Expected Value Decomposition¶

Why It Matters¶

We judge decisions by their outcomes, not their process - the "outcome bias." This makes learning impossible: lucky bad decisions get reinforced, unlucky good decisions get abandoned. Expected value decomposition forces separation: assess decision quality by the probabilities and utilities you knew at decision time, not by which outcome happened to occur. This enables actually learning from experience rather than learning to be lucky.

The Key Move¶

Before deciding, explicitly list possible outcomes. For each, estimate: (1) probability, based on your current best beliefs, and (2) utility, based on your values/goals. Compute expected value (sum of probability × utility across outcomes). Choose the option with highest expected value. Critically: after outcomes resolve, evaluate your decision process, not your outcome. Did you estimate probabilities correctly? Utilities? If you'd do it the same way again with the same information, it was a good decision even if the outcome was bad.

Classic Application¶

Medical treatment decisions. Surgery has 70% probability of full recovery (utility +100), 20% partial recovery (+30), 10% death (-1000). Expected value: 0.7(100) + 0.2(30) + 0.1(-1000) = 70 + 6 - 100 = -24. Non-surgery has 100% probability of continued pain (utility -40). Expected value: -40. Surgery has higher expected value (-24 > -40), so it's the right decision. If the patient dies (10% outcome), this doesn't make it a bad decision - it was the right bet given the probabilities.

Surprising Application¶

Evaluating relationship decisions years later. You chose to move across the country for a relationship that later failed (bad outcome). Outcome bias says: "I made a terrible decision." Expected value decomposition asks: given what you knew then, what were the probabilities and utilities? Maybe 60% chance relationship thrives (utility +100), 40% fails but you learn and grow (utility +20). Expected value: +68. Staying put: 100% certainty of wondering "what if" (utility +10). The decision was correct given your beliefs and values at the time. The failure provides evidence to update your model, but doesn't invalidate the decision process.

Failure Modes¶

Probability overconfidence - expected value is only as good as your probability estimates. Utility misestimation - you might not know how much you'll value outcomes until you experience them. Ignoring risk aversion - expected value treats all uncertainties linearly; humans prefer certain gains to risky bets of equal expected value. Black swan neglect - extreme low-probability, high-magnitude outcomes that dominate expected value but feel ignorable.

Go Deeper¶

Savage, The Foundations of Statistics; von Neumann & Morgenstern, Theory of Games and Economic Behavior, Chapter 3 on expected utility.