Ruth Davidson and Sadiq Khan were the winners of the BBC EU referendum debate

If you had just started to pay attention to the referendum campaign – as many people have – and last night's BBC referendum debate was the first thing you saw, you would have been surprised to be presented not with two opposing arguments, but with two alternative governments.

The format was strange, with three equally matched champions on each side of the gladiatorial combat in the the arena. It meant the principals mainly traded soundbites to enthusiastic cheers and applause from their side’s supporters, while the other side heckled and tried to interrupt.

The first thing you would have heard, though, is that wages will go up if Britain leaves the EU, as Gisela Stuart, the Labour MP and Leaver, said, quoting Stuart Rose, the chairman of the Stronger In campaign. Boris Johnson followed up by quoting one of the Remainers opposite who had said that in too many places immigration has driven wages down, before revealing that it was his successor as London Mayor, Sadiq Khan.

Round one to Leave.

Frances O’Grady, General Secretary of the TUC and a Remainer, challenged the Leavers to promise “every single social and employment right that the EU has won for us”. Johnson couldn’t believe his luck: “We have done that already.”

When it suits the Leavers, they pretend to be an alternative government, promising whatever people want.

Round two to Leave.

Then it started to get a bit bumpier for Johnson, because the thing about being an alternative government is that it has to have policies on everything. That means it has to have a policy on immigration. “Australian-style points system,” said Johnson, happily. Khan quickly pointed out that Australia has twice as much immigration as we have for a country its size.

Later on, because the debate bounced from subject to subject and back again with all the discipline of an unfamiliar pinball machine, the combatants returned to the subject, and O’Grady demanded to know if the Leave alternative government was promising to reduce immigration. Stuart said the Leavers were not an alternative government and that it was up to whoever was the government to decide how much immigration we had, but if we left it would be able to do so. “It’s a con,” said O’Grady.

Round three to Remain.

If new viewers had started here, they would have discovered that Johnson, the prime-minister-apparent of this alternative government that has policies or doesn’t have policies depending on whether it is winning or losing the argument, is a bit of blusterer. He had some great lines. At one point he said: “Jeremy Corbyn – he’s the leader – he said there was no way of controlling immigration in the EU.” He used the word “wrought”. He burbled about selling haggis to America. As soon as he got into anything technical he seemed to get it wrong. He claimed that the EU prevented the British government from cutting green policy costs on energy to help Tata Steel, which both O’Grady and Khan instantly recognised was untrue.

And new viewers in England might have thought, who is that rather forceful Scottish woman who is pushing Johnson and Andrea Leadsom around? They too have just discovered Ruth Davidson, the leader of the Scottish Conservatives. She went for the Leavers’ much-repeated slogan, “Take back control,” by saying: “You lose control by losing your seat at the table.” She quoted Johnson’s recent words saying that Turkey joining the EU was not going to happen, was “simply not on the cards”. She and Khan did a reasonable job of attacking Leave’s scaremongering about Turkey.

If new viewers had not been turned off by the chaotic format, they might have ended up wondering if they would rather have Ruth Davidson or Sadiq Khan as the prime minister of their alternative government.