The Economist's Certain Ideas of Europe blog weighs on the recent Polish proposal:
[...] Poland has grabbed everyone's attention by calling for a change in voting rules, so that voting weights in the EU council of ministers are based on a square root of each nation's population. This is a system that Poland considers much more equitable than the one on offer in the constitution, which says that votes pass when 55% of EU members, representing 65% of the EU's population, can agree.
Economists and game theorists have been busy weighing in on both sides. [...] All the studies of combinatorics that currently fill my email inbox fail because, early on, they concede that in the interests of clarity they assume that coalitions consist of nations taking decisions randomly. But they don't. Luxembourg and Belgium always vote for more European integration. The Nordics vote with Britain and the Netherlands on free trade things. Ireland has low taxes so votes with Britain against tax harmonisation, but has a powerful farms lobby so votes with France to preserve farm subsidies.
The EU is not about mathematics, because EU voting is not about numbers, it is about politics. This may sound like special pleading, given that the author of this posting is a political reporter and not a mathematician. But any analysis that looks at this on the basis of numbers is entirely missing the point.
Well, that's not true. The quoted piece does a very good job of putting the proposed reform into perspective: De jure power in the Council of Ministers is a small contributor to, and poor proxy for, de facto power. This, however, is not the same as saying voting weight reform is irrelevant and that 'the EU is not about mathematics, it is about politics' or that 'any analysis on the basis of numbers is entirely missing the point'. As is the case with the evaluation of any reform, what matters is how the balance of power changes at the margin.
While the UK will not lose 30 per cent of its ability to block legislation as the Spectator claims, it is equally wrong to say that Britain won't be worse off if the Polish proposal is accepted. Given the absence of a suitable theoretical framework and good data on the determinants of de facto power in the Council of Ministers, it is difficult to establish the magnitude of this loss; but this doesn't mean the mathematical approach is redundant.
For those interested in the 'mathematics' of square root voting weights, Vox EU offers an excellent treatment - a must read for budding game theorists and political scientists.
Postscript: The Certain Ideas of Europe blogger also mentions the fact that many countries tend to always vote the same way on given issues. This is a call for the analyst to dig deeper and assess how reform would affect the de jure power of any given country taking into account its effect on the power of its allies. Again, this is not an argument against mathematical analysis; it is a simple re-statement of the perils of simplistic approaches.