Constituencies, First-Past-the-Post and Minority Rule

The other day, I re watched CGP Grey’s excellent videos about the Electoral College. In one video, Grey shows how it is possible to become President with only about 23% of the popular vote. The UK’s constituency-based system shares some key features with the Electoral College, so I wondered whether a similar feat might be possible here. A quick search for data and a few lines of code later, I had my answer.

First, a primer on UK general elections. The data I used was for the 2015 General Election. In this election, there were 650 constituencies making up the UK. During an election, each of these elects one MP to a seat in Parliament using a first-past-the-post voting system. Then, by constitutional convention, the Queen appoints the leader of the party with a majority of the seats as Prime Minister and they form the Government. Since MPs are elected using a plurality system, it is common for them to be elected with less than 50% of the vote. For simplicity, I’ll assume a strict two-party system in my analysis, meaning that winning requires a majority of the vote. It’s a wildly inaccurate assumption, but I’ll get back to that.

Hopefully it is clear from the above that the ‘winning party’ is not necessarily the one that won the most votes, but the one that one that won the most constituencies. Despite efforts to equalise the populations of constituencies, these vary dramatically for historical and geographical reasons. For example, in 2015, the Isle of Wight had an electorate of over 100,000 people. At the other end of the scale, Na h-Eileanan an Iar had an electorate of only about 22,000 people. This variation means that some votes effectively matter more than others. It also makes the constituency system vulnerable to the same trick that Grey pulled in his video.

In order to gain control of the Government (without coalition), a party must win 326 seats in Parliament. By just barely winning the 326 smallest constituencies, they could win these seats with fewest possible votes. When I analysed the data, I found that this tactic could lead to a party being in government with a startlingly low percentage of the votes overall. Even assuming that everyone votes, less than 23% of the popular vote will get you into government.

  Minimum total number of votes for 326 seats Percentage of electorate
Assuming 100% turnout 10,646,336 22.97
Using 2015 General Election turnout 6,791,227 14.65

This campaign strategy is not a realistic one, but the fact that it is even possible to win a two-party election with such a small proportion of the votes is worrying. If we add realism by removing the two-party restriction then things can only get worse, since first-past-the-post then allows for seats to be won with less than 50% of the votes. The issues with first-past-the-post itself are beyond the scope of this post. It’s worth noting that even with equalised constituencies, a similar focus on just barely winning 326 seats could get a party into power with 25% of the popular vote. The big problem with unequal constituencies, then, is that it makes some votes matter less than others.

There you have it. The vast range of constituency sizes makes it theoretically possible to win a majority of parliamentary seats with a shockingly small percentage of the popular vote. It also means that voters in larger constituencies have less of a say in our elections than those in small ones. For those of us who care about the representativeness of our democracy, it is therefore tempting to demand perfect equalisation. We must be careful though. Constituencies are about more than electorate size, so we can’t just go chopping and changing them willy-nilly. For more about constituency boundary reform, see the Electoral Reform Society website.

The code used for my analysis is here and the exact data is here.