The Liberal Democrat leader, Jo Swinson, faces being cut out of televised leadership debates during the general election campaign, as broadcasters begin torturous negotiations over who gets to show the nation’s political leaders arguing with each other on stage.

While the BBC, ITV, Channel 4, and Sky News are all vying for the position, Swinson’s place in any forthcoming debate is less than assured. The Tories are thought to prefer simple one-on-one debates between Boris Johnson and Jeremy Corbyn in a bid to reduce the election to a simple choice between the two. Labour have adopted a similar stance amid fears they could lose pro-remain votes to the Lib Dems due to the party’s pledge to revoke Brexit.

Corbyn’s spokesman said the Labour leader was committed to holding head to head debates with Johnson, with no mention of the Lib Dems. “There are only two possible people who can be prime minister at the end of this election campaign, and those two people should have a head-to-head debate,” he said.

Earlier in the Commons, Johnson dodged a question from Swinson when she challenged him to a three-way-debate. “What the people of this country want is their promises kept,” he said in response.

Channel 4 has already proposed a simple head-to-head leadership format involving only Johnson and Corbyn, according to a source at the broadcaster, while other channels are currently refining their plans. Smaller parties, including the Scottish National party, the Greens, and the Brexit party are also likely to demand the right to take part – especially in any programme on the publicly funded BBC.

While US presidential elections have an independent organisation to agree on debate format, in the UK it comes down to bargaining with political parties by television executives. According to individuals involved in previous negotiations, the incumbent prime minister has the most power over the format of the debate, in part because channel bosses want to ensure they have the “main attraction” before ripping up the schedule and cancelling peak-time programmes that could attract higher audiences.

One major concern for political campaigns is that televised debates are seen as increasingly risky, since short video clips from a debate go viral and reach a far larger audience on social media.

The broadcasters could also struggle given the relatively short election campaign of just six weeks until 12 December, which gives political parties the ability to say they only have time for a handful of head-to-head televised events. Leadership debates have a reputation for sucking up days of campaign time as candidates have to be prepared and tested. Parties are also likely to emphasise the declining audiences for television – 3.5m viewers tuned in for the 2017 BBC leadership debate - and suggest they would prefer to put their efforts into digital campaigning.

There is also the precedent set by Johnson’s team during his party leadership campaign. They ignored Channel 4’s leadership debate completely and let their candidate be represented by an empty chair. Instead, Johnson took part in a chaotic BBC debate involving five rivals and a single head-to-head on ITV with Jeremy Hunt, shrugging off claims he was avoiding scrutiny.

Ever since British broadcasters convinced the UK’s major political parties to take part in live televised leadership debates for the first time in 2010, political parties have been trying to avoid them or shape the format to their advantage. Former Conservative strategist Sir Lynton Crosby blamed David Cameron’s decision to take part in the debates for costing him a majority, after the then Lib Dem leader Nick Clegg was briefly elevated to the top of the polls.

In 2015 the Conservatives spent months wrangling with broadcasters over whether minor parties such as the Greens and Plaid Cymru should be included on stage, while in the 2017 general election the Tories decided to keep Theresa May out of the televised debates altogether – only for her to be widely mocked for her absence, in a symbolic representation of her collapsing campaign.

The often farcical debates reached a new high at the end of last year, during a lengthy back-and-forth involving May and Corbyn and an attempt to hold a public debate over Brexit. This saw both BBC and ITV pledge to hold their own head-to-head programme featuring the two leaders in the same Sunday evening time slot, despite the physical impossibility of both politicians being in two television studios at the same time. In the end neither event went ahead.