Election outcome – what?!

The news outlets have now spent the last 16 hours finding as many superlatives as they possibly can to describe the election we just witnessed. As Britain went to the polls, the opinion pollsters continually had Labour and the Tories neck and neck:


The picture doesn’t make it totally clear (it’s all polls with a smoothed line plotted through), but a visit to, say, UK Polling Report’s polling average makes it more clear.

The outcome, however, is that the Tories polled 36.9% of the vote nationally, and Labour 30.5%, and subsequently the Tories have managed to win a majority, with 330 seats as I write, one more to declare.

The discussion has at least in part centred on why the polls were so wrong. I want to add a minor quip to all of this. As part of my forecasting course I prepared a simple linear regression based forecast model that simply uses nationwide polls alone to predict seat outcomes. I presented it to my students back in March (slide 10), and then also quickly referred to it in a talk at Nottingham Business School on Wednesday (slide 6). Here’s the forecast(s):


Marked on are the outcomes, as they stand. The regression model took each opinion poll with its projected vote share, and also corrected for the number of days until the poll, and whether a party was incumbent. It combined these variables using interaction terms, but remained nonetheless a simple linear regression model. Nothing special.

But it does get Labour’s seat total pretty much bang on. A couple of opinion polls were as optimistic as what’s occurred, but the majority aren’t all that far short of what the Tories ended up with, and certainly this model did predict a much wider gulf between the parties than the naked polls alone did.

What does this say? It probably says that if we corrected polls for their historical performance in predicting seat outcomes, they’re not that far away from what actually happened, in reality. This method does also bias correct polls as well, should they display any bias towards one party or another, and adds a control for an incumbent party – which raises their seat totals, and hence the Tory total being much bigger than Labour despite polling neck and neck.

I’m sure nonetheless that pollsters will get it in the neck, but I thought I’d just point this out…

Forecasting the election – does anyone have any idea?

We’re into the final week before the election, and forecasts abound still. From May2015’s website, most put the Tories ahead, but not by enough to form a majority. May2015 calculate an average of six forecasts and find the Tories 12 seats up on Labour:

A range of bookmakers have been pricing up individual constituencies for some time now, providing an alternative source of information on constituencies to the hugely illuminating Ashcroft polls.

But what do such individual betting markets imply for the national picture? These bookmakers do naturally have overall outcome markets, but to what extent are their individual constituency markets consistent with the overall national picture?

I decided to take the bookmakers seriously with the pricing at constituency level. Each set of odds implies probabilities surrounding outcomes in that seat. However, calculating probabilities for 650 seats to get probabilities of outcomes is a fearsome task. Instead I’ve simulated outcomes: based on the implied probabilities of outcomes in seats, I’ve generated 100 election outcomes for each bookmaker’s set of odds for constituencies (taking any constituency that bookmaker doesn’t have a market for as a certain hold for the incumbent party). The resulting set of outcomes can be thought of as the election occurring according to bookmaker X – what outcome is most likely, what outcome less likely?

What’s the result of this? Considerable disagreement between bookmakers!

Implied Seat Totals

This plot shows what the 18 bookmakers (or betting exchanges, including Betfair) imply for the seat totals of Labour and the Conservatives. Betfair’s exchange is the most conservative, only implying LAB 230 and CON 233, while Betway’s prices suggest that CON will get 300 seats to LAB’s 267. Bet Victor, Stan James, 888sport, Betway, Unibet, and 32Red are the bookmakers whose prices imply CON will win 30-50 more seats than Labour; all remaining bookmakers have the two parties roughly neck and neck.

An interesting aside from this is that as we generate distributions of outcomes according to each bookmaker, we can ask more interesting questions such as: how likely is it that Labour wins most seats? How likely is it the Conservatives get enough for a majority outright? For Betfair’s exchange, there’s a 37% chance Labour wins most seats, a 4% chance they win the same number, and a 59% chance that CON wins most seats. Betfair sees no possibility of either party winning a majority. Conversely, Betway’s prices entertain no possibility of Labour being the biggest party.