Quick reference
| Tool | Plain meaning | Useful form | Concrete example | Misuse to avoid |
|---|---|---|---|---|
| Expected value | Probability-weighted value across outcomes. | EV = Σ p × value | 0.20 × $500 saved − $60 cost = +$40 EV. | Treating money as the only value or probabilities as facts. |
| Base rate | How often a relevant class produces the outcome. | Start outside view; update with case evidence. | Before trusting a career forecast, inspect outcomes for similar transitions. | Ignoring relevant case-specific evidence. |
| Value of information | Best expected outcome after learning minus best now, less research cost. | VOI ≤ avoidable regret | A $25 inspection can prevent a $300 mistake. | Researching when the choice will not change. |
| Utility | Your preference scale, including non-money costs and benefits. | Rank outcomes, then test sensitivity. | A quieter apartment can outweigh a small rent saving. | Pretending one person's utility numbers add cleanly to another's. |
| Minimax regret | Choose the option with the least bad worst missed opportunity. | Compare regret by state of world. | Keep an emergency fund when forecasts are fragile. | Using it when average outcomes dominate and probabilities are credible. |
| Calibration | Confidence should match long-run accuracy. | Of 100 “70%” forecasts, about 70 should occur. | Track weekly predictions in bins. | Confusing confidence with importance. |
Signature tool: should you get more information?
List the realistic actions. If new evidence cannot move you to another action, stop researching.
No change → decide nowName the uncertain variable and two plausible states. Estimate how each state changes the best option.
Focus on decision hingeBuy information only when its likely improvement exceeds money, time, delay, and attention cost.
Benefit > cost → learnWorked tree: inspection before a used bike purchase
Decision now: buy at $300 or walk away. Suppose a hidden repair is plausibly either $0 (70%) or $200 (30%). A $25 inspection reveals the state perfectly and you would buy only if repair is $0.
Without inspection: expected total cost = $300 + (0.30 × $200) = $360. With inspection: expected spend = $25 + (0.70 × $300) = $235, because you walk away in the repair state. The information is worth up to $125 relative to buying blindly in this toy model. Real life adds seller trust, alternatives, and the cost of searching again.
Stopping rule
Write it before browsing: “I will spend 30 minutes, compare three reliable options, and buy if one meets the safety and budget constraints.” A stopping rule protects against research becoming avoidance.
Do not use the calculation literally when the unknown could threaten safety, legality, or a catastrophic loss: then information may matter even when the average looks small.
Frame the decision before calculating
1. Define the action
Use verbs: accept, decline, delay, pilot, insure, delegate. Include the status quo. “Do nothing” is an action with outcomes.
2. Separate outcomes from states
An action is yours; a state is uncertain. Example: “buy warranty” vs “device fails.” Do not assign a probability to your own unmade choice.
3. Add constraints
Some values are thresholds, not tradeable scores: consent, legal duties, a cash floor, a safety margin, or a promise. Screen for them before maximizing.
4. Classify reversibility
Two-way door: cheap to reverse; move, test, learn. One-way door: costly to reverse; seek stronger evidence, options, and consent.
5. Name opportunity cost
Every hour, dollar, and attention unit has another use. A purchase with positive EV can still lose to the best available alternative.
6. Do sensitivity checks
Change the pivotal probability or payoff. If your answer flips from 20% to 30%, do not announce certainty; investigate that hinge or prefer a robust option.
Expected value, utility, and tails
| Situation | Useful calculation | What the calculation misses | Practical correction |
|---|---|---|---|
| Insurance | Compare premium to probability × uninsured loss. | Losses may be unaffordable even if average value is negative. | Protect against ruin; self-insure tolerable losses. |
| Career experiment | Estimate upside × chance, downside × chance, and time. | Learning, network effects, and path dependence. | Use a reversible pilot with a review date. |
| Safety measure | Small probability × large harm can still matter. | Probability is uncertain; harms may be noncompensatory. | Use layers, margins, and precautions proportional to severity. |
| Purchase | Price difference versus expected use value. | Maintenance, resale, and attention cost. | Set a lifetime-cost and usage assumption; test it. |
Risk aversion is not a math error. For most people, the 10th lost dollar matters more than the 10th gained dollar at a given budget level. Expected utility represents that curvature; it is not merely expected cash. The classic expected-utility framework represents preference over lotteries under substantive assumptions, including independence; it is a model, not a command.
