Which coalitions would have the greatest support from the electorate?

Time for some amateur psephology regarding the imminent UK general election. British voters have probably seen many, many graphs like this one which shows the projected share of the vote:

However, these type of graphs don't always reflect the picture among the entire electorate. That's because a sizable chunk of eligible voters do not vote. In the previous 2010 election, voter turnout was 65.1% and this is pretty close to the average from the last four elections (average turnout 64.1%). So let's assume that turnout on Thursday will be about the same, and I'll arbitrarily set it at 65%. This means that the 34.5% of people who are projected to vote Conservative are really drawn from the 65% of people who might actually vote. I.e. the percentage of the electorate who might vote Conservative is only 22.4%. So the most popular party — in terms of share of the vote — may only have the backing of fewer than 1-in-4 possible voters. Let's see how things look if we plot the support for each party based on the percentage of the electorate who might vote for them:

Of course, it's possible that the third or so of people who don't vote may all have strong leanings towards the Conservatives, or towards Labour, or it may be that the 35% contains a representative mix of supporters of all of the parties. I'm not sure if anyone has any good insight into political allegiances of this group of non-voters.

There is already a lot of speculation as to which coalition might end up coming together to form a workable government (there are a lot of permutations). So I'm curious about how well possible coalitions might reflect support from the electorate as a whole vs the combined number of seats they would amass as a voting block. To gain an absolute majority, any coalition would ideally need 325 of the 650 seats.

The following graph plots the number of seats that various Conservative and Labour coalitions might achieve vs the possible percentage of the electorate that might back such a coalition. I've also included separate data points for Conservative and Labour as potential minority governments (circles and squares indicate Conservative/Labour coalitions respectively):

So what does all of this mean? First let's look at the situation for the Conservatives:

  1. Another Conservative/Liberal Democrats coalition would have 307 combined seats, but would only have the backing of 30% of the electorate.
  2. Combining with the UK Independence Party (UKIP) might only give the Conservatives 1 more seat, but it adds a sizable chunk of electoral support (rising from 22.4% to 29.6%)
  3. If the Conservative could combine with the Lib Dems, UKIP, and the Democratic Unionists Party — a party from Northern Island who have often allied with the Conservatives in the past — then they would still only have 316 seats, and this would reflect potential backing of 37.6% of the electorate.
  4. It's hard to imagine any other party supporting the Conservatives, except for maybe on a vote-by-vote basis.

And for Labour:

  1. Support from the Scottish National Party (SNP) would add a huge number of seats to a potential coalition (which has already been ruled out), but would hardly change the national backing from the electorate. The SNP only run candidates in Scotland and despite potentially winning almost every Scottish seat, this may only reflect 2.5% of the electorate voting for them.
  2. In contrast, a Labour/Lib Dems coalition would gain fewer seats than a Labour/SNP deal (293 vs 318) but would end up reflecting much more support from the electorate.
  3. Labour have more potential coalition partners than the Conservatives, and could possibly form some sort of union with the SNP — yes, I know that I've already said that this has been ruled out but you know…politics — as well as the Lib Dems, the Greens, Plaid Cymru, and the SDLP (the Social Democratic Labour Party of Northern Ireland). If they all joined forces, they could amass 352 seats with backing from 34.7% of the electorate.


So in the unlikely scenario of grand Conservative or Labour coalitions, you still end up with a situation where less than 40% of the electorate would have voted for them. Only if Labour can unite with the SNP, will they have a chance of an absolute majority (>325 seats). The best they can do otherwise might be about 300 seats or so.

I find it interesting that the slice of the electorate who probably won't vote is larger than any single party, and larger than all of the potential coalitions listed above bar one (the grand Conservative coalition).

Whatever happens on Thursday — and over the following days and weeks — it will probably be true that any resulting coalition is going to be unpopular with most of the electorate.