## miércoles, 14 de diciembre de 2011

### A mathematical explanation of the previous post...

There is a way to mathematically proof that the 26 are much more likely to be right about their final decision than the UK “if certain assumptions hold”. In a world of uncertainty with nobody knowing the right solution to this problem (to join or not to join this new treaty) the probability of being “right” is, say, (P) and that of being right (1-P). If we assume that biases are qualitatively similar for all countries (that is to say that UK’s motives are not more self-interested than French or German ones) then the probability of all the 26 being wrong while the UK is right is quite low.

The mathematical proof will go that way:
Probability of all the 26 being wrong: (1-P)*(1-P)*(1-P)*…*(1-P)=(1-P)^(26)
Probability of the UK being right: P
In the limit we have this non-linear equation (1-P)^26=P that solves for P = 0,0888.

In other words, and taking into account the aforementioned assumptions, the UK has 8.88 % of possibilities of being right in this decision while the other 26 being wrong.

Caveat: we are here talking about a yes-or-no option. It does not obviously include the extent to which the “right” solution will eventually work: this mathematical explanation cannot say anything about how deep the reform of the treaty should go or anything similar. However, it shows you that being all relatively rational, the 26 seemed to have made a better choice.

This is the mathematical explanation of that old quote about democracy: “Democracy is nothing more than the recurrent suspicion that more than half of the population is right more than half of the time”. Nor does it give you assurances that the best solution will always be picked neither the wisest. Democracy is then for the quote’s author and the mathematical proof a suspicious that the more, the wiser.