Regular readers will know that I have often complained about surveys claiming to show that an issue or policy stance will make people more or less likely to vote for a party. I’ve written about it previously here, here and here.

Polls like this are very popular with pressure groups and political campaigns because they inevitably end up suggesting that the issue they are campaigning on is really important and will swing votes, and MPs better listen to them and do what they say or they’ll lose their jobs. The problem is people don’t actually behave like that – we know from academic studies that people don’t vote on single issues, they vote on broad things like party identification, perceptions of party leaders, perceptions of competence, economic trust, party image and so on. Individual policy stances play into these things, but to reduce the complex drivers of voting behaviour to polling questions purporting to show that “If party X follows policy Y then 14% of people won’t vote for them” is simplistic and naive.

I won’t recite at length why these questions give such misleading data, but there are a number of reasons. Firstly respondents use them to indicate support or opposition to a policy or a party regardless of whether it would actually change their vote. Secondly it gives false prominence to a single issue, when in a real election campaign that issue would be considered alongside other important issues like the economy, leadership perceptions, party competence and so on. Thirdly people simply aren’t very good judges of what drives their own decision making. Working together these produce results that overestimate the impact of single issues on voting intention.

Yet, it is a question that people eternally want asking – and keeps provoking rather silly news stories, full of hyperbole about gay marriage dooming the Conservative party. Hence it is worth trying to do it sensibly.

In the Sunday Times/YouGov poll this week they first they asked what three or four issues would be most important to people in deciding their vote at the next general election. It’s still simplistic of course, and still depends on people understanding the drivers of their own voting intentions when they don’t, but at least it doesn’t give an issue false prominence.

Asked this way, 56% say the economy will be an important issue in how they vote, 42% immigration, 36% health, 28% unemployment and so on down to gay marriage, of which 7% of people say it will be an important issue in deciding their vote. This includes 5% of current Tory voters and 5% of 2010 Tory voters.

Of course, not all these people who care about the issue are necessarily opposed to it. YouGov asked those 7% who said gay marriage was likely to be an important factor in deciding how they voted whether it would make them more or less likely to vote for a party – 54% said more likely, 44% less likely. In other words three and a bit percent of voters claim they are more likely to vote for a party that supports gay marriage, three and a bit percent claim they are less likely.

Looking just at Tory voters, that 5% of Tory voters who say it will be an important issue in deciding their vote are mostly people who would be less likely to vote for a party that supported it… but this still equates to just 4% of Tory voters – that is, about 1 percentage point of their current 34 percentage points of support. Hardly a huge election winning or losing issue.

Even this is likely to be an overestimate of course, because as I said at the start of the post, people aren’t very good judges of what drives their voting intention and individual issues aren’t actually much of a driver of voting intention; party identification, competence, the economy, leadership perceptions are the sorts of things that actually drive votes. On top of that, gay marriage is very high up the news agenda right now – I expect it will be a far less high profile issue in 2 years time. It also ignores whatever positive impact the issue might have.

In terms of a direct effect, my guess is that, by the time of the next election, gay marriage will have negligible impact on Tory support. Potentially more important is the indirect effect – whether, on one hand, that it adds to perceptions amongst traditionalist voters that David Cameron does not understand or reflect their views or, on the other hand, helps build perceptions that the Conservatives are a more modern and tolerant party that is at ease with the modern world.

Things like this are almost impossible to measure in polls, but are probably far more important. My own view is that Michael Ashcroft is right on this – in terms of impact on party perception Cameron may or may not have been right to come down the route of pushing gay marriage, but now he is here he must continue. Changing his mind won’t convince his detractors that he actually agrees with them, it will just make him look weak, while fatally undermining whatever positive impact it has on making the Conservative party look more tolerant and in tune with modern Britain (that said, I’m far from convinced that it is having a positive impact on that front, because the impact of David Cameron supporting gay marriage risks being cancelled out by the impact of right-wing Conservative backbenchers opposing it).

Meanwhile YouGov’s weekly poll for the Sunday Times has topline figures of CON 34%, LAB 41%, LD 12%, UKIP 8%. The mid-week Sun polls clearly suggested the referendum boost was on the wane, but these figures suggest it hasn’t completely gone yet.

