In case you didn’t know, there is a general election in the UK tomorrow. The Liberal Democrats, the third party, have been agitating for a change in the electoral system for some time, because their representation in parliament is consistently much lower than it’s overall share of the vote would suggest is fair.
Without getting into whether or not a change in the voting system is a good idea (personally, I like the current first past the post system), let’s take a look at the figures. I took the results in terms of seats gained and proportion of the vote won in all general elections between 1983 and 2005. Early results for the LibDems are actually for the Liberal-SDP alliance, their precursor party. Data points are colour-coded – blue for Conservative, red for Labour, and yellow for LibDems.

As you can see by the pattern of the data, the parties have to get to 15-20% before they get any seats at all. Given that this is close to where the LibDems have polled this obviously puts them at a disadvantage.
Another way of showing this disadvantage is by calculating the number of seats won per percentage of the total vote achieved. For example, if a party won 25% of the vote and got 250 seats, that would be 10 seats per %.

This chart shows two things. First, it confirms the disadvantage that the LibDems have to fight against. But more interestingly, at every election the winning party gets more seats relative to thr proportion of their vote than the opposition. The Conservatives won the 1983 and 1987 elections by large margins, but also got more seats proportional to their actual vote. The same can be said for Labour in 1997, 2001 and 2005. The Conservatives very narrowly one 1992, where the proportions for Labour and the Conservatives are almost identical, with the Conservatives just shading it. It also shows that the increase for Labour of seats in relation to their vote is more or less matched by the LibDems.
Finally, some stats. The correlation between Conservative seats and vote share is 0.99; that for Labour is 0.96. This shows an almost perfect positive correlation between vote achieved and seats gained (a perfect positive correlation is 1, a perfect negative correlation is -1, and no pattern at all is 0). Weirdly, the LibDem correlation comes out as -0.27, that is the bigger share of the vote they get the fewer seats they win. They really don’t do well under this system do they? Having said that, looking at the first graph does not really show any such pattern for the LibDems, so it is probably a spurious result.











