Decision Theory under Uncertainty

When did decision theory get adopted by economists? What is expected utility? What is the probability of an event that’s never been observed? The Chair of Decision Theory and Economic Theory at Tel Aviv University and AXA Chair of Decision Sciences at HEC, Paris, Itzhak Gilboa, explains some issues with decision theory.

Often we have events for which we can calibrate the probability, or estimate it from past events, and we say ‘OK, toss a coin over and over again, and I’m asking what’s the probability it’s going to come up heads’. You look at the past 100 cases, and you take this as an estimate of that.

In modern language we would call this expected utility. Expected utility theory says you should take the possible outcomes, assign certain numbers that we call utilities to say how desirable they are. So a more desirable outcome gets a higher utility. To the different scenarios you assign probabilities, and then what you do is calculate what we call mathematical expectation, namely probability times value, and add them up. Then you get expected utility, and you choose the act that gives you a higher expected utility.

Things changed dramatically at the end of the 19th century and beginning of the 20th century. Logical positivism came to the rise, defining what science should be like. Mostly dealing with physics, but apparently economists adopted that around 1930s. Economists wanted to have a science that was really respectable, like physics. Which meant that any theoretical concept should be related to observations, and what we call today in economics, the revealed preference paradigm.