357 Responses to “What impact does gay marriage have on voting?”

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  1. @ AW

    I agree with your analysis. But have you any idea how the Telegraph managed to translate this poll into:

    “Twenty per cent of those who said they voted Conservative in 2010 agreed that they would not do so again in light of gay marriage”

    The figures you quote are nowhere near that and yet the paper has somehow got a pretty black and white comment that doesn’t seem open to interpretation (accepting the caveats that what people say in polls isn’t necessarily the truth).

  2. Thanks AW.
    There seems to be a big discrepancy between the polls and the amount of ruckus it is creating amongst the Tory rank and file.I think it will have a negative effect on the Tories come the next election but I might be completely wrong and Cameron`s detoxification strategy might work a treat winning over Labour voters.

  3. @ shevii

    That telegraph article is from the other day and is quoting a Comres poll for the Coalition of Marriage not this poll.

  4. Anthony’s comments pretty much mirror what I posted on this a couple of days ago. I suspect it’s the lack of enthusiasm for Cameron amongst the front line party troops that has the biggest impact.

    Come the election time, I doubt many voters at all will even remember the gay marriage issue, but the steady sense among his party faithfull that they don’t trust their leader does seem to be tipping a number of them towards other parties or just to sit on their hands.

  5. So it’s not clear yet whether the small bounce from the referendum is unwinding. At present, the running averages give the Tories a 2 point bounce, 1 from each opf Lab and UKIP. The last two Lab leads (12 and 7) seem to be at each end of moe for a lead of around 9.5.

    My guess is that the full bounce lasted for precisely 2 polls (with Con on 35) and since then there has been something of an unwind. It’s going to take a while before we see if there has been any lasting effect

  6. @Smukesh

    I think the problem is that “detoxification” of the Conservative party hasn’t actually been successful. The party leadership “detoxified”, but the rest of the party hasn’t. It’s silly to talk about “detoxification” as if it’s been successful when DC is facing revolt over one of the principle parts of his detoxification project.

    The difference is that Blair’s New Labour project had teeth, people in the party were told to get with the program if they wanted any influence, let alone government jobs. DC however, either chose not to, or was too weak in his position, to be that strong in a top-down reform of his party. Chris Grayling’s continued presence in Government for instance.

    This has led to a situation where the Conservative’s new intake rather than being in support of the Detoxification project, have actually opposed it. And the “Grass Roots” activists haven’t been brought on board and are actually lobbying against their own government on a huge range of things.

  7. Parliament will pass the bill and Tories faced with the alternative of a Labour majority from May 2015, will reluctantly continue to vote for them. The Tories will no doubt put billboards up, saying that each vote for UKIP, is a vote for a Labour majority.

    Think Cameron and the Tories will gain more from same sex marriage legislation than they will lose.

    Slightly surprised by todays YT YG poll having predicted a Tory dip. Though looking at some of the crossbreaks, I suspect that the Labour lead is still around 10%. It looks like in the 40-59 age category, that many of those polled were at the upper end of the age range. I should imagine that there is quite a difference in VI between those in the 40-49 age bracket, than those aged 50-59.

  8. @ Leetay

    Thanks- that explains a lot!

  9. Shevii

    The ComRes tables aren’t yet available, but I suspect they did what Anthony describes above – ask people straight out how it would affect their vote. They may even have not asked what people’s actual voting intention was first.

    YouGov did something subtler. They first asked Which of the following issues will be important
    to you in deciding how you vote at the next
    election? Please tick up to three or four
    (an interesting question in itself) and then only asked the 7% of those who chose “Same-sex marriage” as one of their three or four[1] how it would affect their vote. Of this tiny sample (140) most said they would be more likely to vote for a pro-SSM Party by 54% to 44%.

    Of the 28 or so Conservative voters[2] 80% did say it would make them “less likely”, but remember even the nett 60% of this group will have given two or three other issues that will also affect them.

