The Wisdom of Crowds I

The Wisdom of Crowds I

Lecture on 4.10.2007

Under certain circumstances, groups outperform individuals, even experts. If the probability that a member of a group is correct is more than 50%, the probability of a correct answer by the majority of the group increases to 100% as the group size increases. On the other side if there is a probability that a member has a less than 50% chance of being correct, group majority answer tends towards 0% correctness as group size increases.

Condorcet Jury Theorem

examples

Guessing the Gummi Bears

The class was presented with a clear plastic bag with a large number of gummi bears inside, and asked to individually write on slips of paper their guess as to how many were in the bag. The person coming the closest would win the bag.

The bag in reality contained 813 bears. There were 18 guesses, of which one was dropped as the answer was in grams and thus invalid.

The following table gives the individual guesses, sorted by distance from the correct answer.

Guess	Distance
755	58
900	87
698.5	114.5
1000	187
474	339
450	363
384	429
333	480
276	537
251	562
205	608
185	628
1500	687
1500	687
1600	787
1983	1170
3000	2187

After dropping the outliers (largest and smallest guesses, 185 and 3000), the average guess of the group was 820.63, a distance of 7.63 from the correct answer, far better than the best guess of 755/58 (congratulations, Tom!), and a great surprise to the teacher, who had expected it to work but not so amazingly well.

Many gummi bears sacrificed their lives during this experiment in the name of science.