There is a built-in difficulty with all referendums. You ask the voters one question – but you risk getting the answer to a completely different one. Tomorrow's UK-wide referendum on changing the general election voting system has been marked by a mostly dismal campaign that may well produce such an outcome.

The question on the ballot paper is whether to replace the first past the post system with the alternative vote (AV). That issue is straightforward. In the present system, where voters select a single candidate, there is frequently a large majority of votes against – not in favour of – the successful MP. Under AV, where voters number their choices in order of preference, the winner must always have a majority mandate, after a process of redistribution. But that is not the issue uppermost in many voters' minds. For these, the referendum is about how to do down their opponents. In conservative Britain, energetic as ever in defence of the status quo, the unerring aim is to preserve the Tory party's capacity to win a Commons majority on the basis of minority support – as Margaret Thatcher did three times to such divisive effect. In progressive Britain, opinion is more evenly balanced. Most progressive Liberal Democrats are for change, as are many in the Labour party, including Ed Miliband. But large numbers in the Labour party are consumed by a cruder purpose – to bash the Liberal Democrats, Nick Clegg in particular, and preserve a system which also produced three successive majorities for their own party in recent history. To defend this system, large numbers of Labour activists have eagerly jumped into bed with the Tory party. Not a pretty sight.

There is plenty of criticism to dish out in all directions over this campaign. But the otherwise progressive Labour voters who are contemplating a No vote have a special responsibility to think again. A No victory will weaken the Lib Dems. But it will not kill the coalition. Instead it will bind it together on increasingly Tory terms. This will not help Labour as much as these opponents of change imagine. Under new constituency boundaries that eliminate the current pro-Labour bias, with Labour losing its grip on its Scottish heartlands to the SNP, and under new party funding rules that will boost the Tories and make things harder for Labour, the big winner from a No victory will be David Cameron. A Yes vote, by contrast, would inflame the Tory grassroots, threaten Mr Cameron's control over his party and strengthen the resolve of progressive Lib Dems to be more assertive about their party's values on social justice, civil liberty and democratic reform. It would also massively enhance the possibility that Labour and the Lib Dems can work together in the progressive cause in the future.

So, even progressives whose priority is to bash the coalition should vote Yes. But those who have remained focused on electoral reform should do so too. The existing system may be simple. But it is unfair to the ever larger proportion of voters who do not vote for the two big parties. And the alleged complexities of the alternative vote have been overstated. What's not to understand about one, two, three? AV gives a better reflection of public opinion than the existing system while retaining the constituency basis of the House of Commons.

You can't be a fairer society without having fairer politics. Keeping first past the post would mean keeping the system in which general elections mean national media campaigns funded by very rich backers which concentrate all their efforts on a few thousand swing voters in marginal seats. AV would take democracy back to the grassroots and would make more voters matter. Britain in 2011 is becoming a more unfair country both economically and politically. Voting Yes to AV tomorrow will help to stop that process and eventually reverse it. It will help to put the majority in charge, not the minority as at present.