[kennon42]

The primary thing that determines overall group performance (assuming no interpersonal biases like peer pressure or coercion, etc) would be the probability that any individual chooses the "right" answer. If this is greater than 0.5, then according to the Condorcet Jury Theorem, the limit of the group as a whole choosing the right answer is 1 as the group size increases.

Perhaps having a smaller size allows the "noise" in the group to still produce the "right" answer more often than it would in a larger group?

[thaumasiotes]

Well, assuming a standard wisdom-of-the-crowds problem like "how much does that cow weigh?", the answer is drawn from a continuous interval and the probability of choosing the right answer is necessarily zero. Yet, the fact that that's a standard example of a wisdom-of-the-crowds problem suggests that the zero probability of being correct isn't really a big issue.

For a slightly different example like "how many jellybeans are there in this jar?", the answer is drawn from a discretized interval, but I feel pretty safe in assuming that the odds of any one crowd member getting it right are well below 50%.

[tedsanders]

No, that's incorrect in two ways. First, you must also assume that the individual opinions are independent. Second, the 0.5 probability threshold is only correct for binary situations; in real life where they may be a range of opinions, the threshold is much lower.

[wutbrodo]

> Second, the 0.5 probability threshold is only correct for binary situations; in real life where they may be a range of opinions, the threshold is much lower.

The study from the article did focus on binary situations. From the article:

> Where previous research on collective intelligence deals mainly with decisions of ‘how much’ or ‘how many,’ the current study applies to ‘this or that’ decisions under a majority vote.