DAVID CAMERON is in many ways a rather traditional Tory. Unlike some of his more ideological colleagues, he prefers to take the world as it is rather than rage that it is not as he would like it. He quickly concluded after May 6th that allying himself with the cause of modest electoral reform was a price worth paying for power.

For the Liberal Democrats, changing the first-past-the-post voting system that discriminates against them has long been the holy grail. The Conservative promise of a referendum on the alternative-vote (AV) system trumped a superior, but ultimately undeliverable, offer by Labour of more radical reform. A coalition was born.

AV is not proportional representation. It allows voters to rank candidates in order of preference. If no candidate gets more than 50% of first-preference votes, the second choices of those who supported the weakest candidate are redistributed repeatedly until one gets an absolute majority. The Electoral Reform Society, a pressure group, points out that AV can produce results as perverse as first-past-the-post. But if it had been used in this year's election, the group thinks the Lib Dems would have won 22 more seats than the 57 they got—all of them, interestingly, from the Tories.

Labour offered to enact AV and conduct a referendum on a much more proportional system, the single transferable vote (STV). Under STV votes are cast for candidates in big, multi-member constituencies, by order of preference. If the voter's first choice does not need the ballot, either because he can be elected without it or because he has too few votes to get in with it, the ballot is transferred to the voter's second choice, and so on. STV would virtually guarantee that no single party could achieve an overall majority at Westminster. If it had been in operation for this election, the Conservatives would have won 246 seats, Labour 207 and the Lib Dems 162, the Electoral Reform Society estimates.

Though the prize was considerable, as was the enticing prospect of a more or less permanent coalition government based on a “progressive alliance” of the centre-left, the Lib Dems did the maths (together with Labour they do not have a majority) and calculated the cost to their reputation of putting electoral reform ahead of the expressed wishes of the electorate. At the end of the day, said one Lib Dem negotiator, the Tories were “the only game in town”.

Changing the Westminster voting system, more or less radically, is now on the political agenda. So too is a much broader look at reforming institutions. And here all three main parties agree on a lot, although the devil is in the detail. All want the House of Lords to be wholly or largely elected under a proportional voting system. All have similar ideas for cleaning up MPs' expenses and lobbying, giving voters the right to recall MPs who have broken the rules and forcing lobbyists to operate more transparently, with particular restrictions on former ministers.

Labour and the Lib Dems both promised fixed-term parliaments in their election manifestos and the Tories, as part of the agreement with their new partners, have now come into line. The prime minister will no longer have the power to call an election when it suits him: parliaments will run for five years and will only be dissolved if the government loses a no-confidence or dissolution motion by a “supermajority”—a safety valve that may be particularly necessary when a potentially fractious coalition is in power.

In other areas, it is the Lib Dems and Tories who are closest, for example in their zeal for decentralising power and defending civil liberties (the latter a relatively new departure for the Tories, who used to be thought of as the authoritarian party). More specifically, both are keen to cut the cost of politics, reduce the number of MPs and reform campaign finance by limiting the size of individual contributions—all issues that cause problems for Labour. In short, while they will continue to differ about electoral reform, when it comes to wider political reform more unites the coalition partners than divides them.