Why Maximize Expected Value?

Abstract

Standard Bayesian decision theory tells us to maximize the expected value of our actions. For instance, suppose we see a number of kittens stuck in trees, and we decide that saving some number n of kittens is n times as good as saving one kitten. Then, if we are faced with the choice of either saving a single kitten with certainty or having a 50-50 shot at saving three kittens (where, if we fail, we save no kittens), then we ought to try to save the three kittens, because doing so has expected value 1.5 (= 30.5 + 00.5), rather than the expected value of 1 (= 1*1) associated with saving the single kitten. But why expected value? Why not instead maximize some other function of probabilities and values? Two intuitive arguments are presented. First, in certain situations, maximizing the expected number of organisms helped is equivalent to maximizing the probability that any given organism is helped. Second, even in cases where that isn’t true, the law of large numbers will often guarantee a better outcome over the long run.