[cardguy]

(08-28-2013 10:24 PM)Architekt Wrote:  

(08-28-2013 05:59 PM)cardguy Wrote:  

Brilliant blog here. Just stumbled across it.

http://www.futilitycloset.com/

This is probably my new favourite site

FutilityCloset Wrote:

From Gábor J. Székely’s Paradoxes in Probability Theory and Mathematical Statistics, via Mark Chang’s Paradoxology of Scientific Inference:

A, B, C, D, and E make up a five-member jury. They’ll decide the guilt of a prisoner by a simple majority vote. The probability that A gives the wrong verdict is 5%; for B, C, and D it’s 10%; for E it’s 20%. When the five jurors vote independently, the probability that they’ll bring in the wrong verdict is about 1%. But if E (whose judgment is poorest) abandons his autonomy and echoes the vote of A (whose judgment is best), the chance of an error rises to 1.5%.

Even more surprisingly, if B, C, D, and E all follow A, then the chance of a bad verdict rises to 5%, five times worse than if they vote independently, even though A is nominally the best leader. Chang writes, “This paradox implies it is better to have your own opinion even if it is not as good as the leader’s opinion, in general.”

Anyone here help explain how this is true? I am having trouble visualising it.

Really fascinating stuff!