‘You, my friends, are choosing a future prime minister!” declares one of the hopefuls to applause from the 450 activists who have come to hear the two contenders to be their party’s next leader. The audience in a lecture theatre at the London School of Economics asks thoughtful questions. The rivals, taking it in turn to answer, are unfailingly courteous towards each other. There is no shouting, interrupting or name-calling. I have heard ruder conversations between nuns. When one contestant speaks, the other spends a lot of time nodding along in agreement. They even smile at each other’s tepid jokes.

That’s enough clues for you to deduce that I am not talking about the gory competition to be chieftain of the rancorous Tory tribe. The event I attended one evening last week was a hustings between Jo Swinson and Sir Ed Davey, contenders to be the next leader of the Liberal Democrats. This contest is being neglected by the media and it is not hard to see why. Compared with the gristle and sizzle of the Tory struggle, the Lib Dem serving is as exciting as a bowl of tofu. Yet it is a mistake not to pay attention. The next Lib Dem leader could matter a lot. Consider these highly plausible scenarios for the near future: an autumn election, another hung parliament, a minority Corbyn government, a minority Tory government, a cross-party government, a second referendum on Brexit. In each case, the attitudes, skills and mettle of the next Lib Dem leader could be critical.

She or he will inherit a promising hand from Sir Vince Cable, who may be kicking himself that he decided to foxtrot off just before the party got back into the game. A strong showing in the May local government elections was followed by second place in the Euros as both Remainer Tories and Corbyn-repelled Labour voters migrated to the Lib Dems. That has been given rocket boosters by their clear and consistent identity as an anti-Brexit party unequivocally committed to a fresh referendum. Their next opportunity for momentum-building electoral success will be the Brecon and Radnorshire byelection triggered after the constituency’s Tory MP, Chris Davies, was found guilty of false expenses claims.

The Lib Dems have also benefited from a stroke of luck. Some of them feared that they were about to face a potentially eclipsing competitor for the support of anti-Brexit and centrist voters when Labour and Tory defectors combined earlier in the year to create the Independent Group. After a promising launch, the breakaways attracted ridicule for repeated name changes, then fell out with each other over how to fight the European elections, in which they did not win one seat, and have now done the splits. One of the original Tiggers, Chuka Umunna, has already joined the Lib Dems. Others are expected to follow. Ms Swinson mentions that she recently asked the MP for Streatham how he was feeling and received the reply: “I’m just really happy!”

The Lib Dem hope is that success breeds success. Not so long ago, they were languishing at a single-digit rating in the polls, which made them an unalluring destination for Tory and Labour MPs disgusted with their parties. Now that the Lib Dems are regularly hitting 20% or better, they are a more attractive refuge for anti-Brexit Tories and Corbyn-despairing Labour people. Sir Ed claims there are ongoing conversations with half-a-dozen Labour and Conservative MPs who might come across. Ms Swinson says they will be welcomed with “a warm bath of Lib Dem love”.

Both candidates are proof that even Lib Dems can be career politicians. Ms Swinson first stood for parliament at the age of 21 and was elected to the Commons at 25. She was a business minister in the coalition government with the Tories, a period that Lib Dems prefer not to talk about too much. Sir Ed has been working for the party for three decades. He sat in the coalition cabinet as secretary of state for energy and climate change. Both lost their seats in the massacre of the Lib Dems at the 2015 election and then returned in 2017. So both have direct experience of the rollercoaster ride of rise and fall and resurgence that has been their party’s recent story. Both are competently fluent speakers; neither has the oratorical talent to set an audience on fire. Both come over as decent people; neither is ever likely to be ranked among the world’s most charismatic politicians. Both know which buttons to press to please a gathering of Lib Dems; neither says anything remotely challenging to their party.

It is hard to detect much that they disagree about other than which of them would make the best leader. They are both social and economic liberals who were promoted by Nick Clegg. Ms Swinson promises to prioritise building “an economy that puts people and the planet first”. Sir Ed contends: “My radical plan to decarbonise capitalism would make the UK the world’s leading green economy.” Ms Swinson wants to “rally a liberal movement to stand up for our values against the forces of populism and nationalism”. Sir Ed pledges to be a robust defender of liberal values against “the rise of the far right”. You may not be surprised to hear that neither is fond of Nigel Farage.

Both come over as decent people; neither is ever likely to be ranked among the world’s most charismatic politicians

There is some variation in how they think their party should play the politics of Brexit. Ms Swinson is an enthusiast for creating a cross-party Remainer alliance. Sir Ed prefers to promote the Lib Dems as the principal anti-Brexit party.

There is an age gap. Invited to say which TV programme he couldn’t live without, fiftysomething Sir Ed says he doesn’t watch much television and, after some floundering around for an answer, finally offers The West Wing, a fine show that first aired 20 years ago. His 39-year old rival has a readier and more contemporary response, saying she loves Fleabag.

There are mutterings from some Lib Dem staffers that Ms Swinson, who has been deputy leader for the past two years, is difficult to work with. Sir Ed has more support from Lib Dem grandees in the House of Lords. He may suffer from a feeling that Sir Vince’s successor should not be, as one long-standing Lib Dem puts it, “another leader who has got a gong and two testicles”. The Lib Dems, a party that finds it easier to talk about diversity than to practise it, are a bit embarrassed that they have never had a female leader.

They are both stumped when asked to admit to their most illiberal thought. Sir Ed eventually makes a spluttery confession that “some hairstyles really bug me”. Even more lamely, Ms Swinson says she is made intolerant by people who walk too slowly in front of her.

It is a cosy evening that never leaves the party’s comfort zones. Candidates and audience go away feeling extremely pleased about being Lib Dems. It is a refreshing change from both the Tories and Labour to see a party that is broadly united and at ease with itself. Yet there is a downside to the euphoria generated by their recent successes. The contest is avoiding the searching questions that the Lib Dems ought to be posing to themselves as they choose a new leader. One concerns Brexit. For sure, they are profiting from the polarisation of national opinion on the great issue of the day, but there are risks in putting all their hopes in that one basket. Labour voters who are lending their support to the Lib Dems at the moment could head home if their usual choice of party moves to an unambiguously pro-Remain position. While some previously Tory voters have temporarily fallen in behind the Lib Dems, it is still moot what this group will do with their votes at a general election when the Conservatives will try to scare them back to the blue corner with the spectre of a Corbyn government.

It is not yet proved that the Lib Dems have done anything more than exploit favourable circumstances to revive themselves as a receptacle for protest votes. One of their MPs worries that Brexit has made them “a single-issue party” and they will need a broader appeal and a positive vision if they are to sustain support over the longer term. Leading this party can be one of the most thankless tasks in British politics. The role requires the flair to catch the nation’s ear and the creativity to give the Lib Dems the definition that the party has often lacked in voters’ minds. On the showing so far, both Sir Ed and Ms Swinson are good at telling Lib Dems what Lib Dems like to hear. That is necessary to win this contest, but it isn’t sufficient to be a truly effective leader.

• Andrew Rawnsley is Chief Political Commentator of the Observer