT give the same answers. However, some particular problems have arisen where their predictions for rational action diverge such as the Smoking lesion problem – where CDT seems to give a more reasonable prescription – and Newcomb's problem – where CDT seems unreasonable. 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 always diverge in some cases.
- Lewis, David. (1981) "Causal Decision Theory," Australasian Journal of Philosophy 59 (1981): 5- 30.
- Lewis, D. (1976), "Probabilities of conditionals and conditional probabilities", The Philosophical Review (Duke University Press) 85 (3): 297–315