    I reckon that only about 8% of the Other Parties/Non voters put SSM as one of their top issues. Given that 20% of this group are UKIP supporters (allegedly all fiercely opposed to SSM) this suggests that there hasn’t already been an anti-SSM inspired exodus from the Conservatives. Though even if every anti in this group was choosing UKIP that would only make 20% of their support.

    [1] To make a comparison Animal rights got 4%. Though I don’t know how many badgers they asked.

    [2] That is 5% of 550 the lowest percentage of any of the three Parties. Needless to say the tiny samples make all these figures statistically unreliable – the very fact they are so small is their main significance

  10. Off topic as i suspected there is a new poll on Scottish independence the first to use the actual question. It is in the Scottish mail on Sunday, but here is the Herald mobile link to it.

    On topic,

    As I said yesterday, people may have personally preferred marriage to stay between a man and a women but they have put fairness above that. I think Ashcroft is spot on Cameron needs to focus on what the whole country wants and not be diverted by his “tea party”.


  11. Why does anybody put any credence in what newspapers say about almost anything to do with politic’s.
    All their interested is a sensational headline usually based on either their particular political leaning or what they think will boost the sale of there newspapers, usually on the basis of look at the headline never mind the truth.
    The reporting of the issue over gay marriage is a classic case in point, if you read some newspapers you would get the impression it was “ripping the Tory party apart”.
    Which is abject nonsense, it’s true a few supporters are not happy with gay marriage but the likely hood of that putting confirmed Tory supporters off voting Conservative in the next GE is just plain wishful thinking by some.
    It has to be said the newspapers are not alone in this type of news over exaggerating the BBC and Sky News promote this poor journalism at every opportunity with to many one sided arguments extorting views of minority groups as fact which then goes unchallenged.
    The reporting of factual news was always of a fairly low standard but in the last few years the press and media seem to have reached new lows, to many mediocre interviewers, to much twitter, not enough fact.

  12. Whatever the niceties of polling data, if it matters to anyone as an issue which might affect VI, it is with voters who are already tempted by the more forthright conservatism espoused by UKIP.

    There have been Con>UKIP swings in Westminster byelections, and in the May locals… any trend in local council byelections is almost impossble to discern, but there have been some signs that where UKIP finds a candidate and mounts a campaign they can depress the Tory vote. In most instances a Con>UKIP swing doesn’t affect the outcome, but once in a while it will be a cause for concern:

    Norfolk CC Clenchwarton and Kings Lynn South, September 2012

    Lab 45.8% (+34.1)
    Con 23.5% (-15.7)
    LD 15.7% -(13.1)
    UKIP 15.0% (+15.0)
    Lab gain from Con.

    It probably won’t have any effect at all, but if (and that is an if which does worry Tory MPs) there is any appreciable swing to UKIP at the GE, some people will blame it on marriage equlity legislation.

  13. @Billy Bob,

    That’s an interesting poll result. It looks like as well as eviscerating the LibDems that Labour have picked up over 20% from some other source (not listed). Does that suggest that there had previously been another “big candidate” (perhaps a popular independent, or a Green or UKIP or “Liberal Party” etc) that chose not to stand?

    I actually agree with you that there will be a small detriment to the Tories in a few seats from UKIP refuseniks but its an odd example!

  14. Interesting, but not surprising, that David Cameron finds it worth while to meet the presidents of Pakistan and Afghanistan together, mainly, it seems to discuss common strategy and action to end the conflict in Afghanistan; and presumably to brief them on action in Mali. This is against a background in which the Karzai thinks that Pakistan has territorial interests in the border area and is harbouring Taleban leadership and supporting its ambitions. I think it is a good move. If he pulls off any rapprochement, he would deserve a strengthening of his reputation in foreign policy. Whether it would make any difference to his or his party’s position in the polls is another matter..

  15. David Cameron is de-toxifying himself, not his Party. His supporters have been countering rumours that he’ll be deposed by saying DC is more popular than his Party & the election contest will be Presidential: i.e. Vote Labour & you’ll get Miliband as prime minister. Labour could counter this by saying: Vote Cameron & you’ll get the ‘nasty’ Party as your government.

