PUDBROOKE Gardens is not the sort of place where you would expect to find vermin. A cul-de-sac of 1980s-built houses on the edge of the small Hampshire town of Eastleigh, it is spotless and orderly; a good place to bring up children. Yet the approach road to this suburban idyll (Charles Watts Way, named after a former Liberal councillor, not the drummer of the Rolling Stones) is infested with rats. And when Grant Shapps, co-chairman of the Conservative Party, went door-to-door there this week, campaigning for the Eastleigh by-election due on February 28th, local residents wanted to know what he was going to do about it. “I told him straight,” said Andy Hooper, a father of two, “We need a bait-box.”

Mr Shapps, who was accompanying the Tory candidate in Eastleigh, Maria Hutchings, promised to see what he could do. But as the politicians moved off, Mr Hooper, a water-sports consultant with experience in pest control, was sceptical he would act in time to secure his vote: “To be fair, he hasn’t got long.” The other major issue for Mr Hooper, which he appears to share with most other voters in Eastleigh and much of Britain, concerns a different sort of infestation. “I’m not anti-immigrant,” he said. “But how long will it be before we’re exploding with people?”

This exchange seemed indicative of the weirdly telescopic nature of Britain’s parliamentary politics, in which the mightiest Westminster politician, being directly accountable to voters, can find himself mired in the most footling issue. By-elections exaggerate this weirdness. Existing outside the rhythms of a general-election campaign, they tend to see low turnouts and are often fought on local issues; yet, for the same reason, they attract a heavyweight cast of campaigners.

The Tories, who held Eastleigh before losing it to the Liberal Democrats in 1994, are desperate to get it back. So David Cameron, the Tory prime minister, and several of his cabinet ministers have also been canvassing in Eastleigh. The Lib Dems, the Tories’ coalition partners in Westminster, are campaigning even harder. On February 16th and 17th 1,500 Lib Dem activists congregated in the former railway town, many wearing hand-knitted jerseys and “I like Mike” orange badges, in praise of the party’s amazingly uncharismatic candidate, Mike Thornton. According to Sir Menzies Campbell, a former Lib Dem leader who was working the doorsteps of one of Eastleigh’s council estates, “this is a hugely important election.”

That is, first of all, because it is a big test of Britain’s ability to manage coalition politics. There have been coalitions before, including for much of the 1930s. Yet when the Tories and Liberals (the Lib Dems’ predecessors) went toe-to-toe in a by-election in 1922, while also in government together, it led to a Tory victory, the acrimonious collapse of the government and the demise of the Liberals as a party. Many Tory MPs are clearly anxious to see the same thing happen again. To have any chance of winning a majority in the next general election, due in 2015, they will have to wrest a good number of seats off the Lib Dems. Victory in Eastleigh would suggest this is possible.

Whether, in Mrs Hutchings, they have chosen the right candidate is open to doubt. A hardworking mother of four, she is warm and articulate. But she appears to have a shaky grasp of national policy and questionable judgment. Among several gaffes, she has suggested one of her children is too bright to attend a state school and, in effect, criticised the government’s plans to legalise gay marriage—one of Mr Cameron’s dearest projects. At least Eastleigh voters are used to accident-prone politicians. Their last Tory MP, Stephen Milligan, died from auto-asphyxiation while wearing stockings and suspenders in 1994. Their outgoing Lib Dem MP, Chris Huhne, resigned this month after admitting to trying to dodge a speeding penalty. That Mr Huhne’s disgrace appears largely uninteresting to Eastleigh’s voters might suggest what a low opinion they have of all politicians. Most Britons do.

The Lib Dems, who are slightly ahead in the latest opinion polling, need to win in Eastleigh even more than the Tories. In government with Mr Cameron, their support has collapsed: polls suggest it is down by half since the 2010 election. Losing Eastleigh, where the party holds 40 of the 44 local-council seats and has a well-tooled machine, would invite predictions of annihilation in 2015. It might even spell curtains for the Lib Dems’ unpopular leader, Nick Clegg—and perhaps a rerun of the 1922 events.

The bait-box debate

Yet these hypotheses appear to impress no one in Eastleigh. The stampede of politicians and activists passing through its housing developments and moribund high street, lined with charity shops and bookmakers, are received with bafflement, or bemusement at best. No one seems to resent the attention; but the notion that Eastleigh, an indeterminate, uncentred sort of place, neither rich nor poor, town nor country, could set the course for national politics struck everyone Bagehot spoke to as absurd. Opening her door to an unexpected visit from Messrs Campbell and Thornton and a battery of press photographers, Gina Foster harrumphed, “What are you doing outside my house?” She will probably vote Lib Dem, she suggested after they had gone. She usually did, though she couldn’t for the life of her think why.

Yet when a butterfly flaps its wings in Eastleigh on February 28th there will be an uncomfortable draft for someone in Westminster and, if the Lib Dems lose, maybe even a storm. Mr Shapps can congratulate himself on making that prospect slightly likelier. The day after his visit, Mr Hooper did indeed get his bait-box, by special order of the Tory co-chairman. In retrospect, Mr Hooper now worries that Mrs Hutchings didn’t speak up enough on his doorstop. “The man did all the talking,” he frets. “I want an MP who’s going to be prepared to say what she thinks.” In that case, Mrs Hutchings is probably the right choice.

Economist.com/blogs/bagehot