The campaign for a better democracy in Britain has to fight, fight and fight again. According to our ComRes opinion poll today, the No campaign in the referendum has opened up a 6 percentage-point lead, as some of the don't-knows have made up their minds over the past few weeks.

This suggests that after a good start – the Yes campaign held a 10-point lead in our poll in February – the No propaganda is turning the battle. This weekend has seen Conservative Cabinet ministers, David Cameron, Theresa May and Sayeeda Warsi, writing articles for the Conservative press. Yet most of their arguments are mistaken, misleading or just plain dishonest. Now is the time for those who believe that the voters should be given more choice to step up. The No campaign's strategy is simple: it is to confuse people by throwing out so many absurd warnings about the perverse consequences of an unfamiliar voting system that people decide to stick with the devil they already know.

The Yes campaign's fightback needs to do two things. First, it needs to explain the Alternative Vote. Once people realise how simple it is, it will be harder for the conservative (with both an upper and a lower-case "c") propaganda to sow confusion. All AV means is that voters mark the ballot paper with numbers to rank candidates in order of preference. The votes are then counted in the obvious way, starting with the first preferences, until one candidate obtains over half of the votes that mark a preference.

Second, the Yes campaign needs to make the argument that preferential voting gives more power to the voters. It means that the voter may express a true opinion, even if his or her most favoured candidate is unlikely to win in that constituency. By marking one's first preference on the ballot paper, the voter may be sure that his or her views will be counted, so that the true levels of support for minor parties will be known. AV is not a proportional system, so it would not ensure greater representation for minority parties. (Indeed, contrary to the scare-mongering of Baroness Warsi, it would be even harder for a party such as the BNP to be elected under AV than it is under the present system. Only parties that are the second preference of large numbers of voters, such as the Liberal Democrats and possibly the Green Party, are likely to win more seats under AV.) But recording voters' true preferences would make our democracy richer, in that it would provide more information about what people expect of their representatives.

However, the greater gain is that expressed simply by John Clynes, the Labour Home Secretary who nearly enacted AV in 1931, when he said that it would "prevent the election of a candidate against the wishes of the constituency". It means that if two-thirds of the voters in a constituency are strongly opposed to the Nasty Party candidate, for example, but are divided between two Nice Party candidates, they cannot be outvoted by the Nasty Party's supporters.

It means that each elector has the best possible chance that his or her vote will count, because each vote can transfer to one of the top two candidates in the final round of counting. AV allows everyone to have their say in the same way that they would if an exhaustive ballot were held at a meeting of any club, society or political party – and it is similar to the French system of holding a run-off ballot between the top two candidates a fortnight after the first vote, without requiring voters to make a second trip to the polling station.

The Independent on Sunday hopes that, if these two messages can be got across, the people will vote for this modest but important improvement on 5 May. That is why we seek today to expose the 10 main myths of the referendum campaign. In Australia, for example, AV has produced fewer hung parliaments than the British system. And yes, we should acknowledge that some of the arguments of the Yes campaign are embarrassing too, such as the idea that MPs would work harder under AV, or that it would have prevented the abuse of the expenses system. But the ratio of intelligence-insulting tosh lies heavily in the No campaign's favour.

If the British people vote to keep the existing system on the basis of honest and open-eyed understanding of the arguments, so be it. But the worst outcome would be for No to prevail by misinformation and misunderstanding. The Yes campaign must not allow that to happen.