This morning, something unusual will happen. David Cameron and Nick Clegg will give separate interviews on rival television political shows, a competitive conjunction they normally try to avoid. Side by side in coalition since last May, now the two leaders are reverting to head to head. In the words of one adviser to the Lib Dem leader: "You are going to see the gloves come off."

For the sake of the long-term harmony of the partnership, both men will try to abide by the Queensberry Rules. But they will be throwing punches rather than blowing kisses for the 18 days between now and the local elections. They may be partners at Westminster, but David Cameron and Nick Clegg are also leaders of two distinct political gangs who have spent many previous decades battling each other both at local level and in Parliament. Mr Cameron made his contentious speech on immigration – another indicator that there's an election on – in Romsey in Hampshire. That was the scene of a bitterly fought byelection which the Lib Dems won in 2000 at the expense of the Conservatives. The rather synthetic spat about that speech actually served both parties.

The election period is one in which they will both want to put less emphasis on where they agree and more weight on where they differ in order to galvanise their activists and in the pursuit of votes. It will be tricky to navigate. The longer-term, overarching ambitions of both the prime minister and his deputy depend on the coalition going the distance. Once the elections are over, they need to be able to take off their gloves and have a laugh in the dressing room. The challenge for them is to get through the slugfest of an election without anyone saying anything so unforgivable that it does irreparable damage to the government.

They would be perfectly capable of pulling this off if it were only council seats at stake. But something much bigger is in the ring: changing the voting system for MPs. This struggle pits the blue tribe, who loathe electoral reform, against the yellow clan, who yearn with an equal passion to overthrow first past the post, the system which has so often left them short-changed. Senior Lib Dems still speak ruefully about how they managed to harvest nearly a million extra votes on 6 May last year and yet were deprived of five parliamentary seats.

Broadly speaking, the coalition has been a considerable feat of party management by the two leaders and their key lieutenants. On many issues, they have managed to transcend, synthesise, compromise, park or fudge their differences. They have been skilful at presenting their programme in ways which have allowed both parties to claim that they are winners. So, for instance, the Tories get to cut corporation tax while the Lib Dems see the adoption of their policy to take more low earners out of tax. On the referendum, they can't both be winners. This is a binary choice. The voters either say: "I agree with Nick" and vote Yes for voting reform. Or they say: "I'm with Dave" and stick with the status quo. One of them must fail – and that will be seen as a massive body blow to whichever leader is the loser.

AV would not lead to a democratic Utopia – and the Yes campaign over-claim when they suggest that it would. Nor would it lead to endless coalition governments run by Hitler, Mao and Satan – one claim that the desperate propagandists of the No campaign have yet to make, but give them time. AV offers a moderate, incremental, easily understood and introduced improvement on obsolete, unfair and broken first past the post. It would give Britain a voting system more appropriate and responsive to the way most people make their political choices in the early 21st century. Voters have nothing to fear from AV and some things to gain. By contrast, politicians have much to be terrified about. For them, this is a raw, primeval, even existential struggle about power.

Most experts think AV would have given a modest uplift to the number of Lib Dem MPs returned at past elections. Since some boost is better than no boost at all if you are a Lib Dem, a defeat for AV would be a bad knock for Mr Clegg. His party would fear that the cause of electoral reform had been set back for a generation. More Lib Dems would question his strategy; more would ask whether they were getting enough gain for the pain.

The turbulence in his party that Nick Clegg will confront if AV is defeated is not only matched, it is exceeded, by the Tory rage that will erupt under David Cameron if he loses. This is not because AV would necessarily be a disaster for the Conservative party, but because so many Tories have convinced themselves that it would be. First past the post delivered majority Conservative governments on a minority of support for much of the 20th century. It ought not to surprise us that nearly all the money for the No campaign is Tory money, even if they have tried to camouflage this by using as mouthpieces some machine Labour politicians such as Margaret Beckett and John Reid.

I suspect that Conservatives are being overly pessimistic about what AV would do to them. In the recent past – the 1990s – it would probably have worked against them because polling at the time suggested that the second choice for Lib Dem voters was more likely to be Labour than the Tories. In the slightly more distant past – the 1980s – it would probably have helped the Tories because polling indicated that SDP/Liberal Alliance voters were more likely to prefer the Conservatives as their second choice. The smart politician fighting an AV election will reach out beyond their own tribe of voters to attract the second preferences of supporters of other parties – that broadening is one of AV's merits. An untribalistic Tory leader – David Cameron is rather good at being that – could prosper under AV just as a certain style of Labour leader could too.

Nuanced, rational assessment of the effects are not to be heard in the sound and fury of the increasingly ugly battle between the reformers and the antis. The tribal Tories who dominate the No campaign have convinced themselves that AV will be a catastrophe for their party.

The nightmare scenario for David Cameron is that AV is carried by a tiny margin on a poor turn-out. The irreconcilables in his party, the faction that has never much liked the prime minister and hates being in coalition, have their anti-Cameron narrative ready. It goes like this. The lack of robust right-wing messages at the last election prevented the Tories from securing the parliamentary majority they ought to have won when up against an opponent as unpopular as Gordon Brown. David Cameron compounded that failure by conceding the referendum to the Lib Dems. And now the referendum is lost and with it any chance that there will ever again be a purely Tory government.

In my view, every step of their narrative is a false reading of recent history. The Conservatives did not fail to win the last election outright because they were not sufficiently right wing, but because not enough voters trusted them. That is the clear conclusion from post-election analysis of voter attitudes. Agreeing a referendum on AV was the minimum price the Tories had to pay to enable Nick Clegg to persuade the Lib Dems into coalition. AV would make it harder to impose a right-wing agenda – or indeed any agenda – on the country for which there is not majority support, but it does not preclude the Conservatives from ever again forming a government on their own.

The irreconcilables won't be convinced. A narrative can be wrong and still have great potency. The double nightmare scenario for David Cameron is that the result is swung in Scotland and Wales where there is a higher turn-out because the referendum coincides with the elections to the Edinburgh Parliament and Cardiff Assembly. Elements of the Conservative party will go demented with fury if England says no but a Celtic yes vote wins it for AV. The Thatcherite former Scottish secretary, Michael Forsyth, has already described such a outcome as "rigged", which implies he and other Tories might try to resist the introduction of AV on the grounds that the result was not legitimate. One senior Conservative MP on the right predicts that Tories will go "completely mad" if they lose the referendum – to the extent that they might even jeopardise the coalition.

If you are a typical Observer reader, you will be a high-minded person who will cast your vote in the referendum after considered thought about which electoral system will best serve Britain over the longer term. But you may just happen – especially if you are a Labour person – to be wondering how to stir up maximum trouble for the coalition: do you vote No because the Lib Dems want a Yes or do you vote Yes because the Tories want a No? If that is the question that matters to you, here is the answer. A No vote will be a terrible headache for Nick Clegg; a Yes vote will be a skull-splitting migraine for David Cameron.