When you watch the campaign for the next general elections in the United Kingdom, you may get the impression that the two biggest contenders, Ed Milliband and David Cameron are competing for the same voters. They promise this, they promise that in multiple attempts to convince what in political science jargon we call the “median voter”, that is, the person in the very middle of the voter distribution, the one that decides elections. In theory, this is how it works in majoritarian systems. In fact, it’s not.

In the theory, the median voter swings from one side to the other, depending on the promises made by the different parties (there is a movie with Kevin Costner about this). In a perfect bipartisan system, one vote lost for one party is a vote won for the other party. This means that the vote share of one party is more or less perfectly correlated with the votes for the other party: 1% more for one party means 1% less for the other party. This describes very well the relationship between the Democratic and the Republican vote in the US, where there are only two relevant parties. The graph below plots together the vote share of the two main parties in Congressional elections between 1960 and 2008. All points (years) are very close to the line. The R-square statistic means that 82% of the variation in the Democratic vote can be explained by the Republican vote. If the Republican vote increases by 1% of the total vote, the Democratic vote is lower by 1.18%.

Now look at the same graph for elections in the United Kingdom. There is no correlation whatsoever between the level of the Conservative Vote and the level of the Labour vote. The R-squared is close to zero, and the results are not statistically significant. This means that the level of the Labour vote cannot be explained by the level of the Conservative vote: when the Labour vote goes down, the Conservative vote doesn’t go up. They are completely unconnected to each other, which seems to imply that that there are very small voter movements from Labour to the Conservatives (this is confirmed by British election survey data). When the Tories lose votes, they go elsewhere.

Where do these votes go? I have run the same kind of analysis drawing on the UK polling report, which brings together 1913 polls since May 2010. That a very large number of polls which allows to run a few analyses with a higher degree of confidence than election results. What do they show? First, the pattern highlighted above between Labour and Conservative votes is similar: there is only a very weak relationship: only 1% of the variation in the Conservative vote can be explained by variation in the Labour vote. If anything, the relationship is actually positive. If the Labour vote goes up by 1%, the Conservative vote goes up by 0.1%. When Labour loses votes, they don’t go to the Conservatives, and vice-versa. On the opposite, they tend to go up together, even if the association is very weak.

Now look at the relationship between Conservative and UKIP voting intentions. The relationship is much clearer, and the dots are much closer to the line. 20% of the Conservative vote can be explained by the UKIP vote. When the UKIP vote goes up 1%, the Conservatives lose on average 0.26%.

 Something similar happens with Labour: its voting intentions are negatively associated with Greens and UKIP voting intentions. The association between the Green and Labour vote is actually even stronger: R-squared is 0.51, which means that 51% of the variation in the Labour vote can be explained by the Green vote. The relationship goes in a similar direction with UKIP. When the UKIP vote goes up 1%, the Labour vote goes down 0.76% on average, and 58% of the Labour vote can be explained by the UKIP vote.

What about the Libdems? The Libdem vote is positively associated with the Conservative vote (perhaps that’s what happens when you enter a coalition) (R-square: 0.12) but unrelated to the Labour vote.

A few caveats: OLS regression as used here do not seem to be a good method to analyse and predict votes in multiparty systems. However, graphically this provides some insights on the dynamic of electoral competition in the United Kingdom: parties compete for votes within rather than across ideological blocs. Few people switch from Conservative to Labour or from Labour to Conservative. More people switch from Libdem to Labour or from Labour to SNP (within the left) or from Conservative to UKIP (within the right). This tends to indicate that contests between the two main parties and their smaller challengers on each side of the political spectrum are more important than between them. Politics is moving to the extremes and is no longer fought in the center, if it ever was.