I came across this simple theory of overoptimism recently (though it was published years ago). Suppose an agent has at least two actions from which to choose. An action gives either a payoff one or zero. For each, the agent has a subjective probability that the action gives a payoff of one. The probabilities of success are drawn independently from the same distribution G. Agent A then chooses one his actions, the one with the highest mean, according to his subjective beliefs. How do his beliefs about this action compare to those of an arbitrary observer?
Here’s where it gets interesting. The observer’s beliefs are different from agent A’s. They are drawn from the same distribution G but there is no reason that the observer’s beliefs are the same as agent A’s. In fact, the action agent A took will only be the best one from the observer’s perspective by accident. Actually, the observer’s beliefs will be the average of the distribution G which is lower than the belief of agent A since agent A deliberately took the action which he thought was the best. This implies that the agent A who took the action is “overoptimistic” relative to an arbitrary observer.
There are two further points. If there is just one action, this phenomenon does not arise. If agents have the same beliefs (a common prior), it also does not arise. So it relies on diverse beliefs and multiple actions. The paper is called “Rational Overoptimism and Other Biases” and is by Eric Van den Steen.
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November 2, 2009 at 8:58 am
michael webster
I glanced at the paper, and while it looks interesting, there was no simple example which explained the author’s intuitions.
Do you have a simple example?
November 2, 2009 at 2:18 pm
Alex Tabarrok
Here is a related and simple example – suppose there are two roads to get from A to B. Even though both roads are equally good from an observers point of view amazingly most people will always find themselves on the more overcrowded road!
November 2, 2009 at 2:44 pm
mk
I may be missing the point but I don’t see why this is interesting. It’s just playing with definitions.
Basically, suppose the Senate votes on a public option in health care. People who think the public option is good vote Yes, others vote No. But the average senator, a fellow named Bob, thinks the public option is just “so-so”, and likewise Bob thinks that non-public-option route is just “so-so.”
The logic then goes, Bob is average so he is “rational.” So anyone different from Bob is irrational, either excessively pro- or anti- public option.
In other words, whenever a group of people has beliefs that can be placed along a continuum, anyone who is not at the exact center of the continuum is irrational. In particular anyone who advocates for any action is probably overoptimistic about that action.
Two things in response:
1) If rationality is the razor-thin center of a distribution, then it’s already true that almost everyone is irrational.
2) If 4/5ths of people believe in a public option and 1/5th does not, then many supporters of the public option will actually be overly pessimistic about it. So nothing is actually doing work in this model except the idea that “the farther away you are from the average the more irrational you are.” I don’t see any additional explanatory power from this model.
Again I could easily be missing something.
November 2, 2009 at 2:44 pm
Paul Gowder
Oh, this is interesting. I’ll have to read the paper now I suppose to answer questions like “to what extent is this robust to cases where the probabilities for each action are drawn from different but overlapping distributions?” (Which is what we’d expect to be the case if one choice is objectively better & there’s some evidence for that.)
November 2, 2009 at 4:35 pm
Doug
There is a difference between incorrect and irrational.
November 2, 2009 at 4:54 pm
Ben Ho
The simple example I like is the commonly used example that we all think we’re above average drivers. But if person A defines above average as being a safe driver, and person B defines being above average as being a fast driver, then both people could legitimately call themselves above average and both would be right.
November 2, 2009 at 5:05 pm
Dan
Assuming most of the general principles of the article are correct, I think it could be interesting to think about individuals who assume they are doomed to fail (perhaps those with chronic depression, different earlier conditioning experiences, etc). The article notes that greater than 50% of the population believe they will do better than the median, but we all know individuals who expect to do worse than the median and worse than their real success level.(just a quick thought experiment regarding implications)
a) Overoptimist believes that a high-level of success is brought about by personal choices/actions and failure is due to exogenous factors.
b) Underoptimist believes that a high-level of success is brought about by exogenous factors and failure is due to personal/choices actions?
a) Overoptimist will exert more effort to endeavors more important from a cost/benefit perspective, but perhaps also relating to the belief that personal actions result in success and that they have more insulation from exogenous – failure causing – events if they exert a higher level of personal effort.
b) Underoptimist, who believes that success comes as the result of exogenous factors, has no reason to increase effort levels significantly in endeavors that are more important because they do not want personal control over the event. The less control, the more exogenous factors in play and the more opportunities for success?
a) Overoptimists (let’s say in the managerial case) have less bias when some degree of control is taken away from them.
b) Underoptimists have less bias when some degree of control is taken away from them? (interesting in context of rigid rehab or help programs that create accurate (read: more optomistic than initially expected with low exogenous effects) expectations?)
Maybe way too much speculation, but just something to chew on.
November 3, 2009 at 8:48 am
Jim B.
It seems like there’s an easier way to derive this phenomenon: simply suggest that the agent’s payoff is correlated with his guess (which it often is in markets).
November 3, 2009 at 5:37 pm
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