# Expected Value

In evaluating charities, we have to deal with the unfortunate reality that total certainty is unobtainable. There's always some chance that we might be wrong, and the information available on intervention cost-effectiveness often leaves considerable uncertainty as to the results.

We need an approach that takes into account unlikely events without assigning them too much weight. Being hit by a bus whilst crossing the road would be a terrible outcome, but is also unlikely. In dealing with this possibility, we take sensible precautions, but don't avoid crossing roads altogether. We need to apply a similar approach to uncertainty in charity evaluation.

The mathematical procedure for doing this is to use expected values. We multiply the probability of each outcome by the magnitude of its impact, add them together, and compute the expected value.

Expected Value = (Probability of outcome 1)*(Magnitude of outcome 1) + (Probability of outcome 2)*(Magnitude of outcome 2) + ... + (Probability of outcome n)*(Magnitude of outcome n)

Acting so as to maximize expected value is regarded by decision theorists as the best procedure for decision-making in conditions of uncertainty. Those interested in the mathematical details are advised to consult the wikipedia articles on Expected Value and Expected Utility.

## Credences

The Expected Value approach requires us to assign probabilities to each possible outcome. This task may seem daunting, even impossible. The standard approach is to treat probabilities as measuring credences or degrees of belief. So understood, probability is measure of our confidence in the truth of a proposition: a probability of 1 means total certainty, and a probability of 0 means total disbelief. In practice we never have the evidence required to achieve total certainty or disbelief - our probabilities lie between 0 and 1. That is why we need to use expected values in guiding our decisions.

In relying on probabilities and embracing the uncertainty they quantify, we stand the best chance of helping the greatest number of people to the greatest extent possible.