"This claim is wrong, and the formula is correct..."


by Kevin Van Horn Dec 27 2017

This formula is almost universally agreed to be wrong\.

This claim is wrong, and the formula is correct. The formula shown is just a special case of the standard formula for the expected value of any random variable.

What is true is that the decision rule of maximizing expected utility can go wrong if you don't condition on all the relevant information when computing expected utility. What the author has written as

P(oi | ax) and E[U | a_x]

should actually be written as

P(oi | ax, B) and E[U | a_x, B]

where B is all the background information relevant to the problem. Problems with maximizing expected utility arise when B fails to include relevant causal information.