In this post, the team at electionforecast.co.uk discuss the likely relationship between seats and votes in the 2015 general election. They show that the geographical distribution of support for smaller parties can lead to large discrepancies in the numbers of votes required to win extra seats. Additionally, they calculate the probability that the largest party in terms of votes will also hold the most parliamentary seats after May 7th.

1929, 1951, 1974. Spot the pattern?

They’re all elections where the party with the most votes failed to win the most seats. In February 1974, Labour managed to win more seats, despite trailing the Conservatives in the popular vote. This election might see similar perverse outcomes – not just for Labour and the Conservatives, but for almost all the parties.

Let’s start with a simple case, and look at the number of seats won by the SNP. According to the electionforecast.co.uk model, the SNP is likely to poll roughly 3 percent of the vote in Great Britain. With that 3 percent, the SNP is forecast to win 35 seats.

Put slightly differently, if turnout in 2015 is similar to turnout in the last election, the SNP would win one seat for roughly every 26,000 votes it gets. Things are not so fortunate for the Green Party. They’re forecast to get 4 percent of the vote – but only 1 seat. That means one seat for every 880,000 votes.

That astonishing difference results from the very different concentration of the two parties’ votes. Whilst SNP votes are, unsurprisingly, concentrated in Scotland, Green party votes are spread out across the country.

We can see a similar phenomenon with UKIP and the Liberal Democrats. UKIP’s vote share is difficult to forecast. We don’t really know where its pockets of strength are. But because UKIP support is spread out, and once again assuming that turnout is similar to 2010 levels, then each extra seat cost UKIP 1,700,000 votes. The Liberal Democrats, who have spent the past twenty years fighting local battles and building pockets of strength, win one seat for every 150,000 votes

Of course, the big beneficiaries of the electoral system are Labour and the Conservatives. But here, the devil’s in the details. Labour votes tend to be more concentrated. They have fewer wasted votes. And Labour tends to win constituencies with fewer voters. All this means that Labour can win more seats on fewer votes than the Conservatives. That’s still true despite Labour’s meltdown in Scotland.

In order to reach a majority, the we forecast that Labour would need around 36.3 percent of the vote. But for the Conservatives to reach a majority, they’d need more: about 38.2 percent. That difference is likely to matter a great deal in a close election.

What does that mean for the question we posed at the beginning? Will the party with the most votes also be the party with the most seats? Our model simulates many thousands of elections, and we can use the outcomes of these elections to describe the probability of events such as these. We find that if the Conservatives are the largest party in terms of seats – which is forecast as being slightly more likely than not – then they’ll almost certainly be the party with the most votes. However, in just over ten percent of simulated elections, Labour managed to become the largest party in terms of seats, whilst trailing in terms of votes. If that happens, expect a number of commentators to raise the issue of electoral reform – and to challenge Labour’s claim to form a government.

The operation of the electoral system is not the sexiest of topics. But like indoor plumbing, you start to notice it when it stops working. In this parliament, both the Liberal Democrats and the Conservatives have tried to reform the electoral system. Both failed. But this election might produce a odd grouping of disgruntled politicians – not just unhappy Greens and Ukippers, but Conservatives too. A majority for electoral reform might prove easier to reach than a majority for government.

Note: This article was originally published on our sister site, the LSE’s General Election blog.

About the Authors

Jack Blumenau is a PhD candidate in Government at the London School of Economics.

Chris Hanretty is a Reader in Politics at the University of East Anglia.

Benjamin Lauderdale is an Associate Professor in Methodology at the London School of Economics.

Nick Vivyan is a Lecturer in Quantitative Social Research at the Durham University.