By Stephen Fisher.

UKIP are putting up just 377 candidates at the general election, well short of the 624 they had in 2015. Given that the polls are showing that around half of former UKIP voters are planning on voting Conservative this year, and given that the Conservatives clearly benefitted from the collapse of the UKIP vote in the local elections, surely UKIP dropout is a big advantage for Theresa May?

Perhaps not. A good way of assessing this question is to look at the experience of local elections and analyse how much other parties benefitted when UKIP stood a candidate in 2013 but not this year, compared with where they had candidates both times. To make the context more like a general election I focus just on places fought by the Conservatives, Labour and the Liberal Democrats both in 2013 and 2017.

There were 969 such divisions where the BBC collected the full details of the result. Of these 523 had UKIP candidates both times, and 446 had a UKIP candidate last time but not this time – only a slightly higher (46%) dropout rate than that for the general election (40%).

Moreover, just as is being reported for the general election, UKIP failed to field candidates in places of previous strength as well as weakness. Their dropout rate was higher the worse they did in 2013, rising to 67% for places where they got less than 18% of the vote. But even among divisions where they got over 30% of the vote last time, they failed to field a candidate in 61 of the 194 divisions this time.

Regardless of dropout, the swings from both Labour and the Liberal Democrats to the Conservatives were much bigger where UKIP did well last time. The stronger the UKIP starting point the more former UKIP voters there were to switch to the Conservatives.

The swings were a bit bigger when UKIP dropped out. But not that much.

Regression analysis shows that where UKIP started with around 13% (taking their vote share in the 2015 General Election as an example) the swing from Labour to the Conservatives was 3.9 points if UKIP stood again, and 4.6 points if they dropped out. A difference of just 0.7 points.

Similarly, the swing from the Liberal Democrats to the Conservatives was 1.8 points if UKIP stood again, and 2.3 points if they dropped out. A difference of just 0.5 points.

These differences, the dropout effects, get larger the stronger the UKIP starting point. But they are never very big. For the divisions where UKIP got more than 30% in 2013, the effect of dropout is to increase the swings from either Labour and the Liberal Democrats to the Conservatives by just 2 points each on average.

The reason UKIP dropout had such a small effect on the swings to the Conservatives is that it benefitted all three of the other main parties, it just helped the Conservatives a bit more.

This does not necessarily mean that when UKIP drop out all the other parties get some of their voters. Without any UKIP candidate to support, former UKIP voters may just have abstained, leading to an increase in vote share for all the other candidates. But if that were the case then UKIP dropout should have been associated with lower turnout. If anything, after controlling for the tendency for turnout to increase less where UKIP did best in 2013, the opposite is true.

With so many former UKIP voters switching to the Conservatives, it is worthwhile thinking about what kind of UKIP supporter still wants to stick with UKIP. They are likely to be predominantly the ones that are not particularly keen on the Conservatives. If they have not been so far tempted to by Theresa May and her approach to Brexit, they are surely going to be more reluctant to vote Conservative than the average Ukipper, even if there is no UKIP candidate to vote for.

In the general election, UKIP dropout is likely to help the Conservatives a little in those seats where UKIP did well last time, but in most places the dropout effect may well be negligible.

**A statistical curiosity**

On average in the local elections the swing from Labour to Conservatives since 2013 in places where UKIP stood both times was 6.7 points. In places where UKIP dropped out it was 6.7. No difference.

On average the swing from the Liberal Democrats to the Conservatives since 2013 in places where UKIP stood both times was 4.2 points. In places where UKIP dropped out it was 4.0. Barely any difference.

How come? The swings from both Labour and the Liberal Democrats to the Conservatives were much bigger where UKIP did well last time, but UKIP dropped out more often where they did worse. So even though UKIP dropout did help the Tories a bit at all levels of prior UKIP vote, this is offset by the fact that UKIP dropout was occurring most where the swings to the Conservatives were smallest.

This is an example of Simpson’s paradox. It could be replicated at the general election.

Out of interest what was the difference to Labour to Conservative swing with UKIP dropout where UKIP performed worse than 13% in 2013?