BY TRADITION, British political leaders dislike referendums. A gift to demagogues, they grumble, and easily hijacked by irrelevant side arguments. Well, they should know.

On May 5th Britain will hold its first national referendum since 1975, to decide whether to change the voting system for general elections. National politicians and their proxies have barely tried to explain the question on the ballot to voters. Instead, the two sides have staged a mud-pie fight of spurious, partisan claims and counter-claims.

This could have been a chance to debate the sort of democracy the country wants. After all, the ballot offers a distinct political choice. Either keep the current model of first-past-the-post (FPTP), which provides ideological clarity but is not very representative (it offers nothing to parties with minority support in a given area, whether Labour in southern England, the Conservatives in Scotland, or Liberal Democrats, Greens and anti-Europeans all round the country). Or choose a new method, the alternative vote (AV). Though falling well short of a revolutionary leap to proportional representation, this would favour candidates who reach out beyond party lines, because winning under AV often relies on second-preference votes from defeated rivals.

The vote could have been a referendum on British views of competition versus compromise. The current voting system, for all its faults, implies a bracingly free-market, winner-takes-all view of the world: it is no surprise that famous folk endorsing the No to AV campaign are mostly entrepreneurs and sportsmen. In contrast, the AV system is closer to the consensual, corporatist worldview cherished on much of the European continent, in which ideological clarity (and thus accountability) is sacrificed on the altar of majority support. The Yes camp has been endorsed by numerous affable entertainers such as Colin Firth and Stephen Fry.

True, explaining the technical choice on offer is a fiddly business. In the seaside town of Lyme Regis this week, a “Fairer Votes for Dorset” event set out to sell AV to locals with stirring speeches and a mock double election for pizza toppings. Under FPTP, Lyme Regis was a two-way marginal between divisive rivals: Vegetarian Feast and Meat Feast. Then came an AV ballot. Watching from the back, near the tea urn and trestle-table piled with leaflets, Bagehot wondered if the AV demonstration had not misfired: after four rounds of counting, victory went to Meat Feast, presumably annoying quite a few in the room, starting with the vegetarians. The truly consensual option, Cheese and Tomato, was eliminated in the first round.

But the national campaigns have not attempted patient explanation, instead plumping for cartoonish exaggeration. A television broadcast by the Yes campaign shows MPs variously hiding from voters in their big houses, or arrogantly tucking into an expense-account lunch. It claimed AV would force MPs to “work harder” because they would all have to aim for majority support. That is a stretch. A study by the New Economics Foundation, a think-tank, estimates that AV would merely trim the number of safe seats, so that 16% rather than 13% of seats would change hands at a typical election. Furthermore—in contrast with the system used in Australian federal elections, in which all candidates must be ranked in order—the form of AV on offer in Britain would allow constituents to give their favourite a “1” and stop there, turning AV elections into a messy version of FPTP, and allowing candidates to win with a minority of votes cast.

If anything, the national No campaign—which is backed by the Conservative Party but also many Labour MPs—has aimed still lower. Billboard posters unveiled on April 13th urged Londoners to vote No to “Keep One Person One Vote”. That is misleading. Under AV everyone gets the same ballot, but fringe-party supporters can cast, cost-free, a first preference protest vote, confident that their second preference has a good chance of affecting the result. The No camp's nastiest poster simply declares that elections under AV would be much more expensive, and shows a soldier in battledress with the slogan “He needs bulletproof vests NOT an alternative voting system. Say NO to spending £250m on AV. Our country can't afford it.” Given that all democratic elections cost money, this is a perilous argument to pursue very far (it cannot be a good sign that the same poster could be used, with minimal alteration, by the Qaddafi regime on the streets of Tripoli).

Talking past each other

The Yes and No camps bellow and roar about the marvellous or horrible consequences of AV. The ordinary voters Bagehot encountered this week on the campaign trail wanted to talk about something more down to earth: the public's experience of democracy, and whether AV might possibly improve it.

In west Dorset, an AV supporter, Rikey Austin, talked of yearning to cast a first preference for the Greens after years of tactically voting Lib Dem. Accosted by Yes canvassers in the Cambridgeshire village of Kimbolton, John Chadwick suspected AV would “not make a lot of difference”, but hoped it might increase voter turnout by interesting those fed up with the big three parties. In the Manchester suburb of Urmston, a No voter walking his spaniel said a winner should be the person with the most votes: ranking preferences felt like “hedging bets”. (Still others admitted they knew nothing about AV, so would not vote.)

Nobody dares predict a result: the opinion polls are close and turnout risks being very low, especially in London where no other elections are being held on May 5th. One question has already been answered, however. Offered a chance to engage seriously with voters, Britain's political leaders rejected it. It seems that distrust between electors and the elected runs both ways.