The Palestinians and Israelis have had enough of each other. Over the decades, the two populations have tired of the inability of their leaders to find solutions to what ought to be relatively straightforward questions: how to right the wrongs of the past and live together in the future. The problem is that each population is telling itself stories that have little basis in reality.

As the results of the Israeli election are finalised, it is telling how little the occupation featured in the campaign. This was an Israel turning away from regional questions and focusing its fractious politics on internal problems.

Palestinians have come to the conclusion that Israelis don't really want peace, but only, using a word often repeated by Israeli politicians, "quiet". In other words, they want the occupation to continue, the stranglehold on a nascent Palestine to continue, settlement of Palestinian lands to continue - but they want no opposition. No Palestinian protests, no domestic criticism, no international pressure. Just "quiet".

Let the settlers build, let the army arrest and let Israelis get on with their lives - while, a few kilometres away, their neighbours are being killed.

Israelis, meanwhile, have concluded that the Palestinians don't really want peace, that they are not motivated by justice or an end to the occupation, but by irrational feelings towards Israelis. Look, runs this argument, at what happened after Yitzhak Rabin's assassination in 1995: Yasser Arafat ended his peace overtures, and an intifada began. Or look at 2005 when Ariel Sharon withdrew from Gaza, with a trauma to Israelis who had settled there: instead of quiet, rockets rained down on Israel.

Both are compelling narratives. Unfortunately, both are untrue.

To start with, polls suggest that Israelis do want peace. They don't want to think about making peace, they don't want to make big concessions for peace, they don't want a peace that ends in a few months. But they do want it. Israelis want peace with the Palestinians the way people want wedding rings: a one-time, one-price purchase that never needs to be thought of again.

The problem is that no Israeli leader is offering such a peace. Not because the people don't want it and not because it is not achievable, but because Israeli leaders are increasingly beholden to a certain narrative of Israel's security. It is that notion of "quiet": the most Israeli leaders can promise is quiet.

There is no talk of justice, no talk of a genuine attempt to redress the past, no talk of dismantling illegal settlements. It's all about security.

Israeli politicians barely addressed this issue in the recent campaign, even though that is the issue most of the world wants to see advanced. For Benjamin Netanyahu and his hawkish fellow travellers, it is not an issue that matters. Even the centre-right party Yesh Atid, which did better than expected in this election, has not offered any substantive policy on the occupation.

Equally inaccurate is the narrative Israelis have of Palestinians, in particular that "land for peace", as tried in Gaza, is impossible. In fact, no such strategy was tried; there never was a true "disengagement". The Israelis never left. In fact, Israel has increased Gaza's reliance on it, destroying power plants so that electricity must be bought from Israel. Israel controls Gaza's economy and all its borders: any food or medicine that gets in does so at Israel's whim. Gazans cannot export their products, even to the West Bank. The Israeli navy blockades the Strip, so that fishermen cannot fish - even though an estimated 70 per cent of Gazans rely on the sea for food.

At the root of all this is a disconnect between what the public wants and what leaders offer.

Over the past decade Palestinian and Israeli leaders alike have been talking to smaller and smaller constituencies. Not only are few leaders speaking to the other side, most of them are not even speaking to all of their own people.

In Palestine, there is no unifying figure, just the roster of jockeying Fatah and Hamas politicians, talking of revolution but unable to do much. Marwan Barghouti, the closest approach to a unifying figure, languishes in an Israeli prison.

The same process is occurring in Israel. Politicians there speak to smaller and smaller constituencies, usually at the extreme ends of the spectrum. There are no credible Israeli leaders offering solutions rather than threats. In the run-up to the election, Mr Netanyahu said he would not accept the 1967 borders because they would be "impossible to defend".

But why, if there were a genuine peace and not simply an enforced separation, would they need to be defended? Mr Netanyahu speaks as if Palestinians are implacable foes, not offering them a genuine peace.

Unfortunately, the apathy that has gripped Israelis and Palestinians appears to discourage change. There isn't an answer to this, or rather there is an answer but there isn't a person to do it. Cutting this Gordian knot requires statesmanship and leadership. It requires either an internal change - someone to take a big step, like Anwar Sadat with Menachem Begin, or Arafat with Rabin - or an external one, like firmer US policy or stronger international pressure. For now, only the last looks likely.

Palestinian and Israeli leaders are becoming incapable of a genuinely national, let alone bilateral, conversation. And so it becomes more important for the outside world to bring them together, if they cannot find leaders to do so themselves.