Bryan Caplan  

When Orwell Met Aumann

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Cowen and Hanson's "Are Disagreements Honest?" summarizes the theoretical case against "agreeing to disagree."
Yet according to well-known theory, such honest disagreement is impossible. Robert Aumann (1976) first developed general results about the irrationality of "agreeing to disagree." He showed that if two or more Bayesians would believe the same thing given the same information (i.e., have "common priors"), and if they are mutually aware of each other's opinions (i.e., have "common knowledge"), then those individuals cannot knowingly disagree. Merely knowing someone else's opinion provides a powerful summary of everything that person knows, powerful enough to eliminate any differences of opinion due to differing information.

Aumann's impossibility result required many strong assumptions, and so it seemed to have little empirical relevance. But further research has found that similar results hold when many of Aumann's assumptions are relaxed to be more empirically relevant. His results are robust because they are based on the simple idea that when seeking to estimate the truth, you should realize you might be wrong; others may well know things that you do not.
It's hard to find real human beings who reason this way.  What about fictional characters?  One suddenly came to mind tonight: Winston Smith from George Orwell's 1984.  Smith is admirably meta-rational while brilliant Thought Policeman O'Brien intellectually bullies him.
O'Brien was a being in all ways larger than himself. There was no idea that he had ever had, or could have, that O'Brien had not long ago known, examined, and rejected. His mind CONTAINED Winston's mind. But in that case how could it be true that O'Brien was mad? It must be he, Winston, who was mad.
As far as I understand, Aumann's theorem only applies if both Smith and O'Brien are meta-rational.  Otherwise, Smith is epistemically selling himself short.  And the very fact that O'Brien combines intellectual argument with physical torture conveys extra negative information about O'Brien's credibility.  What's striking, though, isn't that Smith takes Aumannian reasoning too far, but that he applies this reasoning in the first place.

COMMENTS (6 to date)
John Thacker writes:

While they may not be precisely reasoning in this way, when politicians reason in a way that largely matches the predicted Bayesian behavior (shifting their opinions to match those of others, especially the last people with whom they talked), it is generally thought of extremely negatively, at least in the abstract.

It's common for people who hold opinion X to tell a story about people who disagree. For example, nativists frequently assume anybody favoring relaxation of immigration laws must be a "Cultural Marxist." Leftists frequently assume anybody disagreeing with them is following some authority.

Chris writes:

Given the argument in Bryan's post, should we question the conclusion of Tyler and Robin's paper? The conclusion shouldn't be that most disagreements are dishonest but that most debaters have different priors.

Justin writes:

If we disagree about priors, it raises the question of why? Some economists and philosophers argue that there should be some point long ago where we had common priors. That is, we disagree today because we disagreed in the past, but our disagreement in the past was dishonest. But many don't like that argument.

Aumann also assumes a countable set of states. I know of one economist who studies this who was not sure if the result would generalize to an arbitrary (i.e. uncountable) set, which maybe explains some disagreements.

Chris writes:

@ Justin
Why does disagreeing today require that in the past we disagreed dishonestly? Unless I read the paper wrong, Tyler and Robin argue that people with different priors can disagree honestly.

justin writes:

Chris - The assumption is that we were born with common priors. That is, nobody knows anything at the time they were conceived, and all knowledge is acquired as we move through life.

Under that assumption, we cannot have an honest disagreement today. Because suppose we did. Then it must be that our priors are different. But our prior today is yesterday's posterior. By Aumann's theorem, either we had a dishonest disagreement yesterday or we had different priors yesterday. If we had different priors yesterday, then just keep repeating this process until we were born. Eventually we must have had a dishonest disagreement at some point because otherwise it implies we had different priors initially. But that contradicts our assumption.

I think Harsanyi has written about it if you'd like to read more. A lot of people don't buy the common priors at conception assumption though.

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