Israeli politics can seem opaque to an outsider in the best of cases, but the current reshuffling of Israel’s government is hard for many Israelis to understand themselves.

Think of it theoretically. An embattled prime minister, standing at the head of dissension-ridden, right-of-center Party A, with 40 members in a 120-member Parliament, is determined to take a dramatic step – to withdraw his country’s troops and citizens from a strip of land that some of his fellow countrymen think is theirs by right. Because of this, two small nationalistic parties, B and C, resign from his coalition, leaving him only with the liberal, anti-religious Party D, which has 14 parliamentary votes and strongly supports both the dramatic withdrawal and the government’s controversial economic policies.

The prime minister now needs to widen his shrunken coalition, which is seven votes short of a parliamentary majority. Potentially, he can turn to either the 19-member, left-of-center Party E, which supports him on withdrawal but opposes him on the economy, or to the 11-member religious Party F, which is against him on both withdrawal and the economy and is too much at loggerheads with Party D to sit at one table with it. What does the prime minister do?

(1) Bring Party E into his coalition with a few concessions on economic issues, thus giving him a stable pro-withdrawal coalition of Parties A, D, and E?

(2) Call for early elections?

(3) Force Party D to quit the coalition while bringing in E and F to take its place?

The correct answer, obviously, is either 1 or 2, since 3 appears to make no sense at all. And yet – substituting the Likud for Party A, Shinui for Party D, Labor for Party E, and Shas for Party F – Answer 3 is the one that has been chosen by Prime Minister Sharon in the coalition negotiations now underway.

Why? Why has Mr. Sharon forced out Shinui, his most faithful political ally, in favor of its archenemy Shas, which has fiercely opposed the Thatcherite economics of his finance minister, Benjamin Netanyahu, while at the same time attacking his Gaza withdrawal plan as dangerous and poorly conceived? It, indeed, seems thoroughly illogical.

And yet, from Mr. Sharon’s point of view, it isn’t at all. The key lies in Party A’s being “dissension-ridden.” All along, in pressing his Gaza disengagement plan, the prime minister’s real worry has been the support, not of other parties, but of his own, a large faction of which has fought against disengagement and done all it could to thwart it. To assure himself of the backing of the Likud’s Knesset members on disengagement – and also – which amounts to the same thing – on taking Labor into the government, as the Likud’s Central Committee voted to do by a wide margin last week – Mr. Sharon had both to entice them with a carrot and to threaten them with a stick.

The carrot is not having to appear as traitors by being the only Knesset members on the nationalistic right to vote for a withdrawal from Gaza, as would be the case with a Likud-Shinui-Labor coalition – a coalition that would be branded by the anti-disengagement forces as a left-liberal hijacking of the Likud. If Shas, most of whose voters are also in the “undivided land of Israel” camp, could be persuaded to come on board in Shinui’s place, the Likud rebels would have a fig leaf for reluctantly voting for disengagement, too. One needn’t, after all, be holier than the pope – who in this case is Rabbi Ovadia Yosef, the spiritual leader of Shas. Rabbi Yosef’s halakhic approval of disengagement is a sine qua non for the party’s acceptance of it as part of a coalition agreement.

And why should Shas and Rabbi Yosef, against disengagement until now, suddenly reverse their positions? Because money speaks more strongly than land. Frozen out of the government by Shinui’s refusal to sit with it, Shas has seen its many religious and educational institutions languish for lack of government funds. The opportunity to tap back into such funding is too tempting to let the Jewish settlements in the Gaza Strip stand in the way, especially since Shas, despite being on the religious right, has no representation in the settler movement and is immune to pressure from it.

As for the stick, this is Mr. Sharon’s threat of early elections – something that Knesset members are rarely enthusiasts of, since they cannot be certain of their place on their party’s next electoral list or of its winning enough votes to elect them. As long as Shinui was in the coalition, the 61 Knesset members needed to bring down the government in a no-confidence vote were unavailable, since Labor had announced that, in order to see disengagement through, it would not lend a hand to toppling Mr. Sharon. Now, with Shinui out, a successful no-confidence vote is a distinct possibility – unless, that is, a new Likud-Labor-Shinui coalition is formed. More than one antidisengagement Likud Knesset member will support a pro-disengagement coalition as the price of hanging onto his seat for two more years.

It’s not pretty or principled politics. But when it comes to disengagement, Mr. Sharon is out to win, not look pretty. His problem has never been the support of the public at large, which has been solidly pro-disengagement all along. It has been the support of the Likud and of the Knesset, in which the disproportionate strength of the antidisengagement forces does not reflect the popular mood. With Shas locked into disengagement by joining the government, and Shinui committed to vote for it even while out in the cold, he will have gotten exactly what he wants.

Mr. Halkin is a contributing editor of the New York Sun.