Suppose an agent with a set of options, who attaches a probability to various outcomes for each option, and who has a set of preferences, or a way of attaching utilities to the various outcomes. A normative decision theory then has the data from which it can recommend some option. A causal decision theory tells the agent to choose the option that (she supposes) has the best chance of bringing about the maximum utility. By contrast an evidential decision theory, also known as Bayesian decision theory, tells the agent to choose the option that is most probably a sign of good fortune or accompanied by good fortune.

In most ordinary contexts, these coincide. But in unusual circumstances, or in the presence of unusual theoretical beliefs they may not. In Calvinism for instance you are already predestined to heaven or hell by God’s fixed decree, and nothing you do can alter that. Whether you sin or avoid sinning is only a (reliable) sign of God’s preceding decision. So suppose that sinning will increase your utility on earth. Then a causal decision theory will recommend that you sin: it means that things are better for you here, and no worse than they will be anyhow in the hereafter. But an evidential decision theory will counsel that since your sinning would be evidence that you are damned, you had better avoid it. In a Newcomb problem causal decision theory standardly counsels taking both boxes, but evidential decision theory counsels taking only the one box. Causal decision theorists claim that in such cases evidential decision theory ‘commends an irrational policy of managing the news so as to get good news about matters which you have no control over' (David Lewis).

If causation acting backwards in time is allowed the contrast is not so stark, since then the evidence of a state may also be a retroactive cause of the state. So your current sinning may not only be evidence of damnation, but the cause or part of the cause of God’s original decision to damn you.