This is a cross-post from the excellent Climate Sock. Thanks to Leo for giving permission to put it up here.

Now UK electoral reform for the Commons has been defeated, First Past the Post (FPTP) is with us for the foreseeable future. I was never convinced that Alternative Vote (AV) would be a game changer for smaller parties like the Greens, but FPTP is particularly bad for them.

There’s no doubt that FPTP exaggerates results. Below a certain share of the national vote, parties get fewer seats than they would under a PR system. Above that level, they get more.

Yet the UK Greens do have one MP, and they are in fact less hard done by under FPTP than the other UK-wide parties of similar size: the UK Independence Party (UKIP) and the British National Party (BNP).

In the 2010 election, the Greens nationally won 286k votes (1.0%); UKIP won 920k (3.1%); and the BNP 564k (1.9%). Yet of the three, the Greens were the only party to win a seat, despite receiving the fewest votes (although this one seat was itself equivalent to only about one sixth of the seats they would have won under a fully proportionate system with that share of the vote).

So, why was this the case, and what does it say about the Greens’ prospects under FPTP?

To win a seat in a multi-way marginal, a party typically needs at least 30%. Caroline Lucas won Brighton Pavilion with 31% of the vote; the next target for the Greens, Norwich South, was won by the Lib Dems with 29%. Other Green targets were won with slightly higher proportions.

Yet, with a lower national share than UKIP and the BNP, explanation is needed for why the Greens were able to mobilise 31% in a particular constituency, while the others were not able to do so.

At least part of the answer is suggested by the huge poll conducted by Michael Ashcroft for the Tories.

A key source for this debate is the question on how likely respondents are to vote for particular parties. A response of 1 signifies that they will definitely not vote for that party, and 10 means that they will definitely vote for that party.

The proportions who say they are extremely likely (let’s say 9 or 10) to vote for each of the three parties is roughly what we’d expect: small, and similar to one another.

But the differences are very interesting when we look lower down the scale:

UKIP support

BNP support

Green support

So both the BNP and UKIP have much more of the electorate fixed against them: 84% and 68% respectively, compared with 55% for the Greens.

If we return to a figure of around 30% needed to win a multi-way marginal constituency, it is clear why this is so hard for the BNP. On a national level, 84% have said they wouldn’t consider voting BNP, leaving very little to play for.

Even for UKIP, to reach 30% of the electorate, the party would need to go all the way down the scale to people who say they are just 3/10 likely to vote UKIP.

Yet for the Greens, winning 30% requires going down only as far as those who are 5/10 likely to vote Green: a much less daunting prospect and a result that suggests that future seats may well be winnable for the Greens.

Just a couple of caveats. Firstly, this makes an assumption of uniform national distributions. Clearly that isn’t the case: it’s an approximate model. Yet, the size of the differences between the parties suggests that it is useful.

Secondly, I’ve treated each party’s scores on these scales in isolation, when that isn’t quite right. A respondent could have said they were 10/10 likely to vote for several parties. What this shows is potential support, not guaranteed support.

For the Greens to win more Westminster seats they would need to take support from the major parties. Given their relatively wide level of latent support, this may be within reach, even under the current electoral rules.