There is an interesting article in the MIT Technology Review on an experiment done at the Cajal Institute in Madrid, Spain. The article deals with a phenomenon termed "the wisdom of the crowd". If you ask a lot of people drawn at random to estimate a quantitative value such as the weight of a specific person or the distance between two geographic places, the average of the guesses is likely to be closer to the actual value than almost all of the individual guesses.
Researchers Madirolas and De Polavieja considered a situation in which people would be asked to judge such a value. They would then be shown the estimate made by another group, and asked again for their judgment of the true value. Some people, more confident in their own original judgment would make small adjustments in the value; others, less confident, would make greater adjustments. The researchers found in an experiment, as they had hypothesized, that the more confident group would on average make a better estimate than the less confident group. They provided a mathematical adjustment to readjust the estimates of the less confident -- as shown in the figure above.
I think race track betting is an example of this phenomenon of the wisdom of the crowd. Parimutual odds have been shown to provide rather good estimates of the probabilities of each horse winning the race. Thus horses that run at one to five odds tend to win about one race in six; those that run at one to nine odds tend to win about one race in ten. There will be some very good handicappers in the crowd who will be confident in their own judgment, but there will also be a lot of novices who bet on the colors of the silks of the riders or on horses whose names they like. Showing the odds as calculated by the parimutual machines at a track will perhaps move the novice betters toward the more accurate odds estimates of the good handicappers. (The good handicappers are likely still to do better on the day than the novices.)
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