If that sounds like wild, lunatic fantasy, it is - for the Middle East at any rate. But something very much like it is happening before our eyes in Northern Ireland. In Sharon's place is Ian Paisley, the octogenarian embodiment of Unionist intransigence, whose Democratic Unionist party is likely to emerge as the largest single party in today's elections for the Northern Ireland assembly. For Ismail Haniyeh, read Martin McGuinness who will serve as deputy first minister. That's right: McGuinness, widely famed as a former IRA commander, will team up with Paisley, who made a reputation denouncing the IRA as bloodthirsty, murdering bastards whose only place was frying in the fires of hell.

At Paisley's side, as education minister, we may well see Gerry Kelly, a former hunger striker jailed for his part in the IRA bombings of the Old Bailey and Scotland Yard. And yes, one of the big issues before the Paisley administration will be the price of Northern Irish water.

Of course, the analogy is not perfect. (Last time I deployed it, several readers shot back that the IRA never rejected Britain's right to exist, in contrast with Hamas's position on Israel.) But it helps convey the scale of the transformation now underway in Northern Ireland. A place that was riven by violent conflict - euphemistically referred to as the Troubles - is striding towards normality. And those who are crafting this peace are the very same people who made the war.

It makes for some eye-popping transitions. The new general secretary of Sinn Féin, set to be charged with governing Northern Ireland, is officially wanted in Northern Ireland for the shooting of a British soldier 30 years ago. When Sinn Féin's conference recently discussed the party's policy on climate change, the debate was led by one James Monaghan. He's wanted in Colombia, where he skipped bail after allegedly aiding Farc "narco-terrorists". Now he talks about carbon emissions.

The people of Northern Ireland have had a few years to get used to all this, but for those outside it can still come as a delightful shock. You only have to imagine the equivalent changes in Israel-Palestine to see how far the province has come. As Paisley himself put it this week: "The political landscape has been transformed in a way that ... many said was impossible." Among the "many" were Unionism's cheerleaders in Britain, in the Conservative party and in the commentariat. I remember columnists Stephen Glover, Charles Moore and Michael Gove all insisting that the IRA was irredeemably bent on war, that negotiations with republicanism were a treachery doomed to fail. They were all wrong.

Of course, things can unravel. The adrenaline junkies who serve as Northern Ireland's politicians tend to take things to the wire and they still might hesitate. Their deadline for forming a power-sharing executive is midnight on March 26. Expect negotiations to be still underway, both sides trying to extract the best possible deal, at 11.55pm.

But it's hard to see what grounds they would have for failing to do the business now. Unionists have got what they never expected: an IRA declaration that their war is over and the verified decommissioning of their weapons. In January Sinn Féin removed the last obstacle in the way, by agreeing to back policing arrangements for the province. There's not much Paisley can ask for that he hasn't already got. One British official says that if Paisley does not go ahead and form a government it will be because the old warhorse simply "bottled it".

And so the campaign in Northern Ireland has not been about bombs and bullets, or the great national question, but about the humdrum stuff of normal politics. The biggest Belfast rally of recent months was about that increase in water charges.

What's more, the parties have fought an oddly consensual campaign. They differ on education - nationalists tend to oppose selection, Unionists support it - but on the rest there is a striking uniformity. "You cannot put a bus ticket between them," says Mick Fealty, of the indispensable Slugger O'Toole blog.

That's no coincidence. The DUP and Sinn Féin, along with the Ulster Unionists and the SDLP, have spent months hammering out what will, in effect, be the programme for the new devolved executive. They know that, whatever votes are cast today, they will all be in government. Those are the rules of the game, as laid out in the Good Friday agreement: a "mandatory coalition" in which every party with a serious number of seats gets a place at the governing table.

The result is a kind of hyper-normality, in which there can be no real policy disagreements because everyone is going to end up on the same side, governing together. It means Northern Ireland is about to jump from civil war to soggy consensuality, without ever passing through democratic, adversarial politics.

And yet the national question is not going away. It's just being resolved in a new way - with not a shot, nor even an argument, being heard.

The driving force is the economic success of the Irish republic, a surge in prosperity which the north wants a part of. All the main parties are calling on London to reduce Northern Ireland's rate of corporation tax, for example, to bring it into line with the investment-attracting south. Even Ian Paisley is in favour of this little piece of all-Ireland harmonisation.

Meanwhile, the secretary of state Peter Hain won plaudits when he demanded mobile phone companies drop their "roaming" charges across the Irish border, replacing them with one rate for the entire island. He's also legislated for a single electricity market covering north and south. Indeed, Hain has said that a single, Northern Irish economy is unsustainable, that only an "island of Ireland economy" makes sense. Paisley heard that as a pro-nationalist message and called for Hain's resignation. But when business leaders backed Hain, Paisley quietly dropped it.

Gradually and through economics rather than politics - still less armed struggle - Ireland is moving towards a kind of de facto unification. There are plans for a new road linking Dublin to Derry. The Irish government has announced that the north is eligible to compete for a share of Dublin's €1bn national development fund.

Each year that passes, the border separating north and south will come to look more obsolete. It will not be Semtex and Armalites that erase it, but the slower, subtler suasions of wealth and convenience. Normality is coming to Northern Ireland - but it's taken a damn strange route.

freedland@theguardian.com