If you strongly agreed with Nick Clegg or Nigel Farage about Britain's place in Europe beforehand, then you probably think that your man won last night's head-to-head debate about Europe too.
YouGov's snap poll of viewers showed that those who believe Britain should stay in the EU thought Nick Clegg won the debate on points, by 60% to 35%.
Those who think we would be better off out saw a Nigel Farage knockout victory, by 87% to 7%.
The UKIP leader had a little more crossover appeal, so led 57% to 36% among all respondents, despite opinion on the in/out question being evenly divided. In particular, the UKIP leader appealed more strongly to Conservatives who saw the debate, by 70% to 26%. This suggests that Clegg’s argument didn’t work for many of the Conservative voters who would want Britain to stay in the club, with some reforms, but without ever becoming enthusiasts for the European anthem and flag.
If Nick Clegg takes one lesson from the first debate into the BBC second leg next week, it should be to spend less time on 'what the real facts show', if he does want to do more than mobilise existing EU-enthusiasts to the Lib Dem banner.
Clegg explained why he took the approach during the debate itself, saying that people just want the facts, and so it was his role to calmly set them out.
But there is a foundational problem with this. To the extent that undecided voters do 'just want the facts', they are likely to trust many other sources ahead of the politicians who are leading the charge for the 'in' or 'out' cause.
Eastleigh voter Madeleine Drake told the BBC ten o'clock news why, having watched the whole debate, she ended as she began: undecided.
'Both sides fire a lot of facts and figures at you, which they bandy around. Facts and figures, in the end you believe what you want. They are both as convincing as each other. That's the problem. And you don't know quite - well, I can't make my mind up - which side is being honest with these figures'.
Both leaders inadvertently showed why many viewers will find their fact-based talking points a little slippery. 'That's the estimate we've made' said Nigel Farage, when asked where his figures for the number of laws made in Brussels came from, before saying he could have picked a much higher number from another source. Meanwhile, Nick Clegg asked Farage what his figure was for lost jobs. 'It might not be 3 million, it might be 2 million or 1 million', he said. His point was that leaving wasn't worth a single job. But both men had made their factual proofs sound rather elastic.
The real role of these claims and counter-claims is not to persuade the undecided.
Rather, their impact is to raise the morale of existing supporters, who find them convincing, and so imagine others are being persuaded too as they enthusiastically retweet them onwards.
That these factual claims do easily land with the already persuaded, on each side, is not because existing partisans have any more capacity to retain the figures. It is rather because the rebuttals confirm their existing mistrust of their opponents' motives. If 'we' are just giving people the honest truth and 'they' are peddling dishonest nonsense, that suggests that the other side must have some hidden agenda behind their willingness to mislead. This will, therefore, have become increasingly evident to on-lookers too.
So Eurosceptics will have been convinced last night that Nigel Farage destroyed Clegg’s '3 million jobs' figure. Pro-Europeans, however, will believe that the 'most laws are made in Brussels' meme was significantly undermined by the debate.
We should expect both to complain ever more loudly when their opponents continue to deploy these claims.
Occasionally, a trusted neutral arbiter may intervene but both sides will always claim to have the backing of rival experts too. Unless the unpersuaded listener has a prior reason to trust one advocate or another, they are unlikely to be able to decide between them.
This doesn't mean that there is no role for factual advocacy in these debates. The moderator, however, is likely to be a more persuasive referee for the viewer than the opposing player.
Nigel Farage struggled considerably more when pressed by Nick Ferrari over his claims about the cost of the EU to the UK. He had found it much easier to brush off Clegg's challenges - by simply asserting that other studies proved the opposite, and challenging his opponent’s claims on 'you would say that wouldn't you' grounds. Clegg did exactly the same to him.
Farage had begun the stronger - on the trust issue of whether a referendum offered by a bigger party would be a pledge that they would keep. But it was the moderator, Nick Ferrari, who drew from Nick Clegg a "read the small print" error.
The UKIP leader's weakest section was on trade and jobs, where he cited figures about the car industry, and the balance of imports and exports, without acknowledging that getting out is a big change which could not be risk-free.
Here, Clegg did better by focusing on voicing anecdotal examples - about Siemens in Hull, or Nissan and Ford - to illustrate his claim that investment and jobs were at stake.
Similarly, Clegg responded on crime with examples of criminals apprehended under the European arrest warrant. This was a far more effective way of animating a point which may be familiar to MEPs but which many people, who don't follow European politics closely, may not have considered before.
‘Why facts are a comparatively ineffective way to persuade’ is the theme of a growing body of political psychology research. Books such as Drew Westen's ‘The Political Brain’ have helped to popularise these lessons for politics rooted in brain science.
Westen writes of US politics that Democrats and liberals "tend to be intellectual. They like to read and think. They thrive on policy debates, arguments, statistics, and getting the facts right. All that is well and good, but it can be self-destructive politically when allied with a belief in the moral superiority of the cerebral at heart, because moral condescension registers with voters. ... They do so, I believe, because of an irrational emotional commitment to rationality - one that renders them, ironically, impervious to both scientific evidence on how the political mind and brain work and to an accurate diagnosis of why their campaigns repeatedly fail".
Those lessons apply to a wide range of issues, on both sides of the Atlantic, but there are two political debates where factual advocacy is especially likely to struggle. They are Europe and immigration, which happen to be the two central themes of the Clegg-Farage debates.
The Europe debate is partly about a rational calculus of the benefits of being in or out: the constraints of pooling sovereignty against the risks of walking away from a seat at the table.
But to think it could be settled entirely on that basis is to miss the point. The Europe debate is also, primarily, an argument about whether to choose between, or how to reconcile, competing understandings of our cultural identity and values.
Claims about mistrust, betrayal and even a conspiracy of the elites are a key motivator of one side of the argument.
This is also true of immigration, where the public have also heard governments of both colours say that the system is broken and not fit for purpose, and believe this to be true. People quickly say they have no reason to believe facts which can not be fully accurate. When Ipsos MORI confronted survey participants, who had significantly overestimated the proportion of migrants in Britain, with the ‘real’ figures the two most popular responses were: ‘I still don't believe it’ and ‘those are the people you know about’. ('I was just guessing' was much less common).
So getting the balance right could see the leaders get more out of the debates as a form of public communication. They should deploy facts selectively, and animate them better with memorable stories and examples.
Nick Clegg did cite the finding from new Centre for Entrepreneurs research that at least one in seven British companies was founded by migrants. That is a fact which could be used to used to tell a story to illustrate the choices we face. Combine that with the story of a French, Polish or Romanian job creator, and the Brits who work with them too, and it could prove bring to life Clegg's central claim that it reflects both Britain's interests and values that we do welcome those who come to contribute positively to our society.
The other problem with so much time spent on this exchange of contradictory studies was that it crowds out other, perhaps more effective arguments too. Farage was not particularly vulnerable to Clegg's claims that his facts were wrong. He can simply say the same back.
Perhaps the UKIP leader may be more vulnerable if asked about his vision of what happens when Britain leaves the EU. Clegg's argument is that it is a risk we shouldn't take and can't afford. He might want to do more to challenge Farage on whether he can paint a convincing picture of what happens next.
If there was one piece of advice to both leaders for next week's rematch, perhaps it should be this: try limiting yourself to a maximum of three statistics in the whole hour. Choose them well, and you might be able to get something across to somebody who didn't already agree with you.