Is Common Knowledge a Necessary Assumption for the Theory of Social Coordination?

|Peter Boettke|

Alex Tabarrok discusses Stephen Landsberg's chapter on common knowledge in The Big Questions.  I haven't read it yet, but I am sure Alex's description is accurate.

What concerns me is not so much Landsberg restating of the Aumann proposition on agreement, but what role the common knowledge assumption plays in theories of social coordination.  As an economists who emphasizes subjectivity in tastes, expectations and knowledge, I always found the Aumann argument to be backwards.  The question isn't why rational actors would ever disagree, but why would would they ever find reasons for agreement.  But, of course, there is the issue on the other side of this that there must be some threshold of mutual knowledge that is required for social conventions to work in producing mutually beneficial social cooperation and coordination.  So there must be some margin of agreement evident in social order, though perhaps we want to see that endogenously produced rather than assumed.*

How can one have an economics of imperfect knowledge, of time and ignorance, and of meaning and interpretation, if the common knowledge assumption is introduced? Or is this simply the wrong way to think about these issues?

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*See Russell Hardin's How Do You Know? for a discussion of what he calls an economic theory of street-level ordinary knowledge.

Comments

[Adam]

If a little knowledge of philosophy is dangerous, Landsberg poses no danger.

Distinctions between different types of knowledge--entailing distinctions between how we (do or should) believe different types of propositions--seems like a first step to any serious social epistemics.

[Greg Ransom]

Prior to shared "knowledge" there some threshold of mutual shared shared behavior patterns, ways of going on together, shared conventions, shared traditions.

Sometimes it seems that economists have never read Wittgenstein or Hayek or Kuhn on this stuff -- and they are still living in the "socialist calculation" world of mental object "givens" assumed by Descartes, Euclid, Hobbes, Plato and Hume, etc. Prior to the existence of that easily manipulable "block world" of shared "givens" of "knowledge", there must be a prior coordination that gives the spaces for those "blocks".

Peter writes:

" there must be some threshold of mutual knowledge that is required for social conventions to work in producing mutually beneficial social cooperation and coordination."

[Mario Rizzo]

The question or puzzlement on the part of some people: Why should rational actors ever disagree? is an example of conceptual realism. It is only a puzzlement to people who accept rational expectations as a description of reality. The phenomenon from which we start in the "life-world", as it were, is the heterogeneity of knowledge. To equate rationality with common knowledge is an artifact of a model. I don't see why any of us have to be chained to that way of thinking. Fritz Machlup was good on the issue of descriptions of reality as distinct from models.

Of course some commonality of knowledge is necessary not so much for rationality but for effective interpersonal exchange, division of labor, markets and so forth. But here the assumptions or inferences about common knowledge are "dictated" by the need to explain certain concrete social phenomena.

I would like to recommend that people look at Randy Barnett's book The Structure of Liberty for an excellent summary of the division of knowledge in society argument.

[Aidan Walsh]

Perhaps I am wrong but didn't Hayek argue that following common rules of behaviour was how we coordinated our behaviour despite the differences in our knowledge. Reasonable people then disagree on what to do where their different knowledge means that different rules should be applied.

There has to be very little little commonality and even less mutuality of knowledge to know which rule to be applied. A shopkeeper need know nothing about you other than you have cash to follow the rules about selling goods and vice versa.

[Lee Kelly]

Pete,

I don't understand what the problem is. People have knowledge in common (e.g. language), but so what? I have no idea what you're trying to get at.

[Richard Ebeling]

We, of course, at one level do (and must) share a certain form of common knowledge.

But may I suggest that one understanding of this form of shared knowledge is that discussed in the Weberian tradition of "ideal types," especially as developed by Alfred Schutz.

The individual is born into a world that has pre-existing structures of intersubjective meaning. The individual learns from all those around him (parents, neighbors, family friends, and others) what the "meanings" are in these intersubjective structures -- the institutions of the meanings of objects, actions, ideas, and relationships in the broadest sense.

This knowledge is "layered" between the most general "typifications" to the most specific and detailed in human interactions and associations.

(That all of these layers of typified and shared, "common" knowledge have, themselves, evolved ove time in Mengerian-style "spontaneous" ways does not change the fact that for any individual at any moment they serve as the absorbed and learned "givens" within which he thinks, acts, and associates with his fellows.)

