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One underlying assumption is that human preferences are ordered. However, the empirical literature suggests that they are only partially ordered. For instance, transitivity may fail. This is usually interpreted as irrationality, but may simply indicate that context matters for preferences that are confused with each other.

Now, preferences may still have mean values that are ordered, and which will enable us to predict choices in most contexts. Preferences with close mean values are more likely (in an informal sense) to be confused than preferences with large differences between their mean values.

I think that confusion makes more sense than error. This can be tested empirically by seeing if non-transitive choices are consistent when the contexts are repeated. If it is a matter of error, they would not be consistent.

BTW, did Keynes say anything about this? I know that he considered probabilities to be only partially ordered.

Stephen: This is fascinating!. I was totally unaware that Arrow's problem could be looked at in this way. And that Condorcet had looked at it this way so long ago!

If I've got my head around this right, what you are then looking for is a Bayesian estimator that can use "data" on individual's rankings to create an estimate of the "true" best ranking. And your estimator must then violate one (or more) of Arrow's assumptions. Independence of irrelevant alternatives?

It never occurred to me to ask Michel that, but I think IIA is one of the things that is violated.

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