Base rates, updates, and calibration
Outside view → inside view
Start with a reference class: comparable products, projects, conditions, or decisions. Then ask which case evidence genuinely distinguishes this case. Example: do not forecast a renovation only from your contractor's optimism; start with comparable completed projects, then update for scope and constraints.
Bayes in plain language
A signal changes a probability in proportion to how expected that signal is under each hypothesis. A positive test is not a diagnosis without a base rate and test characteristics. Avoid arithmetic theater: if the inputs are weak, use broad ranges and consult domain experts for high-stakes decisions.
Calibration practice
Record a claim, deadline, probability, and resolution rule: “70% chance I finish draft by Friday 17:00.” Review in probability bins monthly. A Brier score is the mean squared difference between a binary outcome and a forecast probability; lower is better, but a score is useful only with a clear event definition.
Intervals beat fake precision
For uncertain duration, write P50 and P90: “likely 3–5 hours; reserve 8.” Distinguish an estimate from a commitment. The point is not to predict perfectly; it is to make surprises legible and budgets resilient.
Decision tools by failure mode
Decision tree — uncertainty branches matter
Put decisions in squares and chance events in circles. Work backward from each outcome. Use when sequence matters: a pilot may reveal information before an expensive commitment. Gotcha: a polished tree can conceal invented probabilities; label assumptions and test the branches that change the recommendation.
Weighted matrix — make trade-offs inspectable
List criteria, score each option consistently, and show weights. Example: apartment: commute 35%, monthly cost 30%, noise 20%, layout 15%. Gotcha: do not use a weighted score to smuggle a deal-breaker; write hard constraints separately.
Premortem — surface foreseeable failure
Imagine it is six months later and the plan failed. Ask each person to name one cause, then assign an owner and early warning. Gotcha: pair it with a success case so caution does not become paralysis.
Robust / satisficing choice — preserve slack
When probabilities are too unstable, choose an option that remains acceptable across a wide range: savings buffer, diversified supplier, reversible contract. Gotcha: robustness has a cost; do not demand maximal safety for trivial choices.
Game lens — incentives and commitments
Ask who acts after you, what each person can observe, and what each is rewarded for. Example: an advisor paid on sales has a different incentive from a fee-only advisor. Gotcha: incentives matter without making everyone cynical or malicious.
Common mistakes / anti-patterns
False precision
“27.3%” often means “I have no calibrated range.” Use a range, explain the source, and identify the threshold where your action changes.
Sunk-cost loyalty
Past expense is relevant only if it changes future options. Ask: “If I had not already paid, what would I choose now?”
Proxy optimization
Maximizing a score, salary, followers, or speed can destroy the actual objective. Write the underlying value beside the metric.
Overresearching low stakes
Information has a cost. Use a timer and stopping rule; reserve deep research for high impact, irreversibility, or a close decision.
Confusing probability and importance
A 1% event can deserve planning if it is catastrophic; a 90% event can deserve little attention if it barely matters.
Casual interpersonal utility arithmetic
Your “8/10” and another person's “8/10” are not automatically comparable. Discuss rights, consent, distribution, and uncertainty explicitly.
One-page decision worksheet
- Decision and deadline: What action is actually due, and by when?
- Options: Include delay, pilot, and status quo.
- Constraints: What cannot be traded away?
- States / outcomes: What can happen under each option?
- Base rates and evidence: What is known, guessed, and worth learning?
- Hinge: Which uncertain input would change the choice?
- Reversibility and regret: Can you recover if wrong?
- Stop rule and review: When do you decide and when do you revisit?
For medical, legal, financial, or safety decisions, this framework organizes questions; it does not replace qualified professional advice or consent processes.
Sources and related guides
The expected-utility formula and its representation assumptions are explained in the Stanford Encyclopedia of Philosophy’s decision theory entry; the Principles of Forecasting literature is a useful route into calibration and reference classes. Continue with actual risk dashboard, audit odds, insurance worth it, medical NNT, P(doom) calculator, and lifestyle calculator.