The Liberal Democrats have what the pollster Chris Curtis calls a “Russian dolls” problem. For obvious reasons, the party does best with voters who think any of the following: that the Conservative-Liberal Democrat coalition was a good government, that the Conservative-Liberal Democrat coalition was a bad government but would have been worse without the Liberal Democrats, or that the coalition was a mistake but one they have since forgiven them for.

The good news for the Liberal Democrats is that, taken together, those groups command more than half the electorate; and the really good news is that this group is growing, albeit at what seems to be a glacial pace. Tim Farron’s explanation for this was that, when the Liberal Democrats were in coalition, people thought they were doing a bad job, and subbed them off, but now things have got measurably worse they are coming round to the idea that the party’s influence was more positive than they thought.

As time goes on, this group gets bigger and the Liberal Democrats are once again doing a good job of harvesting local discontent with the big two at local elections. They have had a lot of joy with a “don’t live in a one-party state” message.

But the bad news is that the part of the electorate that thinks the coalition – or at least the Liberal Democrats’ position in it – was good doesn’t overlap very well with the part of the electorate which wants to stop Brexit, the party’s flagship policy. The Liberal Democrats’ big problem is that the “people who want to stop Brexit and people who have positive feelings about the coalition” part of the Venn diagram isn’t very large.

To grow and to gain more seats, they need at least one of the following to happen: for voters who aren’t poorly disposed to them because of the coalition to become more opposed to Brexit, or for voters who don’t like Brexit to become better disposed to the Liberal Democrat presence in coalition. In other words, they need to expand the section of the Venn diagram they can appeal to.

There are a couple of possible routes to that: the first is to make a pro-active argument for coalition as a good in of itself, and try to grow the amount of the electorate which supports the idea of coalition. Vince Cable has ruled that out by vowing not to seek a coalition after the next election, a policy that has been endorsed by his party conference.

The second is to essentially have a semi-perpetual pattern of apology for the coalition, both overtly and subtly. Overtly, most of the Liberal Democrat potential candidates for the leadership have apologised for their time in coalition. (The only real exception is Ed Davey.)

Subtly, the party has done a good job of this by staying in lockstep with the other smaller parties of the left (the SNP, Plaid Cymru and the Greens) – a good strategy and one that Cable has largely followed. Hopefully, palling around with parties with better credentials with the anti-coalition parts of the electorate will absolve the party of its perceived sins. If Caroline Lucas is willing to work with Vince Cable, perhaps voters who abandoned the Liberal Democrats for the Greens will give them another look too.

The problem with this is it squeezes out the Liberal Democrats: the SNP are in government in Scotland and, like the Greens, they have a charismatic and dynamic leader who is good at grabbing headlines, which squeezes Cable and his party out of the picture entirely. But this is something the Liberal Democrats could get better at if they got better at picking eye-catching policies that get people talking about them. (Caroline Lucas’ call for a meat tax is a good example of how to do this well.)

But Cable has blundered today, by announcing that the Liberal Democrats will no longer support Labour motions of no confidence against the Conservative government. He’s done so on the grounds that Jeremy Corbyn is more interested in “playing politics” over Brexit than he is in resolving the Brexit crisis, and he won’t be party to it.

This aggravates every would-be voter not currently in the Liberal Democrat-friendly part of the Venn: pro-coalition voters who don’t want to stop Brexit don’t like it for obvious reasons, while anti-Brexit voters are reminded of the time the Liberal Democrats propped up the Conservatives.

This would have been a rare good time to just quietly row in behind Nicola Sturgeon or Caroline Lucas, who have more credibility on the issue, if the message that the rest of the left parties aren’t going to play Labour’s game anymore needed to be delivered.

So the Liberal Democrats under Cable aren’t doing the best they could at expanding either part of their target market. That leaves them with their last route to expanding the Venn diagram: to bet that Brexit will go so badly that there will be a big increase in the number of people who want to sack it off. (One would assume, too, that if a Conservative government without a Liberal Democrat presence does something incredibly catastrophic it also helps the coalition problem.)

In the absence of a positive strategy this is essentially the default Liberal Democrat position now, unless they can find a more proactive approach – and a leadership candidate with the discipline and eye for a headline to stick to it.