think-expected-value-decision-tree

Expected Value Decision Tree

When a decision turns on outcomes you do not control, the reflex is to argue the options in prose and decide on a hunch. An expected-value decision tree refuses that. It prices the uncertainty: lay out the options as a tree of choice nodes (branches the decider controls) and chance nodes (branches nature controls, each carrying a probability), put values at the leaves, then roll the tree back right to left so every chance node collapses to its expected value (the sum of probability times value) and every choice node keeps its best branch. What survives the rollback is the highest-EV option and the path that produces it. The load-bearing ingredient, the thing a deterministic option matrix cannot express, is the chance node. The output is a decision tree with rolled-back EVs, the chosen branch, and a what-flips-it note, never a bare EV number presented as the answer.

When to Use

• A decision genuinely hinges on uncertain outcomes you can put rough, sourceable probabilities on (a launch with a real failure rate, an investment with uncertain payoffs).
• The structure is sequential - a choice now opens chance events that open later choices ("test first, then decide" vs "commit now").
• The stakes justify making the probability assumptions explicit and inspectable, so a disagreement becomes a disagreement about a named number rather than a clash of intuitions.
• You already have a probability to work with (or can source one), and the remaining question is what to do with it.

When NOT to Use

• The probabilities and values are guessed and then trusted. A tree renders fabricated inputs in the authoritative grammar of arithmetic, manufacturing false precision - the central failure mode. A number with no defensible source does not become trustworthy by being multiplied. Where the probability is the hard part, source a base rate with think-reference-class-forecasting instead of inventing one inside the tree.
• The decision is a one-shot with intolerable downside. EV is an average over many independent repetitions; the law of large numbers guarantees convergence across many bets, not on the single bet in front of you. A positive-EV gamble that includes a small chance of ruin is the wrong call for a one-time, non-repeated decision. The criterion there is risk of ruin or a risk-averse utility, not raw EV - treating the average as the answer is a category error.
• It is mistaken for descriptive truth. EV is normative (what a coherent decider should do given those numbers), not a description of good judgment. People predictably depart from it via the certainty effect and nonlinear probability weighting (Allais 1953; prospect theory, Kahneman and Tversky 1979), and some of those departures are real risk preferences. The tool's job is to surface the tradeoff, not to declare the risk-neutral answer "correct" and the decider's risk aversion a bias.
• The outcome space cannot be enumerated or priced. Deep uncertainty (you cannot even list the outcomes) and incommensurable values that resist a common scale both break the rollback and produce tidy-but-fictional EVs.
• The call is reversible and low-stakes. A two-way door does not need a tree; building one is its own small over-process. Triage with think-one-way-vs-two-way-door first, before reaching for quantitative machinery.