The expected value of an action is what you get if you multiply each possible result by its probability and add them up. A program that has a 10 percent chance of helping 10,000 people has an expected value of helping 1,000 people, the same as a program certain to help 1,000. Expected value lets a giver compare a sure thing with a long shot on one scale.
Why it matters for giving
Much of the most ambitious work in charity is a long shot: research that may find nothing, advocacy that may lose, a campaign to change a norm that may take decades or fail. Without some way to weigh probability against size, a giver can only choose between “certain” and “hopeful.” Expected value turns that into a question with numbers in it.
Three cautions
The inputs are often guesses. Holden Karnofsky of GiveWell argued in 2011 that an explicit expected-value estimate, built from many rough inputs, should not be taken literally even when its errors are not biased in either direction. It should be combined with a prior view of what similar actions usually achieve. The less certain the estimate, the more it should be pulled toward that prior, so a dramatic but weakly supported claim counts for little.
Tiny chances of huge stakes can take over. If a result is large enough, even a very small probability can dominate the sum. Philosophers call the extreme version of this fanaticism, and MacAskill, Bykvist and Ord treat it as a central problem for anyone deciding under moral uncertainty. The philosopher Amia Srinivasan has argued that expected-value reasoning about speculative risks can end up justifying whatever its users already favored.
It ignores attitudes to risk. Maximizing expected value treats a sure good and a gamble with the same average as equal. 80,000 Hours calls ignoring risk aversion a reasonable approximation for its own purposes. Many givers reasonably prefer some certainty. A portfolio can hold both.
Getting the probabilities right
Expected value is only as good as its probabilities. Forecasters can be scored, for example with a Brier score, and a forecaster whose 70 percent predictions come true about 70 percent of the time is calibrated. Charitology’s Forecasting Platform and Forecasting Tournaments are meant to make the probabilities in giving decisions testable.