    I’m of the opinion that it’s easier for Labour to ‘carry’ Ed M than it is for David Cameron to ‘carry’ the 100 backbenchers who are out of step with the majority of Brits.

  16. The answer so far as Scotland is concerned.


    It is a devolved matter and the Scottish Parliament likes to get there first with things like the smoking ban, minimum pricing etc..

    A majority in each party and in the country is for SSM. The debate is over. Two of the five parties have an openly gay leader, and one of these is the Conservative.Conservatives are marginal and UKIP irrelevant.

    Where it will have an effect is that people will see that an internal problem of party management which has no relevance to Scotland gets an unwarrented amount of media and government attention.

    That is nothing new.

    A continuing decay in respect and credence for the media, the Westminster parliament and its political parties is the normal state of affairs and this issue cannot be distinguished from the background.

    That cynicism would help the YES campaign were it not that it is already priced in.They might gain up to five votes

    It is a quarrel in a not very far away country of which we know far too much, while what is important to us and near at hand is ignored.

    The incestious relationships between metropolitan focused media, government,entertainment and celebrity culture is what is driving the demand for independence.

    There might be some in the luxury wedding venue market who are hoping it doesn’t happen so that we can have the Gretna Green trade back again.

    You could probably book a venue now if you were advised by any MSP and I know Church of Scotland and Unitarian celebrants ready to do their bit when asked.

    The Scottish Churches Parliamentary office has the content of the bill on its webste.

    It is as good as over apart from the administrative process, and such things as training registrars.

  17. Re: The Euro Bounce

    Cameron gained noticeably more by using the veto than he did by promising a referendum. (About a 4pt+ gain compared to about a 2pt gain).

    Does this not support the idea – found also in polls – that the majority of British people want to see the UK in the EU and standing up for itself rather than outside of the EU as the sceptics claim?

  18. @Turk – It’s very easy to blame the press for distortion and exaggeration when they are running with a story putting your favoured party in a bad light, but these things rarely occur in a complete vacuum.

    I’ve just watched David Davis on the Politics Show, and he described quite openly a dinner he had with a current serving Tory cabinet minister this week, whose first question to him was ‘how many members have you lost?’. The minister told Davis he has lost ‘dozens’ of members, while Davis admitted his constituency party had also lost ‘a lot’, all apparently as a direct result of the gay marriage policy.

    Now I would accept that Davis has an agenda, so we need to be cautious about interpreting unattributed comments passed on publicly by Davis, but equally you can’t accuse the media of inventing or exaggerating this particular story.

    Last night we also had a leading regional Tory figure from the SW on TV news explaining why he has left the party, and I’m sure UKPR posters have come across other examples.

    While some of the reporting of polling data has been at it’s usual woeful level, my sense is that the general coverage of the issue has broadly speaking been on the mark. There really are ructions within significant parts of the Tory party over this, and it really does look like they are losing key local members and organisers, which could very well have an impact on real votes in due course.

  19. It’s funny how your brain sometimes jumps to conclusions. I just read a headline about fighting extremists in Mali as reading ‘UK Must Fight Extremists in the Mail’.

  20. This made me smile –

    It carries the tag line “Ed Miliband needs to come up with some policies by the end of this year to show he has a “clear orientation” for the Labour Party, Tony Blair has said.”

    I did smile, as while Blair was in power for over 10 years, I still never really figured out what he stood for.

    To be fair, the article does seem sensible though. He talks about the difficult policy choices Labour need to make in the next year or so, which I don’t think many could disagree with.

  21. @NeilA

    Green (8.3%), and BNP (12.1%) both dropped out since the 2009 showing.

    I do hope this doesn’t prompt a breakout of the “BNP are ex-Labour” type posts from some on this board because I get tired of posting the link to AW’s “working class Tories” analysis.

    I don’t think you can say much useful on that level of turnout, perhaps if UKIP didn’t feild a candidate their supporters may have stayed at home, or voted Tory… we don’t know.

