Many moons ago, before I entered the sordid world of journalism, I worked in the sordid world of politics. I was secretary to a Labour Party committee which had been charged with drafting a new constitution for the party, including - how last weekend's events brought the horrors back! - an electoral college.
After weeks of negotiations between representatives of the different wings of the party, it was, I decided, hopeless. The preconditions laid down were irreconcilable. We were doomed to failure.
The chairman of the committee, who had spent his political life knocking all sorts of heads together and understood the pure art of politics, told me not to be so stupid. "Ignore what they are saying. Just ask this question: 'Have they got more to lose if we don't agree than if we do?'"
They had. Our task was not to help them reach an agreement but to save their face; to give them enough ground to be able to maintain that their preconditions had been met. They would be responsible for agreeing the deal; we had to get them to the point of negotiation.
Which is where we now are with the issue of settlements and the peace talks. Both Bibi Netanyahu and Abu Mazen have made their preconditions clear. For the Israeli leader, he must be free not to freeze construction work in the settlements. And for the Palestinian leader, he must have precisely the opposite: a construction freeze.
Which points to an impossible deadlock and the collapse of the talks.
Except that no one involved in them wants the talks to finish. Not the Israelis, not the Palestinians, not the US, not the Quartet; not anyone- except the extremists on either side.
If Abu Mazen fails to deliver even the process of serious negotiations then he is finished as a player, Hamas is given a major boost and the hugely promising progress made by Salam Fayyad, Prime Minister of the Palestinian National Authority, is placed in severe jeopardy.
As for Mr Netanyahu: the last thing he wants is another failed term as Prime Minister, marked only by the collapse of the latest "last chance" of peace and the destruction of the man he now warmly refers to as his partner for peace.
It would be some legacy for Mr Netanyahu to depart with: the clear message to Palestinians currently seeing real economic progress in the West Bank that Hamas was right - Fatah cannot deliver.
So he, too, needs to carry on. And that's what matters. Not public words and pre-conditions.
That brings us to the role of Tzipi Livni, whose stock deserves to fall with every passing day. Since last year's election, she has berated Mr Netanyahu for his approach to the peace process. And yet she has placed her own partisan advantage far above that process.
If Ms Livni was a statesman she would, now that push has come to shove, make clear her backing for Mr Netanyahu's participation in the talks. At a stroke, she would remove his worry that his coalition may collapse.
Yet she will not do that because she wants it to collapse. She wants his job. It is her ambition, not her principles, which are preventing a united Likud-Kadima front; a deep irony considering that Kadima was only created to enable a push for peace - the disengagement from Gaza.
But although Mr Netanyahu will not announce a freeze, that doesn't mean he won't implement one. It is actions, not words, which matter in politics.
My understanding is that the Palestinian negotiators would even live with renewed building, so long as it was in areas expected to be part of Israel in any agreement.
So the odds, surely, must be on talks continuing.
All that said, we'd better hope that the analogy with the formation of Labour's electoral college is misplaced. As last weekend's vote showed, the problem wasn't with the politics, which got the job done. The problem was a fundamental flaw with the end product, which has saddled Labour with a leader its members didn't want.