Historians are sometimes divided into lumpers and splitters. The splitters like to chop problems up into lots of small bits. The lumpers like to link them altogether.

Would-be Middle East peacemakers can be categorised in the same way. The lumpers want a “comprehensive peace settlement” that links together all the problems in the region – Iraq, Lebanon, Syria, Israel-Palestine, even Iran. The splitters want to deal with all these problems separately.

David Miliband, Britain’s foreign secretary, used the day of the US presidential election to come out as a “lumper”. He made a speech arguing that “the only way to settle the Palestinian issue is as part of a wider drive for a new alignment in the Middle East ... At its core is a Palestinian state, but as part of a broader peace between Israel and the Arab world.”

Mr Miliband even sees Iran as part of the same lumpy problem. He argues that the “Iranian nuclear programme poses a threat not just to Israel, but to the stability of the Middle East ... which makes the case for a comprehensive approach that much more urgent”.

The attractions of lumping are obvious. The idea of fixing the whole of the Middle East in one go is delightful. And it is true that all of these problems are linked. To take just one example, Iran’s poisonous relationship with the US has encouraged it to make trouble in Lebanon and Palestine, by sponsoring Hizbollah and Hamas.

But while lumping works as an argument, it risks failing as a policy. There are three obvious problems. First, there is the risk of being over-ambitious. If nothing is resolved until everything is resolved there is a risk that you will end up with nothing.

Second, there is the problem of which end of the lump you attack first. The much-reviled neoconservatives were also lumpers. But they thought that change in Iraq was the key to the transformation of the Middle East. Mr Miliband, in common with most mainstream European politicians, sees an Israeli-Palestinian peace settlement as the key to the lump.

This brings us to the third problem with the lump thesis. It is not clear that progress in one area will necessarily unlock the others. Let us say that the Iranians are miraculously persuaded to abandon their nuclear ambitions. Does that automatically lead to the establishment of a viable Palestinian state? Clearly not. Or put it the other way round: let us say the Israelis are miraculously persuaded to grant the Palestinians a viable state. Does that persuade the Iranians to abandon all thoughts of pursuing nuclear weapons? Clearly not. In fact, linking Iran and Israel-Palestine could inadvertently do the Iranians a favour, by tacitly conceding them a legitimate role in Gaza and in Lebanon.

What probably is true is the more modest claim: significant progress in one area would improve prospects in another. So if there were a rapprochement between Iran and the US that involved the Iranians cutting off support for Hamas, the Israelis would feel more secure – and that might make a Middle East peace settlement easier to achieve. Similarly, the establishment of a proper Palestinian state would remove a source of anger and anti-western grievance across the region, and so undermine an angry, anti-western regime such as Iran.

So how will President-elect Obama respond to all this – and will he be a lumper or a splitter?

I think, as a matter of practical politics, Mr Obama will have to be a splitter. The state of the American economy is going to eat up most of his working day. When he turns to foreign policy, the Israeli-Palestinian problem will come fairly low down his list of priorities – behind, in rough order of urgency, Iraq, Afghanistan, climate change, Iran, international economics and Russia. He will see the Iranian nuclear issue as too important to await progress on Israel-Palestine. Withdrawal from Iraq is a central pledge of his administration, regardless of what is happening with Israel. If an Obama administration sees chances to make progress on Lebanon, or with Syria, it will take them as they arise.

European diplomats who have dealt with the new American team say that they have been assured that Mr Obama does regard the Israel-Palestine problem as a priority and something that the new administration intends to start work on quickly. (It is generally held that President Bill Clinton left the Middle East peace process until too late in his second term and that this mistake has been repeated by President George W. Bush.) A “serious” commitment by Mr Obama need not mean launching immediately into an important global conference. Simply appointing a high-profile envoy would be regarded as a good earnest of intent.

Mr Obama may well oblige on the envoy front. But I doubt he will want to spend much political capital and time on the Middle East peace process when there are so many other priorities clamouring for his attention.

A decision to put the Israeli-Palestinian question on the back burner would, however, be a shame. That is not because it necessarily holds the key to solving all the other problems of the Middle East. It is because the situation – although relatively quiet at the moment – remains dangerous, unstable and a disaster for the population. Ignore the Palestinian problem when things are quiet and it is liable to force its way back on to the agenda – by blowing up at an even more inconvenient time.