    It doesn’t amount to a “trend” but fwiw here is another result from the same day (change since May 2011):
    Dartford BC Castle
    Con 43.0% (-13.3)
    Lab 25.6% (+4.6)
    UKIP 13.5% (+13.5)
    Residents Association 11.3% (-2.6)
    Eng Dem 7.2% (-2.2)

    Whatever the truth of the polling on this matter, it hasn’t stopped a number of MPs (and cabinet members reportedly) getting heated on the subject in the media. “Ruining the chances of Conservatives being reelected at the next election” according to one.

  22. New indyref poll: Yes 32, No 47, Unsure 20
    28% was the lowest support for Scottish Independence since the referendum was announced, unless I am mistaken. The -0.3% GDP & the potential EU referendum announcement (+ Tory poll bounce?) have probably been the drivers for a small increase in support for Yes.

  23. Turk

    I completely agree. Devolution makes the relevance to Scottish Conservative voters (who have no party further right to go to) even less.


    Which is the chicken, which the egg?

    Europe energises right wing Cons – the more innumerate among them (like the labour left when there was one) do not realise that FPTP is their enemy, not DC. They flirt with UKIP – UKIP get attention in press and improve in the polls – righty cons imagine there is more and growing support for their position – the latent UKIPers wake up – they think they have more support than they had realised. SSM energises righti wing cons – etc.

  24. Excellent article, Anthony. It could almost have been written by me.

  25. @AW, Martyn, Statgeek or other statistical guru. People on this site commonly refer to MOE of a typical YouGov poll as around 2 to 3 percent. My memory of my statistics classes includes things like variance and confidence limits but does not include MOE. Can you tell me how MOE is defined?

    And however it is defined my assumption is that the MOE of the difference between the percentages for Conservatives and Labour will be greater than the MOE of the individual percentages for either. (As an example, if the ‘true’ labour vote is 42 per cent and the true Conservative Vote is 32 per cent, it is easy to imagine that random variation would lead to contrasts of 44 to 32 or 41 to 34 i,e, small random variations in the underlying numbers can lead to leads of 7 or 12 percent)

    So my basic questions are – what is a rule of thumb MOE for voting percentages in a YouGov poll and what would it be for a ‘lead’ (both questions applying to labour and conservatives)?

    And while I am writing this, many thanks to Martyn for sorting out a statistical question about the Poles. I failed to reply because by the time I read the post the thread had changed.

  26. Amber

    “Small” is the right word to describe any change in Scottish VI.

    There was a report of a ComRes poll a week or so ago which reported hardly any movement from the 2011 election.

    So much for the prediction of the Labour poster here that as if by some natural law the SNP would be down in the dumps at this point in the electoral cycle.

    The list vote has trained the electorate to treat each election separately. It is entirely possible for them to vote NO, support EM at Westminster to keep the tories out, vote for local compentent sitting members of any party in the constituency and give the SNP a list vote even greater than previously.

    Maybe that approach also means that if you ask for VI you get recalled last vote until very near the poll.

    I know that I’ve changed my vote on the way to the poll, and its only 100m.

  27. Martyn/Charles

    I missed the discussion about Poles (not Polls).

    There are immigrants temporarily resident here but not domiciled. They aren’t here at Christmas for sure. How many times are the same people counted when they come in? How are they counted when they go out?

    Is the data robust enough to be fit for the purposes to which it is put? Would we be better off without it?

  28. Peter Kellner on R4’s [email protected] was making broadly similar points to AW. In addition he speculated that if there was any affect it might be along the lines of “party x is a divided party” …he has long thought that to be a negative for VI.

    Is this still true though? The Conservative party has shown a high degree of division ever since Cameron made his move against the 1922 Committee within days of the May 2010 GE. Perhaps as as issue it has been subsumed by wide ranging Coalition rifts.

    I share your interest in a lead to – on? – MOE in the difference between the two main parties. Recent comment has been of a “dip” from 12 to 7 percent in the Labour lead, and refers to a diminishing or recurrence of the referendum bounce, but a previous exchange with Anthony confirmed that, in similar movements causing excitement among commentators, probably there has been no dip, just a movement within the MOE, and probably due to anomalies in polling.

