Expected value

The Expectedexpected value is a concept used in situations in which it is desirable to establish the value of different options with uncertain outcomes. The expected value of an actionact is the sum of the value of each potential outcomeof its possible outcomes multiplied by thetheir probability of that outcome occurring. Expected value is useful for selecting between projects.

Illustration

Imagine you'reConsider a person choosing between two medical interventions. The first intervention is a drug that succeeds in 60% of cases, and that gives an extra year of healthy life when it succeeds, and has no impact if it fails.

SupposeConsider another drug that succeeds with a 40% probability, and gives two years of healthy life when it succeeds, but causes harm equal to half a year of healthy life lost when it fails.

Then the expected benefit of this projectintervention is:

Todd, Benjamin (2021) Expected value: how can we make a difference when we’re uncertain what’s true?, 80,000 Hours, September.
An introduction to the concept of expected value.

BibliographyFurther reading

alternatives to expected value theory | altruistic wager | cluelessness | credence | decision theory | moral uncertainty | risk aversion | value of information

alternatives to expected value theory | altruistic wager | cluelessness | credence | decision theory | risk aversion | value of information

Expected value reasoning in everyday lifeBibliography

From https://reducing-suffering.org/does-vegetarianism-make-a-difference/

Sometimes people agree that meat production harms animals, but they say that their own individual meat consumption won't make a difference compared with the scales of production decisions that meat companies make.

The argument might go:

"The only decisions that will actually affect the amount of animal suffering are massive investment choices: whether to build a new factory farm or whether to put an addition on a colossal chicken house."

"One consumer cannot even change the bulk purchases that each individual grocery store or dining center makes, much less the collective demand that all of these retailers exert."

"A certain amount of meat will be produced whether I am vegetarian or not, so why shouldn't I at least subsist off those excess scraps, instead of letting them go to waste?"

However, in reply:

Suppose that a supermarket currently purchases three big cases per week of factory-farmed chickens, with each case containing 25 birds. The store does not purchase fractions of cases, so even if several surplus chickens remain each week, the supermarket will continue to buy three cases.

This is what the anti-vegetarian means by "subsisting off of surplus animal products that would otherwise go to waste": the three cases are purchased anyway, so consuming one or two more chickens simply attenuates the surplus.

What would happen, though, if 25 customers decided to buy tempeh or beans instead of chickens? The purchasing agent who orders weekly cases of chickens would probably buy two cases instead of three.

But any given consumer can't tell how far the store is from that cutoff point between three vs. two cases. The probability that any given chicken is the chicken that causes two cases instead of three to be purchased is 1/25.

If you do avoid the chicken at the cutoff point, you prevent a whole case—25 chickens—from being ordered next week. Thus, the expected value of any given chicken is (1/25) * 25 = 1 chicken, just like common sense would suggest.

So, in fact, it is true that any given individual is unlikely to make a difference through meat-consumption choices, but there's a small chance that they make a huge difference, and the expected value works out such that avoiding eating one chicken or fish roughly translates to one less chicken or fish raised and killed. (This ignores some considerations about the price elasticity of meat, but these don't substantially change the conclusion.)

Further reading

GiveWell. 2016.Conley, Sean (2016) Deworming might have huge impact, but might have close to zero impact., The GiveWell Blog, July 26.
An example of research using expected value thinking.

Karnofsky, Holden. 2016.Holden (2011) Why we can'can’t take expected value estimates literally (even when they'they’re unbiased), The GiveWell Blog, August 18 (updated 25 July 2016).
A caution about taking applied expected value estimates literally.

Wikipedia. 2016a.Tomasik, Brian (2006) Does vegetarianism make a difference?, Essays on Reducing Suffering (updated 25 January 2014).
Another example of expected value reasoning.

Wikipedia (2010) Von Neumann-Neumann–Morgenstern utility theorem, Wikipedia, April 10 (updated 13 February 2021‎).
For proofs that rational agents should select projects with the highest expected value (note that this does not imply economic risk neutrality).

Wikipedia. 2016b. Expected value.
A more technical discussion, including a more general definition.

Wikipedia. 2016c. Subjective expected utility.
More advanced.

alternatives to expected value theory | altruistic wager | cluelessness | decision theory | risk aversion | value of information

alternatives to expected value theory | altruistic wager | cluelessness | decision theory | value of information

alternatives to expected value theory | cluelessness | decision theory | value of information

Related entries

alternatives to expected value theory | decision theory | value of information