John Rentoul: Here we go again, voting tactically...

"It will cause a plague of boils, locusts will swarm, the sky will fall, and darkness will sweep the Earth." One of the best political adverts I ever heard was a radio commercial in Massachusetts, which mocked the opponents of a proposition for a law to encourage bottle recycling. The No campaign in the state referendum, funded by the retail and glass industries, predicted that, if the proposition were carried, the economy of most of the north-east United States would be plunged into recession. The Yes campaign responded with satire.

If only the Yes campaign for the modest improvement in our voting system could respond with a similar lightness of touch to the preposterous misrepresentations of the naysayers about the referendum to be held in a month's time. Instead, Sayeeda Warsi, the Conservative chairman, says the Yes people want to boost the British National Party, while Chris Huhne, her fellow coalition minister, accuses her of propaganda worthy of Goebbels.

Nice. And a good illustration of Godwin's Law, which holds that, in any internet forum, the probability of someone making an analogy with the Nazis approaches 100 per cent as the length of the thread increases.

It was ever thus, except that the last time the Commons debated a Bill to bring in the Alternative Vote (AV) was in 1931, before comparing people with Nazis had quite the meaning of which it has now been mostly drained. Then, Captain Sir William Brass, a Conservative MP, quoted David Lloyd George's election leaflet, which promised action on unemployment and ended: "Vote Liberal, and put this pledge to the test." Sir William accused the Liberals of breaking that pledge, because they preferred a deal with Ramsay MacDonald's minority Labour government to secure a change in the voting system.

That time, supporters of AV were accused of causing mass unemployment. This time they are accused of letting babies die (one No to AV poster of a newborn baby says: "She needs a maternity unit, not an alternative voting system"). Having spent some time reading 1931 Hansard, I can confirm that wilful misunderstanding of preferential voting is not a phenomenon confined to the 21st century.

I do not feel strongly about AV, except when I see the outrageous propaganda of its opponents. It is a small change, which was explained with commendable clarity by John Clynes, the Labour Home Secretary in 1931. AV fell short of "absolute perfection", he admitted. "It does, however, prevent the election of a candidate against the wishes of the constituency." That is more or less all there is to it. Allowing voters to number candidates in order of preference ensures that the winning candidate is chosen by a majority of those who express a preference. I support it because it would allow me, as a voter, to express my full range of preferences, which is more fun than "X". I think it matters, even if it is purely for show, that Labour supporters in the shires should be able to express their true preference while still choosing between the Tory and Lib Dem front-runners. Or whatever. More importantly, it means that I can choose between the two candidates most favoured by my fellow citizens without my having to guess who they might be.

Everything else is secondary. Or wrong. The change would probably benefit the Liberal Democrats a little: a minor consolation after the loss of half the party's support when it joined the coalition and the further losses it will suffer as a result of boundary changes. But so what? If it is more democratic in principle, a party advantage shouldn't sway the argument for the rest of us either way.

As for Baroness Warsi's BNP argument – that it would encourage mainstream candidates to pander to far-right voters in the hope of winning their second preferences – that was conclusively dealt with by Sunder Katwala of the Fabian Society: "Since the BNP has under 2 per cent of the vote and 80 per cent of voters very strongly disapprove of them, any association with them is going to be toxic."

The passion of the argument among the tiny minority who take an interest is out of all proportion to the importance of the issue. The indifference of the majority seems to drive both sides to increasingly strident claim and counter-claim.

When Deborah Mattinson conducted her focus groups among the new middle class for this newspaper, she found that people understood neither AV nor the arguments of the Yes campaign. Although some of the groups disapproved of the No campaign material, its mostly untrue messages penetrated the apathy more deeply: "You end up with a party you dislike"; "AV would mean more coalitions"; "If you vote Tory first and Lib Dem second, would the Lib Dem get in?"

There are elections on 5 May that matter more than the referendum, including for the Scottish parliament, Wales and Northern Ireland assemblies, local councils in much of the country and a parliamentary by-election in Leicester South. In Scotland, Labour is likely to advance and the Lib Dems to retreat, so the intriguing possibility of the Lib Dems being simultaneously in coalition with Labour in Edinburgh and with the Tories in Westminster is in the balance.

Yet the voting reformers and anti-reformers are more interested in how these elections will affect turnout in the referendum. Turnout is likely to be low in those places, such as London, Cornwall, Wiltshire and Shropshire, where there are no elections – although in Wales last month, when a referendum on more powers for the Assembly was the only reason for making the trip to the polling station, turnout was 35 per cent.

In the end, this referendum may be decided on the strength of feelings toward the three main party leaders. A Yes vote is good for Nick Clegg, and mildly good for Ed Miliband, who supports AV; a No vote is of middling benefit to David Cameron, whose party hates it. Whom do voters most want to annoy?

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