Misconception

Contrary to an autistic bookworm like me, many of our administrators are all for meetings. A common romantic reason that they put up is: Three idiots are more wise than a genius (三個臭皮匠，勝過一個諸葛亮).

Alas, this statement appears absurd as soon as you translate it into English.

Of course there are good reasons for our forming of this opinion: True genius is rare. By probability, it is more likely to have a good idea coming from one of the three ordinary persons than a seemingly clever one.

There is actually a mathematical proof for this phenomenon. In short, on any given matter, if the probability of the clever person to give a better opinion than an idiot is 70%, the combination of three idiots who think independently could almost turn the table around - they can give a better opinion than the clever person in over 65% of the cases.

Some of you may notice there is a tipping point in this case. If a wise person has an 80% probability of giving a better opinion than an ordinary one, combination of three of the latter will not beat the wise man, whose chance of winning is now 51.2%.