  30. In the two years from Dec 2010 – Nov 2012, YG gave the LDs 12% just once (in April 2011).

    Today the LDs are on 12% for the fifth time in the last two months.

    Perhaps evidence that the long-awaited slow, gentle recovery in support has begun.

    In my neck of the woods (Camden), I’ve generally found the reception on the doorstep over the last two years much warmer than the polls and the media would suggest.

  31. @Charles

    I can’t give you a geeky answer better than the others mentioned, so will defer to better minds.

    However, my latest article does highlight the most recent ten polls:

    Also on Twitter [email protected]://

  32. Its not the loss of voters that will be significant. It will be the loss of workers. It takes motivation to trudge the streets delivering leaflets and knocking on doors. That motivation is getting less and less for the core Consevative activists.

    As Conservative structures crumble and their voice wains. UKIP’s gets stronger and louder.

  33. Trends in your Government Approval & Leadership Approval graphs are interesting Statgeek.

    Thank you.

  34. David,

    “In my neck of the woods (Camden), I’ve generally found the reception on the doorstep over the last two years much warmer than the polls and the media would suggest.”

    Have you tried leaving your own doorstep and trying someone else’s?


  35. @David

    “Perhaps evidence that the long-awaited slow, gentle recovery in support has begun.”

    It’s pretty clear that this isn’t a gradual improvement, but a single rapid 2 point bump at the end of November. The reason is not obvious, but Leveson is a fair guess.

  36. Having been a member of a couple of local Conservative Associations in my youth, I don’t actually think it is a bad thing for the party if a few dozen Ultras leave due to misgivings over gay marriage. In fact it is perhaps just the physical manifestation of what Cameron is trying to achieve.

    If you want a party to move from what was widely perceived as an “anti-gay” stance to a “pro-equality” stance then you probably need to lose the members for whom doing so is a dealbreaker.

    If in the process there are a few young people with generally right wing views who have shied away from party politics because they are gay, or because they are pro-equality, and who now join the fold, then I think it is a net plus even if they’re outnumbered 5 to 1 by those leaving.

    The reactionary views of local party members and officials have been a drag on the Tories for a long time – restricting the range of candidates that can be selected and forcing politicians to pay lip service to some obsolete thinking.

    Bring it on.

  37. @PeterCairns,

    Very droll, I didn’t laugh out loud but there is a smirk on my face and there was a rush of air from my nostrils.

    I do actually agree with David though. I think the worst is behind them for the LibDems.

  38. @Billybob
    Party disunity can lose votes, I’m sure. But a show of unity brings them back fairly easily. Major’s 1992 victory, following all the bloodletting about the Poll Tax, Europe, and the fall of Thatcher shows how it’s done. Whether the Tories will be able to verifiably decommission their hatchets is a different question.

  39. Pease note that I have been away at the annual “New-Thead-Senior-Monitors” conference at the Travelodge, Hastings for the past few days.

    It was a handy venue as it meant I could visit my guitar maker re. new 11 string guitar. He lives near Battle, which, by an amazing coincidence, is near where the Battle of Hastings was fought in 1066 !!!!!!!!!!!!!!!!!!!!!! This was one of the eariest examples of the French cheating against the plucky English.

  40. Part 1: How does margin of error relate to the variance?

    * The MOE is half the width of the confidence interval[4]
    * For a 95% confidence interval, half the width of the confidence interval is 1.96*m, where “m” is the standard error of the sample mean[3]
    * m is n/p, where “n” is the sample estimate of the standard distribution of the population and “p” is the square root of the number of elements in the sample[2]
    * If we assume that the sample estimate of the standard distribution of the population is the same as the standard distribution of the population, then n/p is the same as q/p, where “q” is the standard distribution of the population
    * But q/p is the formula for “r”, where “r” is the the standard deviation of the sample mean[1]
    * And of course, r = s, where “s” is the square root of the variance of the sample mean, which is what Anthony means when he says “the variance of the sample”.

    So MOE = 1.96m = 1.96(n/p) = 1.96(q/p) = 1.96r = 1.96s = 1.96 times the square root of the variance

    So the margin of error for a 95% confidence interval is approximately twice the square root of the variance.


