I am working on a column for next week’s FT Magazine about the mathematics of voting power. Here’s what I have learned.
It might seem unfair that the Liberal Democrats have received 23 per cent of the votes but just 8 per cent of the seats, while the Labour party has 29 per cent of the votes but five times as many seats. But it’s naive to think that 8 per cent of the seats translates to 8 per cent of the influence.
For example, imagine a 100-seat parliament with seats distributed Blue: 40, Red: 30, Yellow: 25 and Green: 5. Imagine which combinations of parties could win a majority and you realise the three big parties might just as well have been given one vote each, with no votes for Green, which is never the decisive partner that makes or breaks a coalition.
There are two commonly used ways of translating voting blocks into voting power, the Shapley-Shubik method and the Banzhaf-Penrose method. (Want them explaining? Wait for my column.) But suffice to say that assuming 307 Tory MPs, 261 Labour MPs and 55 Lib Dem MPs, both methods conclude that Labour and the Liberal Democrats actually have the same voting power. With 23 per cent of the votes, the Liberal Democrats actually have 23-24 per cent of the voting power. The Conservatives have 37-38 per cent of the voting power, just fractionally above their share of the popular vote. (Evidently, these blank-slate methods omit some important considerations, such as ideology.)
If you want to do these calcluations yourself, go to Professor Dennis Leech’s website and click on ipdirect or ssdirect. “Quota” is 326 and the allocation of seats currently looks something like.
1 1 1 3 3 6 8 55 261 306 [Update: 1 1 1 3 3 5 6 8 57 258 307 - includes Sinn Fein and gives last 2 uncertain seats to Conservatives. This gives Labour and Liberal Democrats 21 per cent of voting power, each.]
Paste it in and tweak to your taste.
Last night, when everyone was saying “this looks like a hung parliament and a bad night for the Liberal Democrats”, that statement struck me as absurd. The mathematics back me up.
Update: The twitterati have misunderstood what I am saying here. It’s not that the Liberal Democrats are always fairly treated by the electoral system. Evidently not. But they have a perfectly decent crack of the whip this time round as I think we’ll see. They have 8 per cent of the seats but more than 8 per cent of the influence.