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Private Knowledge Vs. Public Knowledge

January 14, 2010

Arnold Kling hits another home run today with a post on market failure. He offers a definition where failure represents the victory of entrenched interests over disruptive invention.

If innovators can succeed by out-competing incumbents, then the market is working. If incumbents have a self-reinforcing system that keeps out innovators, then we have market failure.

One of Hayek’s great insights was to suggest that market prices align decision-making power with knowledge. The further apart the requisite knowledge is from a person making a decision, the less prosperous that system will be. This is another way of looking at Kling’s contention: the more we reward incumbents and discourage new entry, the more we assume the established leaders have all the knowledge necessary to make productive decisions. The corollary is that we assume away whatever knowledge individual innovators might have.

The desire to imitate established interests and ignore private information inhibits the deliberative power of a democracy. I don’t have the book at hand, but there’s a fable described by Cass Sunstein in Why Societies Need Dissent. (It’s really an experiment he describes that demonstrates our willingness to trust the group over our own judgement.) Since I can’t cite the original, let’s call it the fable of the two urns.

  • In Urn A, the experimenter has placed 99 balls, 66 of which are RED, and 33 of which are WHITE.
  • In Urn B, the experimenter has placed 99 balls, 66 of which are WHITE, and 33 of which are RED.

Nothing distinguishes the appearance of one urn from the other. They look identical. Then the experimenter takes one of these urns and places it on a table at the head of a classroom. Next to the single urn, he places a piece of paper.

Now he instructs the subjects to line up one by one. When a subject steps up to the urn, he pulls one ball out. No one else can see what color ball this person has pulled. After looking at the ball, the subject writes down on the piece of paper which urn he thinks this urn is—whether it’s Urn A or Urn B.

If you pull a red ball, then the rational choice is to say it’s Urn A. And if it’s white, you ought to guess Urn B. (Because you ought to assume you had a higher probability of choosing the dominant color from either urn.)

Let’s say that the first 4 subjects act in this fashion and each has pulled a white ball. Accordingly, they’ve guessed Urn B. When the fifth guy steps up to the urn, he pulls a red ball. Now he looks down at the piece of paper and he sees that the first four have guessed Urn B. Acting on his own information though, the fifth man ought to guess Urn A and write it down. But in light of the group’s list of guesses, he may choose to disregard his own information and instead guess Urn B with the group. (Remember, he doesn’t see what color ball the others have pulled, only which Urn they think it is.)

What is the rational thing to do for this fifth man? Guess Urn A or guess Urn B? What if the fourth man reasoned exactly as he did? If we tally all the votes at the end of the pulling, and that determines the group’s Urn choice, what’s the optimal rule each person should follow when making a guess?

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3 Comments
  1. January 14, 2010 11:14 pm

    If the red and blue guesses are within one of each other, write down your ball colour. Otherwise, vote with the majority.

  2. January 15, 2010 2:02 am

    If the group’s goal (and each individual’s goal) is to make the count at the end accurate, then each should write down the urn based solely on the color of their ball. There is no payoff to an individual writing down the right urn.

    To specify exactly what the rational choice is, you have to specify the payoffs.

  3. Mike Gibson permalink*
    January 15, 2010 3:15 am

    No payoffs, good point! I also shouldn’t have specified what color balls the previous pulls were.

    I can’t remember how the original experiment was set up. If any one has the reference, I’d like to know what it was.

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