THE Liberal Democrats look set to come out in favour of an arcane new electoral system called the Single Transferable Vote (STV) when they debate electoral reform on September 24th at their conference—not only because it is fairer but because they think it is especially good for them. Tony Blair, though he has promised a referendum on a new voting system, says he is “not persuaded” of the case for change, because it would inevitably prevent strong majority government. Only the Tories are still unbending opponents of change in Britain's first-past-the-post electoral system which, they think, maximises their chances of forming a single-party government.

All three parties should think again. A simulation of the 1997 election, carried out for The Economist by John Curtice of the Centre for Research into Elections and Social Trends, suggests that their assumptions are flawed (see table).

• The Lib Dems. STV, which combines multi-member seats with the listing of candidates in order of preference, is not uniquely good for them at all. They do slightly better under a minimal electoral reform, called the Alternative Vote (AV), whereby voters are given a second preference vote as well as their first preference vote. In 1997 pollsters found that 62% of Lib Dem voters gave Labour as their second preference, compared with 24% for the Tories; and 81% of Labour voters gave the Lib Dems as their second preference. The effect of AV (which allocates second preference votes to the top two candidates) is to tip many seats from the Tories to Labour or the Lib Dems. Indeed, under AV, the Lib Dems would have become the biggest opposition party. They would have done even better under the Additional Member System (AMS), a system akin to that to be used for the Scottish parliament, which tops up constituency members from a national list.

• Labour. Reform would not deprive Mr Blair of the chance to form a majority government. Under AV in 1997, he would have had an even larger overall majority. Even under STV, he could still have an overall majority, despite winning only 44% of the vote. This is because STV does not yield perfect proportionality. This is particularly true of the variant used by Mr Curtice for these calculations, which is based on seats returning an average of four MPs each.

• The Tories. Theirs is the biggest error. They still fail to appreciate the huge bias against them in the existing electoral system. This arises because the Tory vote is spread rather evenly across the nation, whereas the Lib Dems and Labour concentrate their support in seats they can hope to win. Tactical voting by Lib Dem and Labour supporters exacerbates the current anti-Tory bias of first-past-the post.

Two of the three PR systems considered by Mr Curtice would have improved the Tories' performance in the last election. Or think of it this way: suppose the Tories and Labour had had equal shares of the national vote in the 1997 general election. Labour would still have won 82 more seats than the Tories under the existing electoral system, giving Mr Blair a comfortable overall majority. Just imagine how the Conservatives would have reacted to that.