Did Vote Leave's overspending win the referendum for Brexit?

An Oxford professor’s claim that it was “very likely” that overspending by Vote Leave swung the referendum for Brexit has taken off like wildfire. Professor Philip Howard’s analysis made the front page of yesterday’s Independent under the headline: ‘Illegal Facebook spending ‘won 2016 vote for Leave”. So do the numbers behind the headline add up? Prof Howard, director of the Oxford Internet Institute, calculated that:

Around 80 million Facebook users saw the Vote Leave campaign ads on social media during the period of excess spending;
10 per cent of users clicked through;
10 per cent of those users switched their vote as a result, giving over 800,000 switched voters.

This argument falls at each hurdle. An obvious point is that the 80 million Facebook users exceeds the entire UK population. This error appears to have been caused because Prof Howard added together daily users reached by Vote Leave. The posts are likely to have been seen by the same people across different days, meaning the total reach would be much smaller than 80 million. The numbers also wrongly conflate Vote Leave’s boosted paid reach, with people organically sharing its messages on Facebook. Organic sharing cost Vote Leave nothing, meaning that it could not have been part of their overspend. It is also worth asking another question: how many voters can Facebook reach? Recent research by the British Election Study team suggested that 55 per cent of Brits are on Facebook; Twitter is substantially less popular, with only 19 per cent of Brits using the site. If you assume that 55 per cent of the 46 million people registered to vote in Britain were on Facebook at the time of the referendum, at most an audience of 25.6 million electors could have been exposed to the adverts. The second claim, that 10 per cent of users clicked through on the advert, also seems dubious. An estimate for the UK in 2016 put the figure of those clicking on digital ads at 0.5 per cent. In the United States, that figure is estimated at an average of 0.9 per cent. This is based on impressions – rather than users. There is some debate about the direct success of online advertising which, at the very least, calls into question the figures behind Howard’s claim. Typically, display advertising is used to build presence and awareness, supporting other campaigns. Thirdly, suggesting that 10 per cent of people who clicked through on these ads changed their vote from Remain to Leave is a large stretch. This study of targeting and political adverts, suggests the effects of such adverts are ‘small’ and ‘often conditional. By contrast, causing 800,000 voters to switch from Remain to Leave in ten days would be fantastically effective. Influencing 3.1 per cent of electors means outperforming canvassing or phone calls for getting out the vote. For a digital comparison, an intrusive social media banner encouraging people to vote in the 2012 US election was estimated to increase turnout by only 0.24 points. Prof Howard’s 2005 book, New Media Campaigns and the Managed Citizen, also argues that we should apply a different calculation to that submitted to the High Court. His book says to apply a one per cent click-through rate, where 10 per cent “believe” what they read; and of that 10 per cent act. This ‘belief’ stage appears to have been omitted in the High Court submission’s final calculation. Using these rates, this calculation turns 25.6 million people into 2,560 changed votes – hardly enough to have swung the referendum for Leave, given that their margin of victory was over a million votes. If we share a belief in accuracy, this erroneous claim should have limited reach.