Why aren’t the Liberal Democrats doing better? This is an election in which both major parties are campaigning in favour of a radical transformation to the British economic model. Jeremy Corbyn believes his interests are best served by emphasising his radicalism, while Boris Johnson thinks that his aims are best facilitated by stealth. But a victory for either means a bold overturning of the status quo. The Liberal Democrats, the only party whose plans would mean the United Kingdom in 2024 looks very much like the United Kingdom today, ought to, at least, be the natural home for those with something to lose from that change.

One reason why the Lib Dems entered this election in high spirits is that they saw themselves as well-placed to take advantage of a vacuum in British politics: in Scotland, they are the only party unambiguously in favour of the Union between England and Scotland, and between the UK and the European Union, both of which command majority support north of the border. In England, they are the only home for the significant bloc of voters who abhor both Brexit and Corbyn. But the party’s campaign is stuttering.

Jo Swinson, the Lib Dem leader, began by talking about her ambitions to become the next prime minister. But by 24 November she said on the BBC’s Andrew Marr Show that the most likely outcome was that Johnson would remain in 10 Downing Street – and that her aim was to prevent him winning a majority. What has gone wrong?

Part of the problem is that Swinson’s pledge to stop Brexit via a parliamentary vote, rather than another referendum, has not been as popular as the party hoped. The pledge had been meticulously tested in polls and focus groups, but since Swinson persuaded her party to adopt it, there have been two unexpected developments. The first is that Corbyn did not, as many Lib Dems expected, adopt an unambig-uously pro-Remain position. The second is that Johnson did change the Conservatives’ position: from upholding red lines that could only end with a no-deal Brexit to supporting a Brexit deal, though one that is granite-hard.

Another problem is Swinson herself: according to the polls, she has become less popular the more voters see her. That has reawakened grumbles about her within the party. Although Swinson won the leadership election by a landslide, she had only a narrow majority in the parliamentary party, and some MPs have taken to speculating that they would be better off had Ed Davey won.

The Lib Dems’ biggest problem, however, is not about strategy but structural weaknesses. At every election, their challenge is to convince the electorate that a vote for the third party isn’t wasted. The party’s famous bar charts – in which electoral contests are cherry-picked, images manipulated and statistics spun – are its oldest weapons.

Within the party, campaigners share stories of their favourite bar charts with a mixture of pride and shame: a narrow win in one council ward presented as if it were the seat as a whole, a distant election deployed as if it were the recent past. Mark Pack, who is running against the Edinburgh West MP Christine Jardine for the party presidency – the chief organisational role – even hosts a podcast called Never Mind the Bar Charts.

Outside the party, a shared resentment at the Lib Dems’ fondness for a doctored y-axis is the lubricant of many a cross-party friendship. One Tory MP recently showed me his back and forth with a Labour counterpart: it consisted solely of photos they sent each other of particularly egregious Lib Dem bar charts.

The charts have a dual purpose: to secure tactical support from backers of one of the big two parties, and to convince people that they can back the Lib Dems without throwing away their vote. Now that the party is flush with cash, it can afford more sophisticated methods. The high command decides where to put resources based on the YouGov MRP model that accurately predicted the 2017 general election and 2016 European referendum results. Meanwhile, local parties are invited to co-finance a smaller constituency poll to generate a good local news story and/or a handy leaflet. It doesn’t always work: one local party opted not to run a poll showing it was comfortably ahead because of a fear that it would hinder rather than help efforts to persuade Labour voters to vote tactically. Another paid for a survey of a constituency in which the party’s modelling and its own canvassing returns showed it was way out in front, only be told that it was behind.

The worry that a vote for the Lib Dems is perceived as wasted haunts the party, but it is particularly damaging when voters believe that the outcome of the election as a whole is uncertain. While there are plenty of voters – particularly in the affluent, largely Conservative and pro-Remain constituencies where the party hopes to gain seats – who dislike both Brexit and Corbyn, there are very few who dislike both equally. Most voters are willing either to put aside their doubts about Brexit to prevent a Corbyn-led government, or to sacrifice their concerns about Corbyn to stop Brexit.

Swinson’s attempt to cast herself as a potential prime minister was a way to square the circle, and her support for a maximal Remain position was intended to facilitate the realignment to make that possible. But it hasn’t worked. Instead, it has emphasised that the choice in the election is Johnson or Corbyn.

And yet, having failed to convince voters that they can avoid choosing between Johnson and Corbyn, the Lib Dems could find success in this election if they can sell voters on the idea that the election is now a foregone conclusion – and that adding to the ranks of backbench Tories is the truly wasted vote.