I am proud to be a citizen of a country where the prime minister can be investigated like an ordinary citizen, said Ehud Olmert on July 30, announcing that he would resign as prime minister in September to defend himself against corruption allegations. He should be even prouder: Three of Israel’s last four prime ministers were under investigation for corruption when they left office.

To be fair, it was a stroke, not the corruption charges he was facing, that finally drove Ariel Sharon from office, and Benjamin Netanyahu subsequently beat the charges against him after being forced out as prime minister. Politics in Israel is a blood sport, and only the strong survive. Not one of the country’s last five prime ministers has managed to serve out a full term of office.

What happens next is hard to predict. Tzipi Livni, the foreign minister, and Shaul Mofaz, former army chief of staff and now transportation minister, are the leading candidates to succeed Olmert as leader of the Kadima party, but even if the succession struggle does not split Kadima and wreck the ruling coalition, an election is probably no further away than the spring of 2009. The likely winner of that election is Bibi Netanyahu, who is once again the leader of the right-wing Likud party.

Indeed, the main thing that has kept Ehud Olmert in office for the past two years, despite the disastrous miscalculation of his 2006 war against Lebanon, has been the fear on the center and left of Israeli politics that the only alternative was a return to power by Netanyahu. And that, in turn, is a reflection of the great division that paralyses Israeli politics: between those who think the “demographic danger” requires major compromises on territory, and those who do not.

The demographic danger is that Israeli Jews will end up as a minority within the territory ruled by Israel. It is almost a reality already: The 600,000 Jews who lived in Israel when it was founded in 1948 have grown to six million, but despite the huge number of Palestinians who fled to surrounding countries in the various wars, a higher birth rate means that there will soon also be six million Arabs living in territory under Israeli control. And then there will be seven million, and then eight million... Only a little over a million Palestinian Arabs still live within Israel’s 1948 borders and actually have Israeli citizenship, but the rest are not far away, in the West Bank and the Gaza Strip, which have been under Israeli control for more than 40 years. If Israel does not find a way of turning those territories into a separate Palestinian state, then sooner or later they will shift from supporting the “two-state solution” to demanding the one-state solution.

All of Palestine was a single colony under British rule. The partition of 1948, though mandated by the United Nations, was never enforced, and the real division of Palestine, accomplished by war, had very different borders: The Palestinians ended up with about one-sixth of the territory, not half. Then all the rest of former Palestine was conquered by Israel in 1967 — and although the Israelis never describe what happened as the reunification of Palestine, they promptly began building Jewish settlements all over the captured territories.

So in a sense, the single political space of the old British mandate of Palestine has been recreated, although only Israeli citizens can vote for the government that decides what happens there. Since the Oslo Accords of 1992, there has been a “Palestinian Authority” that exercises some control over some of the occupied territories, but it is not an independent state. Moreover, for the past year there have been two rival Palestinian “governments” in the West Bank and in the Gaza Strip.

Olmert was absolutely clear: If this single political space persists, and the Palestinians become the majority population within it, they will stop asking for their own state. They will just demand the vote — and Israel will have to choose between granting them their demand and ceasing to be a Jewish state, or rejecting it and ceasing to be a democracy.

That dilemma has been implicit ever since the Israeli conquests of 1967. It is now explicit and imminent. In fact, it is already the position of the Hamas movement, which controls the Gaza Strip. So Olmert wanted to make a deal that gave the Palestinians their own state, in order to preserve an Israel that was both Jewish and democratic.

He never even came close, partly because the Palestinians are now deeply ambivalent about the two-state solution, but mainly because the Israeli electorate has never been able to choose between the two options. Too many Israelis want to hang onto the territories and preserve a Jewish democracy, and do not accept that those goals are incompatible. Benjamin Netanyahu was their standard-bearer in the late 1990s, deliberately sabotaging the Oslo Accords when he was prime minister, and he still is today.

Olmert, for all his faults, backed the two-state option. Netanyahu does not, although he says whatever is necessary to placate Washington, and he will probably be back in power within a year. The long paralysis in Israeli politics will continue.