Evidential Decision Theory

Evidential Decision Theory (EDT) is a major framework within formal decision theory. It operates on the principle that a rational agent should choose actions that maximize expected utility, where utility is calculated using standard conditional probabilities. In simple terms, EDT advises you to take actions that are highly correlated with good outcomes, even if those actions do not directly cause the outcomes.

The Mathematical Core of EDT

In EDT, the expected utility of an action A is calculated by summing the utilities of all possible outcomes O, weighted by the conditional probability of each outcome occurring given that action A is performed:

EU(A) = ∑ P(O | A) * U(O)

Because it relies on the conditional probability P(O | A), EDT does not distinguish between an action that causes an outcome and an action that is merely a symptom or indicator of that outcome. If performing action A provides strong evidence that a highly favorable state of the world exists, EDT recommends action A.

EDT and Newcomb's Paradox

EDT is the philosophical foundation for "one-boxing" in Newcomb's Paradox. In Newcomb's scenario, taking only Box B (Action B) is highly correlated with Box B containing $1,000,000, because the Predictor is highly accurate. Therefore, the conditional probability of Box B being full given that you choose only Box B is nearly 1. EDT calculates a massive expected utility for one-boxing, making it the uniquely rational choice under this framework.

Criticisms of Evidential Decision Theory

The primary criticism of EDT is that it can recommend actions that are causally impotent or even harmful, simply because they correlate with positive states. This is often illustrated by the "Medical Newcomb's Problem" (or the Smoking Lesion thought experiment):

• Suppose a genetic lesion causes both a strong desire to smoke and a high risk of lung cancer. Smoking itself does not cause cancer; the gene does.
• An evidential decision-maker who wants to avoid cancer would choose not to smoke, because smoking is evidence that they have the bad gene.
• However, since they either have the gene or they don't, and smoking has no causal impact on the gene, refusing a cigarette does nothing to alter their actual cancer risk. Critics argue that EDT's recommendation to abstain is irrational in this context.

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