The wisdom of the crowd is an idea that stems from the fact that the average estimation by a group of people is better than by individual experts. In other words, when a large group of non-experts (not biased by knowledge!) possessing diverse opinions starts predicting a quantity, their assessment tends to form a kind of bell curve – a large pack in the middle and outliers nicely distributed on either side.
In other words, the outlier of the crowd has a lower probability of estimating it accurately. Mark this line; we need it later.
Estimating the weight
Let’s go back to Francis Galton (1907) and the story of the prize-winning-ox. It was a competition in which a crowd of about 800 people participated to predict the weight of an ox after it had been slaughtered and dressed. The person whose prediction came closer would win the prize. On the event in which Galton participated, he found a nearly normal distribution of ‘votes’, and the middlemost value, the popular choice or the vox populi, was 1207 lb which was not far from the actual dressed weight of 1198 lb.
Bidding for the meat
Now, change the scenario: the winner is no longer the predictor of weight but who will pay the most. Therefore, by definition, the people in the middle of the pack, those with a better estimation of the actual value of the meat (estimated weight x market price), are not going to get the prize. The bid belongs to the person furthest outlier (to the right) of the distribution. This is the winner’s curse – the winner is the one who overvalues the object. The only time it doesn’t apply is if the winner attaches a personal value to it, such as collecting a painting.
References
Vox Populi, Nature, 1907, 75, 450
