Prime Minister David Cameron told one of the BBC's most senior journalists to go "back to school" today after accusing him of failing to understand the electoral reforms being voted on in Thursday's referendum.
Mr Cameron said it was "worrying" that the Radio 4 Today programme's lead interviewer, John Humphrys, had given listeners incorrect information about how the alternative vote (AV) system works.
And he later took a second swipe at the broadcaster, saying it was "staggering" that he appeared to believe that the UK's first-past-the-post system was not used anywhere else in the world.
Mr Cameron's outburst came as he was interviewed about the May 5 vote on ditching first past the post for the AV system, which involves voters ranking candidates for Westminster elections in order of preference.
Under AV, the candidate receiving the fewest votes in each round is eliminated and the second preferences of his or her supporters redistributed between those remaining until one of them has more than 50% backing.
If the count goes to several rounds, this means backers of fringe parties could have their vote counted for a number of different candidates, while those supporting the eventual winner will have it counted each time for the same person.
Mr Cameron said this would result in a system where "you start counting some people's votes more than once".
But Mr Humphrys retorted: "No, you don't. That simply isn't true, that you count some votes more than once."
The Prime Minister replied: "Yes, you do. You count all the votes, and then you start eliminating candidates and then you count people's second preferences."
Mr Humphrys: "And I have a second preference as well as you or anybody else and you count them again as well, so you don't count some people's votes more than others."
Mr Cameron: "You are completely wrong. That's not the way it works. It's complicated."
Mr Humphrys: "No, it isn't, it's terribly simple."
Mr Cameron: "You are wrong. If you vote for the Labour candidate and I vote for the Monster Raving Loony candidate and the Monster Raving Loony comes last, my second preference is then counted again."
Mr Humphrys: "So is mine."
Mr Cameron: "No, it isn't. That's where you are wrong. It is quite worrying if actually the lead broadcaster on the BBC doesn't understand the system.
"You don't understand the system you are supposed to be explaining to the public. I do think that's worrying. Back to school."
Mr Humphrys: "I will go back to school, and I will choose my teacher."
Later, the two men clashed once more, this time when Mr Cameron pointed out that only three countries in the world - Australia, Fiji and Papua New Guinea - currently use the AV system for general elections.
The broadcaster retorted: "As opposed to our system that is used in none other - no other major democracy."
"Try America," replied Mr Cameron, provoking the response from Humphrys: "They have primaries in the United States."
Mr Cameron went on: "I find it staggering that the lead broadcaster in the BBC thinks our system is not used anywhere in the world.
"You have got to change your briefer. Our system is used by half the voters in the world. I'm absolutely staggered."
A BBC News spokesman said: "BBC News, including Today, has spelled out in great detail how AV would work and the referendum campaign has been covered extensively across our outlets.
"During a lively Today interview, David Cameron and John Humphrys disagreed over a technicality when the AV referendum was discussed.
"John was trying to reflect the point of contention between the campaigns over whether some people, in effect, have more than one vote under AV. In hindsight, he could have made this clearer."