PARLIAMENTARY arithmetic, personal compatibility and shared ideas all played their part in bringing the Conservatives and the Liberal Democrats together in a coalition government last May. But the compromise without which the deal might not have happened was the Tories' offer to hold a referendum on the Lib Dems' cherished goal of electoral reform. Scheduled for May 5th, the plebiscite will ask whether Westminster's first-past-the-post voting system (FPTP) should be replaced by the alternative-vote model (AV). It could be the most fraught single issue to face the coalition in 2011, and perhaps in the whole five-year parliament.
The proposed reform itself is fairly modest. Under FPTP, voters can only back one constituency candidate at a general election. Under AV, they would rank the contenders according to preference. If no candidate won 50% of first preferences, second and subsequent preferences would be tallied until somebody did. This is not the proportional representation of Lib Dem dreams. Indeed, some experts say AV would sometimes be less proportional than FPTP, if the make-up of the resulting parliament is measured against the first-preference votes cast for each party. Still, as the natural second-choice party for many, at least until the collapse in their support during the young life of the coalition, the Lib Dems would stand to benefit.
The internal politics of the referendum are more complex than the change itself. Were the public to endorse AV, Nick Clegg, the Lib Dem deputy prime minister, would have something important to show for his participation in a government with which many of his tribe feel increasingly uneasy. But that result could inflame the Tory right, which resents the influence of the junior branch of the coalition, and fears that AV would make it impossible for their party to govern alone again. (According to YouGov, a polling firm, at the last general election Lib Dem voters were more likely to have given their second preferences to the Labour Party than to the Tories.)
If, however, voters reject AV, the already beleaguered Lib Dem leader could face a crisis. The cause of electoral reform would be set back for years. And his party is expected to take heavy losses in local elections on the same day. Those Lib Dems who feel marginalised in the coalition, and who regard Mr Clegg as a drag on their poll ratings, might even try to remove him. A change in Lib Dem leadership would not necessarily mean the fall of the government, but it is hard to imagine anyone else working quite so well with David Cameron, the Tory prime minister.
The result of the vote is hard to predict. Opinion polls suggest it is a close race. Lib Dem supporters are overwhelmingly in favour of AV, Labour ones prefer it slightly, and Tory backers are broadly against it. This reflects the positions of the three parties' leaderships. Ed Miliband, the Labour leader and a longstanding believer in electoral reform, is campaigning for AV, along with much of his shadow cabinet. But he is tolerating dissent on this issue, and many Labour MPs (including former cabinet members) are taking the other side.
For his part, Mr Cameron opposes AV, but might not campaign against it as vigorously as many of his Tory colleagues will. Eager to prop up his troubled deputy, he will not want to be seen as instrumental in defeating AV, should it be rejected.
The circumstances of the referendum are controversial in themselves. Labour says the government should not have included the authorisation for the plebiscite in the same bill as measures to reshape parliamentary constituencies: seats are to be made more similar in population size, which will erode some of the advantage Labour derives from having lots of small seats where relatively few votes are needed to win. Timing is another gripe. Holding the referendum on the same day as elections for the Scottish Parliament, Welsh Assembly and some English local authorities may result in differential turnouts across the country and a skewed result. Mr Clegg, who oversees constitutional reform, says it will save money.
Whichever the outcome, there will be trouble for the coalitioneither from angry Tories or fed-up Lib Dems. On balance, a rejection of AV would be more destabilising. The Lib Dems have already been traumatised by the government's decision to raise the cap on university-tuition fees. They expect their poll ratings to fall into single figures. They could do badly, and perhaps even finish third, in the by-election in Oldham and Saddleworth, in north-west England, on January 13th. But these could seem like the good old days for Mr Clegg if he fails to secure even a limited kind of voting reform in May.
The biggest challenges facing the pro-AV camp are on its own side. Many of its leading lights actually prefer other voting systems: it will be hard to disguise that lack of enthusiasm during the referendum campaign. The other liability is Mr Clegg himself. The referendum will allow voters to punish him for his perceived betrayals by voting against the change.
The man whose efforts in the general election and its aftermath forced electoral reform onto the agenda will be implored to keep his distance from the cause. Perhaps nothing captures better the bizarre political turbulence of the last year, and the drama of the year to come.