    [1] h ttp://
    [2] h ttp://
    [3] h ttp://
    [4] h ttp://

  41. @Charles

    Part 2: what is the MOE of the lead?

    * The MOE of the lead is the MOE of z, where “z” is the lead
    * But z = (x-y), where x is the VI of party x and y is the VI of party y
    * So MOE(z) = MOE(x-y)
    * But MOE(x-y) = 1.96s, where s is the square root of the variance of (x-y)
    * But the variance of (x-y) is the same as the variance of (x+y). Yes, really.
    * So MOE(x-y) = 1.96t
    * Now square both sides
    * So square(MOE(x-y)) = 3.8416square(t) = 3.8416(variance of (x+y))
    * If we assume var(x) and var(y) are the same, then variance of (x+y) is the same as variance of (2x), which is 4 times var(x).
    * So 3.8416(variance of (x+y)) = 3.8416 times 4 times var(x).
    * So square(MOE(x-y)) = 3.8416 times 4 times var(x).
    * Now square root both sides.
    * So MOE(x-y) = 1.96 times 2 times the square root of the variance of (x)
    * Rearranging gives us MOE(x-y) = 2 times 1.96 times the square root of the variance of (x) = 2 times 1.96t, where “t” is the square root of the variance of (x)
    * But 1.96t is MOE(x).
    * So MOE(x-y) is 2 times MOE(x)

    So. The margin of error of the lead is double the margin of error


  42. @PeterCairns
    I promise you I have ventured beyond my own doorstep!

    I agree December’s figures were better than November but January was better than December. If it was just Leveson wouldn’t the effect be receding rather than becoming stronger?

  43. @John B Dick

    I hope you’ll forgive me if I don’t answer that today: I’m a bit busy


  44. @Charles

    (corrected version)

    Part 2: what is the MOE of the lead?

    * The MOE of the lead is the MOE of z, where “z” is the lead
    * But z = (x-y), where x is the VI of party x and y is the VI of party y
    * So MOE(z) = MOE(x-y)
    * But MOE(x-y) = 1.96s, where s is the square root of the variance of (x-y)
    * But the variance of (x-y) is the same as the variance of (x+y). Yes, really.
    * So MOE(x-y) = 1.96t, where t is the square root of the variance of (x+y)
    * Now square both sides
    * So square(MOE(x-y)) = 3.8416square(t) = 3.8416(variance of (x+y))
    * If we assume var(x) and var(y) are the same, then variance of (x+y) is the same as variance of (2x), which is 4 times var(x).
    * So 3.8416(variance of (x+y)) = 3.8416 times 4 times var(x).
    * So square(MOE(x-y)) = 3.8416 times 4 times var(x).
    * Now square root both sides.
    * So MOE(x-y) = 1.96 times 2 times the square root of the variance of (x)
    * Rearranging gives us MOE(x-y) = 2 times 1.96 times the square root of the variance of (x) = 2 times 1.96u, where “u” is the square root of the variance of (x)
    * But 1.96u is MOE(x).
    * So MOE(x-y) is 2 times MOE(x)

    So. The margin of error of the lead is double the margin of error


  45. Charles

    Margin of error (MoE) is basically the same as the 95% confidence limit. I tend to prefer the term as there can be confusion with confidence limits or intervals as to whether the full range or half of it is meant. MoE is usually expressed as a +/- figure so a bit clearer. The Wikipedia entry on the topic is quite good:

    However whatever you call it you need to be careful about what your sample size is. For example the headline sample size in today’s ST poll is 2030. But 20% of those said they would not vote or didn’t know who for, so the real sample size is around 1624 because the Party percentages are based only on the 80% who did give a preference. This matters less for YouGov who have larger sample sizes, but it has a big effect with some other pollsters who start with say about 1000 and, because of using likelihood to vote might only end up with an effective sample of 600. That could increase the effective MoE from +/-3 points to +/-4.