But this Schutzian form of understanding (to use Georg Simmel's question)"How is society possible?" does not require a rational expectations notion of "knowledge" and "rationality."

Rather, it enables to understand the the institutional "meanings" order within which individuals would, then, go about using and applying their diverse Hayekian types of knowledge for interpersonal coordination through the pricing and market process.

Richard Ebeling

[Roger Koppl]

The common knowledge stuff is about Bayesian updating. As far as I know, you can't really gainsay the mathematical result. If we have common prior probabilities and common knowledge, we'll have common posterior probabilities too. I think the issue is what to make of this result.

I would not pooh-pooh the common knowledge literature in general or Aumann's 1976 paper in particular. Aumann's paper revealed something deep and important about rational inference, I think. Your conclusions can give me information about your private information, and that information can improve my probability estimates. This is disciplined common sense at its best. Just by asking which has a higher latitude, Rome or New York, I may alter the probabilities you attach to each possible answer. Aumann showed that a similar mechanism can cause convergence of posterior beliefs in certain idealized cases.

Nevertheless, I don't think such common-knowledge results are all that informative about real human disagreement. People do not have common priors. They don't update by Bayes' Rule. Even if we did all update by Bayes' Rule, the fact is not common knowledge. Posteriors are not well defined and therefore cannot be common knowledge. And so on. I just don't really see where it gets you that far in the context of ordinary social life.

I really don't know how to square the frailty of reason and the division of knowledge on the one hand with the mathematical assumption if common knowledge on the other hand.

[Jerry O'Driscoll]

To add to Richard's astute observations. Hayek distinguished among types of rationality. On the one hand, there is the rationality of deductive reasoning and logic. On the other hand, there is the rationality of the mind fitted to comprehend reality around it and learn from experience. Also important is Hayek's emphasis on tacit knowledge. What may be known in common can be tacit and hence not necessrily articulated.

[Peter Boettke]

Roger,

Isn't this the point: "I don't think such common-knowledge results are all that informative about real disagreement. ..."?

Pete

[Roger Koppl]

Pete:

Sure! That is indeed the point. I put in the other stuff for two reasons. First, some of our readers may not be in a position to know that "common knowledge" has a pretty tight technical meaning and context. Second, saying that Aumann-type epistemics don't get you that far in concrete applications does not mean it has no value. It helps unpack, for example, what's involved in the assumption of "convergence" to Nash in a one-shot game.

[DG Lesvic]

I have been unable to post a response to Prof Horwitz at the thread below, Why the Reinflationists Are Failing to Understand the Costs of Recalculation?

Have you shut off comments at that thread?

[Barkley Rosser]

Pete,

Yes, and more.

I have not read the book, and by Alex's account Landsburg does a good job describing Aumann's result, although from comments on his post on MR, it looks like Landsburg may be off on some other stuff and bit overly arrogant about his own knowledge (one of these self-proclamied polymaths who then does not always know what he is talking about, apparently, on some things anyway).

The common knowledge assumption is very strong, as Roger knows. It involves assuming that we all have an infinite level of knowledge. We all know what each other knows about what we know about them and that they know of what we know about what they know about what... The theorem is correct, but based on utter nonsense, and certainly not all that useful for answering the problem you pose, although maybe Robin Hanson thinks differently, but I doubt that Ken Binmore does.

[Roger Koppl]

"utter nonsense"? Wow, Barkley, you out-Austrianed me! :-)

Seriously, do you think my limited defense regarding the Rome/NYC thing is too kind to Aumann?

[Barkley Rosser]

Too kind. Once you are playing with these sorts of assumptions, one is in danger of not even being able to invoke Bayes' Theorem on convergence.

[Roger Koppl]

Diaconis & Freedman? Maybe . . .

I didn't think I was too kind, but the answer to Pete's question is the same anyway.

[Eli Feigenbaum]

I love this blog. But, Pete, please proofread your entries before you post them.

[scineram]

The concept of common knowledge is so complex. I finally understood it through a logical puzzle.

http://terrytao.wordpress.com/2008/02/05/the-blue-eyed-islanders-puzzle/

[computer programmer question]

They are cut climate population or medieval crystals to come them from ideal radioactive people, and apprentice mouths exacerbated in black holes or people.