This is the third of a five part series on the 2017 United Kingdom general election. Join us every Tuesday until election day (June 8th) for parts 3 and 4!
This election cycle has seen a lot of commentary on the historic unpopularity of UK Labour Party Leader Jeremy Corbyn. Sitting at a 27% approval rating, Corbyn is certainly an unpopular leader, but he’s not the only disliked party chief the United Kingdom has ever had.
Looking at the approval rating of the Prime Minister minus the approval rating of the opposition leader (I call this the leadership’s “approval advantage”) over time, we see that the UK has a storied past of dynamic satisfaction with government. We also observe that Corbyn is indeed a comparatively unpopular party boss — the third most disliked since polling began in 1977. Right now, PM Theresa May’s approval (technically “satisfaction,” via the poll wording) is nearly 30 percentage points higher than his.
Can we use this information to forecast election outcomes? We sure can!
In 2015, some political scientists used party leader approval ratings to effectively predict the outcome of the otherwise surprise election. Back then, Conservatives leader David Cameron was roughly 11 percent more popular than Labour leader Ed Miliband. Cameron’s conservatives, of course, went on to win by a 6 point margin — much better predicted by his approval rating (or his “approval advantage” over Miliband) than by polling. Will Theresa May achieve the same feat?
We can answer that question by looking at May’s “approval advantage” within the context of history. Looking specifically at the modeled relationship between approval ratings and the win/loss vote margin of the incumbent party since 1979, we see a very strong relationship. In fact, it’s almost as strong as you could hope for an election indicator.
This “approval advantage” accounts for an incredible 92% of variation in election outcomes. In other words, there is very little error when using approval numbers to predict UK elections (in the United States, the error with this approach is much larger). The mean absolute error is a very small 1.9% with low uncertainty; after accounting for the small sample of UK elections, we can expect the error from these predictions to be no greater than 5.5 percentage points in either direction 95% of the time. This is multitudes better than polls of UK elections, which have an average error of 4.4% within a 12 percentage point 95% confidence interval.
We can “plug and chug” the numbers for 2017 to estimate the Conservative Party’s win margin. With May’s approval rating resting at 56 percentage points, 29 points higher than Corbyn’s dismal 27% approval, I estimate that Prime Minister May’s party should win by 15.6 percentage points. As mentioned, there is a fair amount of error in these estimates — 5.5% either way, so the Conservatives should win by no less than 10% and no more than 21.1% of the final vote share in the UK. That’s true ninety-five percent of the time; error could be worse in rare upsets.
As I’ve said, this model has done a good job at forecasting past elections. Notably, where polls erred by 10 and 5.5 percentage points in the 1992 and 2015 elections (picking the wrong winner in the former), the model had errors of only 3.9 and 0.8 percent.
And to illustrate just how significant the model’s increase in accuracy is over polling, here is a similar plot and trend to the one above, this time with polls.
Curiosity prompted me to test how the model would perform when including the leadership’s vote margin in the past election as a second variable. Formally define, that model is:
Leadership’s Vote Margin = -3.85 + (0.49 * Leadership’s “Approval Advantage”) + (0.46 * Leadership’s Margin in Most Recent Election)
This makes sense in theory as a party with a big win in a recent election, though unpopular, could be more advantaged than an equally unpopular party that barely scraped by last time around. Doing so aids our forecasts accuracy by a modest amount, increasing the explanatory power of the model from 92 to 95 percent. Average absolute error decreases from the 1.9% above to 1.5% — again, not too significant a decrease, but noticeable. The error in our litmus tests (1992 and 2015) shift to 2.6% and 1.6%. Our improved prediction for the Conservative’s win margin decreases to 13.5 percentage points with a smaller 4.2 percent confidence interval of error in either direction — so May’s party should win by anywhere from 9.2 to 17.6 percent 95 times out of 100.
Error in UK Election Approval-Based Forecasts
Margin (%)| Election (%)| Error(%)| |— |1979 | -3.8| -7.0| 3.2| |1983 | -13.6| -14.8| 1.1| |1987 | -12.8| -11.4| 1.5| |1992 | -4.8| -7.5| 2.6| |1997 | 12.7| 12.5| 0.2| |2001 | 11.3| 9.0| 2.3| |2005 | 1.8| 2.8| 1.0| |2010 | -7.4| -7.1| 0.4| |2015 | -4.9| -6.5| 1.6| |2017 | -13.4| ?| ?| |Average|||1.5%| |95% Confidence|||4.2%|
Margin is Labour’s margin of loss/victory. Source: Ipsos MORI Historical Polling
And, again, the model taking into account leader approval and lagged vote share is much better than polling. Here is a graph of all election outcomes, modeled predictions, and polled predictions since 1979:
In sum, we can learn a lot from Jeremy Corbyn’s unpopularity besides the usual “he’s not fit to run Labour!” take. Indeed in historical context there has been only one or two party leaders less popular than he. Make no mistake, Corbyn is a disliked leader even among his own party, and as such is expected to perform very poorly in this year’s election. Yet, I offer the final caveat that much can change in the final weeks of the race, to which Labour’s ongoing rise in polls attests. Finally, we haven’t talked about how actual seats get allocated yet — even if Labour does improve on their vote share from 2015, the Conservatives have coalesced such massive support to squash almost any seat gains at which a shift in votes could hint. Yet, if they do improve, things will get very dicey, very quickly. I will leave you with my usual point — that, for all the reasons above (and more) the UK election is a lot less certain than it seems. Though, via the use of approval ratings, we are a lot closer to the truth than we are with polling. At least, that’s what history says.
Come back next week for part four of five in a series on the 2017 United Kingdom “snap” election! If anything happens between now and then, you’ll hear from me right here.
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