Friday, June 27, 2008

The Wisdom of One

I've written a couple of blog posts on The Wisdom of the Crowd in the past, but The Economists notes a study about how asking a single person for different answers can yield better answers than asking just once. The results are better if the time between answers is longer. I'm not sure why this is all that surprising. The researchers, Edward Vul and Harold Pashler believe this phenomena may be that the brain is making hypothesis and then updating ones that are incorrect. This is probably true to some degree. But another possible reason may come from the field of machine learning.

Fundamentaly, the memory is simply a feature extracture and like all feature extraction techniques they can be quiet noisy. For example, it has been shown that doctoring images can make people remember events differently, even if they were at the event in question. In effect, by asking many people or asking the same person multiple times is taking a statistical sample, for which the mean is a better indicator on average (minimizes the square error loss). Another effect seen here is that better answers are gained by lengthing the time between questioning. This can be explained by Monte-Carlo Maximum Likelihood (MCML). One noted effect in MCML is that neighboring samples are correlated, but by taking samples spaced farther apart, the correlation decreases and closer to being independent and identically distributed.

I wonder if this could be an explanation considering something missing in the hypothesis by Vul and Pashler: what feedback was given to people to say their first answer was wrong? True, simply asking a question again probably makes the person question is correctness, but a control study group would be needed. One example is to tell people upfront that they will be given two guesses, but they will be rewarded inversely proportional to the combined answer. For example, if the correct answer in "guess a number I am thinking" is four, but one person bets four and nine, while the other person bets three and five, then the second person gets the reward.

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