tl;dr version. If you think Tory defectors will bring 45% – 55% of their vote with them (alternately: that the Conservative retention ratio is less than 55%), then four Tory MPs would do better by defecting. But this is unlikely.
In today’s Financial Times, research by Matt Goodwin is quoted as providing support for the claim that
four Conservative MPs [those in Amber Valley, Cleethorpes, Bury North, and Dudley South] would be more likely to retain their seats at the next election if they defected to the UK Independence party
I had a strong negative reaction to this claim. I find it implausible. This is despite my prior belief that anything Matt says about UKIP is generally worth credence. Matt probably knows more about UKIP than anyone outside the party, and possibly more than some within the party as well.
Part of the reason for my negative reaction is that it’s very hard to provide good evidence-based estimates of the likelihood of something happening, if that thing has never before happened. No MP has defected to UKIP and subsequently contested a general election under that party’s banner. (Bob Spink did defect, but contested Castle Point in 2010 as an “Independent Save Our Green Belt” candidate). Given this, I’m not sure how you can calculate either
- the MP’s current probability of winning under the Conservative banner, or
- the counterfactual probability of winning under the UKIP banner.
As I’ve learned doing electoralforecast.co.uk, it’s very difficult to calculate the first of these even given a reasonable amount of information.
But this is a philosophical objection. I think there are more important practical objections. Let’s assume a number of things to get some numbers on the table.
First, instead of talking about the probability of retaining one’s seat, we can talk about the expected gap between the incumbent and the nearest challenger (in all cases, Labour). This is really just to avoid talking about probability, which is… tricky.
Second, assume that we can gauge the expected gap between the incumbent and the nearest challenger, in the situation where the incumbent fights under the Conservative banner, by applying a simple uniform swing based on what is currently reported by UK Polling Report. This suggests that the Conservatives will lose 4.1%, that Labour will gain 5%, that the Liberal Democrats will lose 15%, and that UKIP will gain 12.9%.
If you do this, you could expected outcomes like this:
If you make this assumption, then these four MPs are indeed in trouble. I am making this assumption for the sake of argument : I do not think that it is very plausible. I do not think that the polls reflect the likely outcome in May. In particular, I disagree with Matt when he says
I can see no reason why Ukip’s average poll rating will fall significantly this side of the election.
Now, there’s wiggle room in that quote. But there are reasons why UKIP’s average poll ratings might fall significantly — and that’s simply that, looking at elections since 1979, parties have generally performed closer to their previous general election share than the polls would suggest. So in assuming away any significant decline in UKIP vote share, I’m being charitable to Matt’s argument.
Of course, Matt could equally well argue that the swing towards UKIP in these four constituencies will be greater than the swing nation-wide, because UKIP will concentrate effort in these four constituencies were there a defection. So, depending on your beliefs about concentration of the vote and UKIP fade-off, this assumption may be either favourable or unfavourable to the argument.
Third, we can speculate about what might happen given a defection by keeping the Labour and LibDem votes constant, and transferring increasingly larger shares of the Conservative vote to UKIP. It will be helpful to think of this as the Conservative retention ratio (CRR). If the CRR is zero, then defection is perfectly efficient, and there are no deadweight losses of any kind. If the CRR is one, then defection is a simple substitution. It should be clear that the CRR is unlikely to be zero: that would mean, in effect, that the Conservatives didn’t stand a candidate, something they are hardly likely to do.
Again, this assumption is unrealistic. Even absent a defection, the Labour vote share in any given constituency is not simply what you would expect given a uniform national swing. The Lib Dem vote in Amber Valley can’t be what you would expect given a uniform national swing, since it’s zero! But this is a simplifying assumption.
Given these assumptions, I’m going to plot the expected benefit of defection on the vertical axis, as a function of the CRR. That will be in a solid line. To the right of the figure, where the CRR is high, defection becomes a simple substitution. To the left of the figure, where the CRR is low, defection approaches perfect efficiency. As the CRR increases, the expected gap to Labour under defection becomes greater than the expected gap to Labour without defection. The expected gap to Labour without defection is shown with a dotted line.
These trade-offs are plotted in the figure above. For all four constituencies, there’s a break-even point. It’s 44% in Amber Valley and Bury North; 53% and 54% in Cleethorpes and Dudley South respectively. If the Conservatives retain a greater share of their vote than this, then defection hurts defectors.
So the question then becomes: is it reasonable to suppose that the Conservatives will retain less than 45 or 55% percent of their vote?
Imperfect evidence comes from three sources:
- Bob Spink’s re-election campaign in 2010
- the Clacton by-election
- SDP defections in 1981
Let’s take these one by one.
The Spink spat
In 2005, Bob Spink won Castle Point with 48.3% of the vote. In 2010, the Conservatives polled up 3.7% on their 2005 performance. Thus, we might have expected that had Spink not defected, the Conservatives would have polled 52%. In fact, with Rebecca Harris they polled 44%, which equals a retention rate of 84.6%.
The Carswell coup
In 2010, Douglas Carswell won Clacton with 53% of the vote. At the time of writing, the Conservatives are down 4.1% on their 2010 vote share. Thus, we might have expected that had a by-election been forced for reasons other than defection, the Conservatives would have polled 48.9%. In fact, with Giles Watling they polled 24.6%, which equals a retention rate of just over 50%.
Thanks to Wikipedia, I identified twenty-eight Labour defectors to the SDP. For eighteen of these, I was able to calculate the Labour share of the vote in 1979 and 1983. Note that in 1983, Labour’s share of the vote dropped by 9.3 percentage points. The average Labour retention rate was 87.2%. The lowest Labour retention rate was achieved in Caithness and Sutherland, where Robert MacLennan (SDP) did rather well. The next-best retention rate was 55%, in David Owen’s seat of Plymouth Devonport.
Now, for the reasons noted above, none of these is an exact comparator. Generally, retention rates amongst parties that suffer a defection are north of 55%. It therefore seems that the above claim — that four Conservative MPs would do better electorally by defecting — is only true if Carswell is the rule rather than the exception. I rather think that it would be foolish to take either (a) a generally respected constituency MP, or (b) the most Eurosceptic constituency in the country, as the rule for Conservative defections.