Expected Value: How Can We Make a Difference When We’re Uncertain What’s True?

Core claim

Because every action has uncertain consequences, impact should generally be assessed by considering each possible good and bad outcome, weighting it by its probability, and summing the results. But maximising expected value is a theoretical ideal, not a command to calculate everything: real decisions often call for robust heuristics, moral constraints, risk sensitivity, and humility about model error.

The basic idea

• In practice, we never know all the effects of an action, especially its indirect and long-term consequences.

• Expected value provides a way to compare uncertain options:

  expected value = Σ (value of an outcome × probability of that outcome)

• Both benefits and harms belong in the calculation. A free beer with a 1% chance of containing poison is not attractive because the small probability is outweighed by the severity of the bad outcome.

• A rescue effort with a 10% chance of saving 100 people has an expected value of 10 lives saved. One with a 20% chance of saving 50 people has the same expected value.

• Real estimates are rarely this precise. The point is not that probabilities are known exactly, but that a rough, informed estimate can be better than ignoring either likelihood or magnitude.

Why use expected value?

• If someone repeatedly selects options with the highest expected value, they should statistically obtain more value over time.
• Every action already involves uncertainty, so refusing to weigh possible outcomes does not avoid the problem; it leaves the weighting implicit and inconsistent.
• Expected value is attractive because it is a simple, general, and comparatively defensible way of combining:
  • how good or bad each possible result would be;
  • how likely each result is.
• It prevents two common errors:
  • chasing spectacular outcomes without considering how unlikely they are;
  • preferring certainty even when a somewhat riskier option offers far more expected benefit.

The article’s four qualifications

The rest of the piece limits the naive slogan “always maximise expected value” in four ways:

1. Expected value is an ideal of evaluation, not always the best day-to-day decision procedure.
2. Impartial impact is not the only morally relevant consideration.
3. Classical expected value assumes risk neutrality, which is inappropriate for many resources with diminishing returns.
4. Tiny probabilities and enormous stakes generate paradoxes for which decision theory has no settled answer.

A theoretical ideal, not a practical methodology

• There is a difference between a criterion of success and a method for choosing actions.
• If the aim is greater positive impact, then—other things equal—the ideal target is the option with the highest expected impact.
• It does not follow that every decision should be made with a spreadsheet of explicit probabilities and utilities.
• Quantitative estimates can fail through:
  • model error;
  • omitted variables;
  • motivated or overoptimistic probability assignments;
  • Goodhart’s law, where optimising a proxy breaks its connection to the goal;
  • the time cost of analysis itself.
• Explicit calculations are useful when options and outcomes are sufficiently legible, such as comparing established global-health interventions.
• In many other situations, better methods include:
  • rules of thumb;
  • robust arguments that survive many assumptions;
  • qualitative comparisons;
  • intuition or quick decisions when the stakes do not justify more analysis.
• 80,000 Hours itself rarely gives careers explicit, quantitative expected-impact scores. Instead, it uses proxies such as importance–neglectedness–tractability, leverage, and career capital.
• A valid proxy must preserve both halves of expected-value reasoning: the size of possible outcomes and the chance of achieving them.

Expected impact is not all that matters

• The article uses expected value mainly to compare impartial consequences, but rejects treating impact maximisation as the only source of reasons.
• 80,000 Hours does not generally endorse doing harm in one’s career even when the person believes the action has positive expected value.
• Serious downside risk and damage to a field deserve special care, partly because agents are fallible and may be systematically overconfident about offsetting benefits.
• Rights, character, honesty, and other moral considerations may constrain which actions are permissible.
• Personal values—including duties or loyalty to friends and family—also matter.
• The result is moral pluralism: expected impact is an important dimension of a decision, not a licence to ignore everything else.

Risk neutrality and diminishing returns

When risk neutrality can make sense

• For outcomes valued approximately linearly, a riskier option can be clearly better. The article prefers a 50% chance of saving 100 lives (50 expected lives) to certainty of saving 10.
• Individual altruists may sometimes rationally take more career risk than conventional advice recommends, especially when:
  • the upside is unusually high;
  • downsides are contained;
  • they retain a personal safety net;
  • others in the cause are pursuing uncorrelated strategies.

