MPs don't get punished much for the stances they take

A new working paper shows voters were only slightly less likely to vote for incumbent MPs with the opposite view on Brexit

Next Tuesday, MPs will vote on the government’s proposed Withdrawal Agreement (WA).

When they vote, MPs will have to weigh several different factors.

One of those factors is public opinion — and more particularly, opinion in their constituency.

According to the polls, the government’s deal is the worst form of Brexit — except for all the others.

Some have tried to use public opinion to persuade MPs.

“Vote down the deal”, they say, “else you might lose your narrow majority”.

But does that claim really work? Are MPs punished for positions which are out of sync with those of their constituents?

According to a new working paper that I’ve authored together with Patrick English and Jon Mellon, the answer is, “no, not really”. Voters are slightly less likely to vote for incumbents with whom they disagree — but these effects are so small that, in 2017, they would only have changed the result in four seats, with no net effect on the government’s majority.

We base this claim on an analysis of how respondents to the British Election Study voted, given their own position on Brexit and given the position of their MP (which we've taken from the BBC's handy running tally of May-June 2016).

The large sample size (~25k) and the broad range of questions asked in the BES allow us to test this relationship in a very detailed fashion — but you can get some flavour of our findings just by looking at the following graph.

The graph shows the change in the vote share of Conservative and Labour incumbents (on the vertical axis) according the Leave vote share in the constituency (horizontal axis) and whether they supported Leave (blue circles ○) or Remain (yellow crosses +).

Looking at the left panel, we see that Conservative incumbents generally did better the Leavier each constituency was. But that trend held true whether or not each individual Conservative MP supported Leave or Remain. We might have expected Leave-supporting candidates to do better the more strongly Leave each area was — but instead, the trend lines are identical.

Looking at the right hand panel, it seems like there's more of a pattern — although Labour prospects get worse the more Leave the seat, the slope is steeper for Remain supporting MPs. But that might just be an artefact — a consequence of the very small number of Labour MPs who supported Leave.

At this point, you might be screaming (or tutting loudly at your computer) that we're confusing (partial) correlation with causation, that we're committing an ecological fallacy, and doing many of the other things social scientists do when they're feeling a bit mischievous.

You'd be right, and that's why we've also conducted an individual level regression analysis using the BES. The full details of our model, and the control variables we include, are in the paper. The take-away is shown in this graph, which shows how much more likely respondents are to vote for an incumbent who shares their position on Brexit.

It's probably best to focus on the final, right hand column, which shows the combined effect. Voters are 3–4 percentage points more likely to vote for incumbents who share their Brexit position.

That might sound like a lot to you — but it's not going to help you win many votes. If I, a Remain-supporting MP, switch sides to gain a vote from you, a Leave-supporting constituent, then I'm going to lose a vote from the Remain-supporting constituents who were previously unhappy with me. Only if my constituency is very lop-sided — if I'm a Remain-supporting MP in a seat that's heavily Leave — does switching really pay off.

We can refine this analysis a little bit. Sometimes supporting an MP who doesn't share your position on Brexit might not be great, but you might not have a realistic alternative. If you're a Leave supporter in a contest pitting a Remain-supporting Labour MP against a Remain-supporting Liberal Democrat, then you might fallback on all the other political issues that aren't Brexit-related (of which some do still remain).

We therefore tested whether these effects were greater where there was a clear contrast in the seat. That's to say, we looked at seats where:

• the incumbent supported Remain, and where the nearest challenger (based on past election results) was from the Conservative party or UKIP; or where
• the incumbent supported Leave, and where the nearest challenger was from anyone apart from the Conservative party or UKIP.

As you might have expected, the effects were greater in these seats with contrast (plotted with circles ○) than in the seats without contrast (plotted with triangles △):

In seats with contrast, respondents are 5 percentage points more likely to vote for incumbents who share their Brexit stance.

In seats without contrast, our best guess of the effect is close to zero.

What does this mean in practice? Here we'll have to quote at length from our paper:

37 of the 524 MPs considered here lost their seat in the election. Of these, sixteen were also out-of-step with their constituency. Seven of these fifteen MPs, because they faced a challenger who had a contrasting position, could have reliably improved their vote share by switching. In four cases, the increase in vote share might plausibly have exceeded the challenger’s margin of victory. In Kensington, Victoria Borwick would have gained four percentage points by switching from Leave to Remain, greater than the very small majority won by her Labour challenger (0.05%). In Canterbury, Julian Brazier would have won one percentage point, once again greater than the majority of his Labour challenger (0.33%). Had these two Conservative MPs switched,
the Conservative party would still have lost its majority, but would have been slightly less reliant on the Democratic Unionist Party. Conversely, two Labour MPs could have retained their seats had they switched. Rob Flello, MP for Stoke-on-Trent South (which voted very heavily to Leave) could have secured 4.5 percentage points more by switching, exceeding his (Conservative) opponent’s majority of 1.6 percentage points. Alan Meale (Mansfield) could similarly have beaten the Conservative candidate Ben Bradley. The net effect on seats of this kind of perfectly foresightful incumbent switching would have been zero.

Our paper is just about the electoral consequences of MPs' positions. They are not, in themselves, a reason for MPs to act on way or another.

They do, however, make it more difficult for some arguments to be sustained.

If you're the Anti-Burke, someone who believes MPs should slavishly follow constituency opinion, then these kinds of findings are a problem for you, because they show that MPs' face limited incentives to follow constituency opinion. (I mean, I think your bigger problem is that you have a seriously impoverished notion of representation, interests and preferences, but that's by-the-by).

Our paper doesn't mean "MPs can do whatever the hell they want". We've focused on electoral accountability, but the heart of accountability is, quite literally, giving an account: a reasoned statement of why you did what you did. Whether it makes their seat less marginal or not, a lot of MPs need to give quite careful thought to their account of how they intend to vote on Tuesday.