Friday, December 21, 2012

Lisbon Treaty voting system: WIN^27 situation

I have recently become puzzled by a simple question. Does the Lisbon Treaty actually weaken the position of the Czech Republic in the Council of the European Union compared to the Treaty of Nice? I therefore went ahead and studied both, actually all three, basic variants of the voting system: the plain Nice voting system, the extended Nice voting system when a member state wants to bring the population share criterion in, and the Lisbon voting system. Besides some basic observations, I could not come to a general conclusion as I was able to find scenarios in which a member state both won and lost, depending on the treaty in use.

I clearly needed to consider all possibilities and evaluate them to be able to come with a clear judgement. Given there are currently 27 member states, there are exactly 2^27, or 134217728, different votes in which all member states participate and vote either for or against the proposal. This is still a small enough problem space for the modern computer equipment to exhaustively explore in a reasonable amount of time so I went ahead and constructed a small Python script which goes through all possible votes and evaluates them with respect to all three considered voting systems and the interest of the state from whose perspective the evaluation is made. I soon realized I can compute the results for all member states, not only for Czech Republic. Here are the results.

Member state Votes (Nice) Votes share (Nice) Population share Wins (Nice) Wins (Nice+) Wins (Lisbon) Lisbon improvement
Austria 10 2,90% 1,67% 67980524 67980509 70037478 1,53%
Belgium 12 3,48% 2,17% 68147346 68147331 70380860 1,66%
Bulgaria 10 2,90% 1,49% 67980524 67980509 69914262 1,44%
Cyprus 4 1,16% 0,16% 67461254 67461241 68996390 1,14%
Czech Republic 12 3,48% 2,10% 68147346 68147331 70332762 1,63%
Denmark 7 2,03% 1,11% 67723582 67723567 69653426 1,44%
Estonia 4 1,16% 0,27% 67461254 67461241 69071824 1,20%
Finland 7 2,03% 1,70% 67723582 67723567 69625576 1,42%
France 29 8,41% 12,95% 69302512 69302519 77686128 6,25%
Germany 29 8,41% 16,27% 69302512 69302527 80252488 8,16%
Greece 12 3,48% 2,25% 68147346 68147331 70436030 1,71%
Hungary 12 3,48% 1,99% 68147346 68147331 70257314 1,57%
Ireland 7 2,03% 1,70% 67723582 67723567 69625852 1,42%
Italy 29 8,41% 12,70% 69302512 69302505 77037338 5,76%
Latvia 4 1,16% 0,44% 67461254 67461243 69189842 1,29%
Lithuania 7 2,03% 0,65% 67723582 67723567 69335640 1,20%
Luxembourg 4 1,16% 0,10% 67461254 67461241 68955580 1,11%
Malta 3 0,87% 0,08% 67374448 67374441 68939830 1,17%
Netherlands 13 3,77% 3,31% 68228986 68228971 71165244 2,19%
Poland 27 7,83% 7,60% 69200228 69200213 73490170 3,20%
Portugal 12 3,48% 2,12% 68147346 68147331 70345358 1,64%
Romania 14 4,06% 4,26% 68309352 68309337 71839368 2,63%
Slovakia 7 2,03% 1,80% 67723582 67723567 69631656 1,42%
Slovenia 4 1,16% 0,41% 67461254 67461243 69168020 1,27%
Spain 27 7,83% 9,18% 69200228 69200231 74883076 4,23%
Sweden 10 2,90% 1,87% 67980524 67980509 70173958 1,63%
United Kingdom 29 8,41% 12,43% 69302512 69302509 77295044 5,95%

Note that there are also votes in which not all member states participate due to an opt-out from some policy area or in which some member states abstain from the vote. I did not consider this in my simulation as the problem space would significantly increase in size to 3^27, or 7625597484987, and thus make the simulation unacceptably long. Moreover, the voting systems tend to get complex when this situation occurs. Also note that for the sake of simulation, my script assumed rules that apply for Commission proposals. Proposals not initiated by the Commission need to meet stronger criteria than ordinary proposals.

As for the results, the chart above clearly shows that all member states will benefit from the transition to the Lisbon Treaty voting system in 2014/2017 as they will win the vote in more cases. Winning the vote in this case means that the proposal is accepted when the state votes in favor of it and rejected when it votes against the proposal. The table does not indicate whether the won votes for the proposal prevail over the won votes against the proposal or vice versa. The table also shows that the benefit is smaller for smaller states and bigger for bigger states.

There is one small trouble with the result. Even though the Lisbon Treaty comes out victorious from this comparison, we don't know which are the important votes so even though all member states win the majority of votes, the really important ones may fall into the lost minority. To solve this problem, we would need to know in advance what are the essential proposals and how will the member states vote on each of them. The possession of such knowledge would, however, be equivalent to having a magical crystal ball. For the time being, the purely statistical outlook will need to suffice.

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