# 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!

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.

# The BBCDebate: absentees more influential?

Last night the BBC aired its debate of the challengers, as it put it, with leaders of the five opposition parties squaring up to each other. Prime Minister David Cameron and Deputy Prime Minister Nick Clegg did not participate, and the latter was at pains to point out that he wasn’t even invited.

There’s little doubt this wasn’t the biggest Twitter event of the election campaign, but nonetheless well over a thousand tweets per minute were recorded, and in total we collected 151,417 tweets surrounding the event. Most activity, understandably, came towards the end of the debate as each politician tried to leave viewers with their version of events:

The spike towards the end could perhaps be explained away by the three “major” parties going into spinning overdrive as the debate closed; this seems clearer looking at the numbers of tweets per party:

The second Ukip spike, just after 8:30pm, appears to coincide with Nigel Farage’s attack on the audience both in the studio and at home, while nearer 9pm is when the debate moved to immigration; at this point Ukip were getting more than twice as many mentions on Twitter as any other party.

As Sylvia outlined in our last post after the seven-way debate, we’ve created out own sentiment index, and below we plot the index for each of the parties, including the two not participating in the debate:

What is perhaps most notable is that the index with the biggest range is the Conservative one, despite David Cameron not participating; just before 9, not long after the question on defence, Conservative sentiment is at rock bottom, but just before the end of the debate (perhaps co-ordinated?), Tory sentiment is soaring, although in the final minute Labour’s sentiment is almost identical. The SNP, widely noted for their social media campaigning, also show a late burst, although Sturgeon’s somewhat disappointing final comments appear reflected in the last minute tail off in sentiment.

Overall it’s clear that very little is clear regarding who “won” last night, and whether indeed it was one of the two parties that didn’t participate – at least in the televised debate…

# How Accurate are Constituency Polls?

An additional source of data to calibrate forecast models for the forthcoming general election this time around is the sudden abundance of constituency level polls, almost exclusively thanks to Lord Ashcroft.  This undoubtedly is an awesome resource, but there’s at least two problems:

1. Some of them must be inaccurate, writes Stephen Tall: On the basis that 1 in 20 statistical tests will produce an error if we choose a 5% level of significance, so 1 in 20 polls, statistically speaking, must be wrong. Hence with close on 200 constituency polls thus far, at least 9 must be wrong – which ones, though?
2. How do we calibrate constituency polls into forecast models? In order to do so, we need some historical precedent – a previous election, for example.

As with Stephen Tall’s article, I don’t wish to reduce the importance of, and the welcome addition of Ashcroft’s polls. However, I do wish to try and dig a little deeper into both of these questions.

The only historical precedent we have for Ashcroft’s polls are by-elections, where we know the outcome. Wikipedia’s page on constituency polling, which can with a little bit of pain be turned into a use-able spreadsheet, and marshalled for this purpose.

There have been six by-elections for which constituency polling was carried out in this parliament: Clacton, Eastleigh, Heywood and Middleton, Newark, Rochester and Strood, and Wythenshawe and Sale East. For these by-elections we can plot the opinion poll vote share against actual vote share each party received in the by-election.

The 45-degree line represents a polling ideal: opinion poll vote shares are exactly equal to outcomes. Clearly this is unrealistic for every poll, but pollsters must aim to be near to this line, assuming voting intent does not change between the polling date and election date. Points above the line show that a party got more votes on election day than they were polled to, while points below suggests they got fewer.

Plots are undoubtedly informative, but quantifying potential biases needs more serious statistical work; a linear regression of by-election vote shares on poll shares can reveal the extent to which polls may be biased towards or against particular parties.

The purple dots above the 45 degree line are indicative of a downward bias in polls for Ukip’s vote share; linear regression analysis shows that this is significant, and represents about six polling points: Ukip’s actual vote share in these by-elections was six points more than it was polled to get. Hence pollsters under-estimated Ukip support. Equivalently, Labour’s red dots are generally below the line; pollsters over-estimated Labour’s vote share by three points in these by-elections.

Now, to some extent, it can be argued by-elections are not representative of reality since they often constitute protest votes by fed up voters. And these two biases (the rest are insignificantly different from zero) definitely suggest a protest vote away from the major party (Labour) to the fringe party (Ukip). But were this to be the case, it should be that pollsters pick up this sentiment when polling likely voters?

Nonetheless, this mini-analysis does suggest that, by and large, constituency polling is accurate – deviations from the 45-degree line are marginal at best (except for Labour and Ukip)…

# Have the bookies adjusted for Ashcroft?

Last Wednesday social media was ablaze with Lord Ashcroft’s latest set of Scottish polls, which suggest that Labour are still on course for a Scottish wipeout on May 7. Has this affected what the bookies have to say?

As before, we look at mean implied probabilities for bookmakers, and this time consider the markets for banded ranges of seats for Labour. The impact of worse than previously anticipated polling in Scotland ought to be reflected in a lower seat expectation than previously. Betfair, Bet365, SkyBet, Ladbrokes and William Hill report markets on bands of seats a party wins at the election, and the bands are

• less than 200 seats
• 201-225 seats
• 225 seats and under
• 226-250 seats
• 251-275 seats
• 276-300 seats
• 301-325 seats
• 326-350 seats
• 326 seats or over
• 351-375 seats
• 351 seats or over
• 376-400 seats
• 401 or more seats

Clearly the options towards the bottom of that range are hugely unlikely (bookies rate anything above 375 seats as less than 5% likely to happen), but it’s the upper half of the range when the action has been:

The black vertical line is March 4, when the Ashcroft Polls were released. Hence prices have moved since the announcement, but with the range 276-300 falling in likelihood only from 35% to 34% and 301-325 from 23% to 21%, the impact doesn’t appear to have been dramatic. Lower seat totals like 251-275 increased from 28% to 32%. Less likely events saw bigger moves, with 326-350 seats falling from 12.5% to 7% today.

Overall, the numbers would appear to suggest that the Ashcroft polls are reinforcing the current trends, at least in terms of bookmaker prices; an update to the plot of bookmaker implied probabilities for most seats from two weeks ago emphasises this: