Pay attention at the back

I await with no little anticipation the outcome of this week's EU Summit. Nevertheless, it is with deep regret that I note the absence of any valid explanation in the yellow press of Poland's announced position on EU Council voting procedures. As the cognoscenti will be aware, our Polish chums advocate the introduction of a vote weighting procedure based on the square root of the population of the relevant Member State (although I gather that territorial area comes into it as well).

The best explanation I have been able to find is in this - rather abstruse - website:

Where, you may ask, does the square root come from? The answer requires a bit of maths. Consider a randomly selected yes-no issue and suppose that member nations decide their stance on this issue by a referendum; define PN as the probability that a typical citizen’s vote is critical in the referendum outcome. Then the member states vote in the Council; define Pms as the probability that the member state is critical in the Council vote. A citizen’s probability of being critical is thus PN times Pms and our fairness metric requires this to be equal for all member states.
Pms has nothing to do with the number of voters (proxied by population), but PN falls at the square root of population. This sounds peculiar since most numerate people would think the probability of being critical in a national election decreases in a straight-line relationship with population. But this misses a subtlety. Two things change with the voter headcount. The probability of a typical voter being critical to a particular winning coalition decreases linearly with the headcount, but the number of distinct winning coalitions rises with the number of voters. The probability of being critical falls at a less than linearly pace. The mathematics of combinatorics gives us an exact formula assuming a voter’s stance is randomly determined on a randomly selected issue. Taking M as the minimum number of votes in a winning coalition and n as the number of voters, one can use the binomial distribrition to work out the answer. The precise, the formula is complex , but it can be well approximated as the square root of 2/np, where n is the number of voters (this is Stirling’s formula). Hence the square root.

Yes, while I take the point, this really leaves me no wiser. I suppose that Mr Blair understands it? But I demand to know what the Scottish Executive's Europe Minister, Ms Linda Fabiani MSP, thinks about this.