When it does not

• Expected-value reasoning in its classical form assumes the decision-maker is neutral between variance profiles with the same mean.
• Many resources have diminishing marginal value. The first $1 million may be easy to allocate effectively; after $10 billion, additional high-quality opportunities become much harder to find.
• Consequently, doubling a very large resource pool adds less altruistic value than losing the pool destroys. Maximising expected dollars is then not the same as maximising expected good.
• Risk neutrality is more plausible when the actor is small relative to the cause and their outcome is not correlated with what happens to other funders or workers.
• At the level of an entire cause, the article guesses that money often has roughly logarithmic returns, implying substantial risk aversion.
• Moral uncertainty, model uncertainty, and general reasons for moderation provide further arguments against 100% risk neutrality.

Objections and extreme cases

• Expected-value theory becomes controversial when tiny probabilities are paired with enormous or unbounded amounts of value. Classic examples include Pascal’s wager and the St Petersburg paradox.
• The article’s central thought experiment offers:
  • a 51% chance of doubling the future value of the world;
  • a 49% chance of ending the world.
• In a simplified arithmetic sense, the bet can have positive expected value. Yet the authors would refuse it, even if the stated probabilities were known to be accurate.
• Repeatedly taking bets of that structure drives the probability of eventual extinction toward 100%, highlighting a conflict between one-shot expected value and acceptable long-run strategy.
• This shows that naive expected-value maximisation can fail even as an ideal, not merely as a practical calculation tool.
• Alternative decision theories have paradoxes too. Cases involving vast stakes, tiny probabilities, and “fanaticism” remain open questions in ethics and decision theory.
• 80,000 Hours explicitly rejects fanatical behaviour, especially harmful action justified by speculative upside. Considering multiple moral perspectives normally rules such actions out.

A practical decision procedure

The article implies a layered approach:

1. Define the relevant outcomes, including indirect benefits and serious harms.
2. Compare magnitude and probability together; do not optimise one while neglecting the other.
3. Use explicit estimates when they clarify the choice, but prefer robust proxies or heuristics when detailed numbers would be spurious.
4. Adjust for diminishing returns and correlated risk, especially when managing large pools of money or strategies shared across a community.
5. Apply moral and personal constraints concerning rights, character, loyalty, and unacceptable harm.
6. Stress-test extreme conclusions for model error, fanaticism, and sensitivity to tiny probabilities.
7. Remain uncertain about the theory itself rather than committing completely to a single formal framework.

What expected value contributes even without numbers

• It disciplines intuition by forcing attention to both stakes and likelihood.
• It explains why a low-probability intervention may still be worthwhile when its potential benefit is large, without implying that every enormous speculative claim deserves support.
• It helps identify useful proxies: a cause-prioritisation framework can be understood as an attempt to approximate expected impact where direct calculation is impossible.
• It separates disagreements about facts (“How likely is success?”) from disagreements about values (“How good would success be?”).
• It provides a common target against which practical decision rules can be judged, even when those rules outperform explicit calculation in real life.

Takeaways

• Under ordinary uncertainty, expected value is usually the best starting point for thinking about consequences.
• “Use expected value” does not mean “trust any numerical estimate.” A calculation is only as good as its outcomes, probabilities, and omitted assumptions.
• Maximising expected impact does not erase rights, character, personal obligations, or the possibility of catastrophic downside.
• Risk attitude should track the thing ultimately valued. Risk neutrality about lives or welfare does not imply risk neutrality about money when money has diminishing returns.
• Extreme cases expose genuine unresolved problems; confidence in the framework should decrease precisely where speculative stakes make its recommendations most radical.

Notes & Observations

• The most important distinction is between expected value as a criterion and explicit expected-value calculations as a decision procedure. Much criticism aimed at the latter does not refute the former, while defending the former does not validate careless quantification.
• The article is notably anti-fanatical: it introduces expected-value reasoning but repeatedly builds safeguards against using it to rationalise harm or reckless bets.
• The discussion of risk becomes clearer when framed in terms of utility rather than raw resources. Diminishing returns are not an exception to expected-value theory; they change what should be assigned value in the calculation.
• The piece leaves a real tension unresolved: if the 51/49 extinction gamble has positive expected value under the stated utility function, refusing it requires revising that utility model, adopting a different decision rule, or treating extinction as a constraint. The authors acknowledge the problem rather than pretending there is consensus.