The polls were correct, we just didn't understand the question.

<![CDATA[Numbers are authorative – this is probably a perception picked up in our school years, when mathematics seems so black and white: the answer to a sum or calculation is either right or wrong; there is no scope for debate or subjective judgement. Only those who go on to degree level or higher see that subjectivity creeps back into mathematics.
It is no surprise, therefore, that Douglas Adams chose a number to be the answer to the question of life, the universe and everything.
So, that the numbers which constitute the polls which dominated the media during the election campaign should so dramatically fail to predict the outcome has created a small storm. Some have started to blame this on people changing their mind, or simply lying to the polls, although why this should be more prevalent in this election than others is not clear.
However, looking closely, the polls seem to be actually pretty accurate – the problem, like the answer to life, the universe and everything, is not being clear about the question.
Looking at the various polls included in the BBC Poll of Polls, all work in very similar ways. They select a group of 1000 people at random and ask them how they will vote. The differences between the polls include the wording of the question asked, how the group is selected, and any normalisation to remove bias in the group selection.
This means, of course, that the poll is indicative of how many people will vote for a given party.
Comparing the various polls (using the values from the 6th May just before the election; source, with the actual results are interesting:

Conservative Labour UKIP LibDem Green
BBC Poll of Polls 34% 33% 13% 8% 5%
Survation 33% 34% 16% 9% 4%
TNS-BMRB 33% 32% 14% 8% 6%
Opinium 35% 34% 12% 8% 6%
Populus 34% 34% 13% 9% 5%
ICM 35% 35% 11% 9% 3%
Ipsos Mori 35% 30% 10% 8% 8%
ComRes 35% 32% 14% 9% 4%
YouGov 34% 34% 12% 9% 5%
Result 36.90% 30.40% 12.60% 7.90% 3.80%

or as a graph
To me that looks pretty accurate – certainly well within the expected margins of error.
The problem is, of course, that in our First Past the Post system, seats aren’t allocated according to the total percentage, but by the winner in different electorial regions. The relationship between the percentage vote and the actual number of seats the party actual wins, is both complex and messy. As such the polls are (still) a good predictor of a parties overall votes, but a poor indicator of how many seats they would win.
This seems pretty obvious but given that this has always been the case, why has it suddenly become an issue in this election? Well, not least of all because we’ve moved from a two party system, with various smaller parties becoming more significant, the discrepancy between the overall percentage votes and seats is much greater this time, as many commentors have observed:
Some will argue that this is necessary to ensure we have definitive winners and strong parliaments, whilst others will argue that this is unfair and our electoral system needs reform, and that coalition parliments are more democratic rather than weak.
However, the real problem lies in a misunderstanding what the polls tell us when there is no clear leader in the overall percentage vote.
If a party has a 20% lead in the polls, it doesn’t mean it will get 20% more seats – it is instead a good indicator that the party will get a majority of the seats
If the party had a 40% lead rather than indicating an increase in the majority, it really indicates that you can be more confident that that party will win a majority of seats; on the other hand a 10% lead means the reliability of the prediction is less.
Hence, a poll with the two lead parties running neck to neck does not tell us that we will get a hung parliament (as the media constantly reported) but rather than the poll’s ability to make a prediction is extremely weak (which admittedly the media also talked about the outcomes uncertainty but not quite for the right reasons).
It remains to be seen what influence the polls (or rather the misinterpretation of the polls) on how people voted (and whether this had a significant impact), for example how many people voted tactically assuming on the basis that the outcome would be a hung parliament.
One notable feature of all the polls however is that the SNP was lumped together in the “Others” category, which may explain why its performance came as such a surprise to the media and politicians.]]>

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