    Another point often missed is that MoE depends on what you are measuring. So the calculated figures for today are Lab 2.39, Con 2.30, L/D 1.58, UKIP 1.32. So Labour and Conservative ratings will appear to move about more than those of less popular Parties.

    Finally you’re perfectly correct that the MoE does not apply to the lead which is the difference between two figures which are not independent of each other (eg when one goes up the other is likely to go down). It would be impossible to work out what the MoE should be for that except that it would be a lot more.

    In addition you’ve got to remember that you’re looking at the difference between two figures that have been rounded to the nearest integer. So a lead of 7 points could really be one between 6.01 and 7.99. In fact half the time a ‘7 point’ lead would actually round to 6 or 8 points. So it’s as well not to get too obsessed about the lead. (Not that anyone will take a blind bit of notice – any more than they do over Scottish sub-samples. Sigh)

  46. @Anthony

    “……that said, I’m far from convinced that it is having a positive impact on that front, because the impact of David Cameron supporting gay marriage is risks being cancelled out by the impact of right-wing Conservative backbenchers opposing it).”

    I think, buried deep in your preamble to this thread, you touch on the real danger for the Tories on issues like gay marriage and the EU. They scratch lingering sores, perpetuate and publicise deep divisions in the party and present the most unattractive traits of the Tory Party to the general public. They also risk alienating more of the party’s already dwindling army of foot-soldiers. The very mention of these issues gives high profile platforms for just the sort of people who remind voters why they don’t like party. Wheel out Bone, Cash, Redwood, Hannan, Chope, Reckless etc and the horses are well and truly frightened once again and the Nasty Party perception is reborn.

    Cameron is in a terrible “damned if he does and damned if he doesn’t” position on these policy areas although, as a critical friend to the Tories, and conscious that maybe I shouldn’t intrude on private grief, I think he’s better off being in the “doesn’t” camp. Far less damnation, I suspect.

    A back to form Rawnsley was very, very good on this subject in his column the Observer today.

  47. @paulcroft – ” …where the Battle of Hastings was fought in 1066 !!!!!!!!!!!!!!!!!!!!!!”

    Glad to hear you’ve had a productive time on your travels.

    Nick Austin has spent many years questioning historical orthodoxy. English Heritage have agreed to assess his rival site for the Battle of Hastings. This is generating some controversy, not least because the new site near Crowhurst (it’s not that far away from Battle) is due to be bulldozed for a link road later this year:


  48. @Martyn.
    Re MOE of lead: isn’t that only true if the variables are independent, as RogerM points out. Funnily enough, though, Lab and Con VI seem to be pretty much independent at the moment – Lab gains or loses to the LDs, the Tories to UKIP. Perhaps someone more numerate than I could quantify the correlation?


    I think this idea is much more credible than Crowhurst.

    The site lies at the other end of Battle High Street from The Abbey. The area has a street named “Mount Joy” ( I always do a double take here-my dentist has his practice nearby!)and -as mentioned in the article , a “Malfose Ditch”.

    Can’t see English Heritage wanting to examine this too deeply though. Their set up at the Abbey site, with audio visual guides & a splendid Museum is well established as a tourist attraction.

  50. @Martyn, Roger Mexico, Statgeek and John Pilgrim

    Many thanks for your very helpful answers. My underlying concern was John’s – to wit that we get excited about variations in the lead when we should be looking at the more stable vi percentages. My ‘mathematical’ worry was the one raised by Roger – to wit that I would not expect the conservative and labour vi independent of each other. In practice they seem curiously independent. I correlated them at one stage admittedly over a short run and found a correlation of 0 which was not what I had been expecting. And I am relieved that Martyn’s maths fits what I vaguely remembered to wit that like the sum or difference of two variances is the sum of the two added together and that the MOE obeys the same rule.

    So having sorted out the theory, could anyone give a rough rule of thumb of how big the MOEs would be given a typical YouGov sample size and conservative and labour VIs roughly where they are at the moment? Equipped with this yardstick we could then go back to the figures Statgeek has collated with a greater sense of sureness about what has been happening. I think that this might avoid a great deal of unnecessary excitement and dispute. But then again that might be a pity!

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