1. Monday night’s interaction initiated by President Reuven Rivlin marked the first working meeting between Likud head Benjamin Netanyahu and Blue and White leader Benny Gantz since Gantz stepped down as chief of staff in 2015, at the end of a term that Netanyahu, then, as now, prime minister, had extended to a fourth year, in appreciation of his skillful command.

In the campaigns ahead of last week’s and April’s elections, by contrast, Netanyahu condemned Gantz as a weak man of the left, who cannot be trusted to keep Israel safe. Gantz, for his part, has declared that Netanyahu has become a despotic liability to the country, and should leave the stage to deal with the corruption allegations against him.

2. During Sunday’s and Monday’s consultations with the representatives of the nine parties that won Knesset seats on September 17, Rivlin returned time and again to the imperative to establish a stable government and avoid a third round of elections.

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Sources at the President’s Residence quoted on Israel’s Channel 13 news on Monday night said Rivlin believes he has “ideas” that could help encourage Netanyahu and Gantz to forge a unity coalition, including a formula by which they could rotate the premiership. Whatever he pitched, it was evidently sufficient to persuade the two candidates to keep talking: he invited them to come back on Wednesday, with their negotiating teams getting together on Tuesday.

If there is to be a unity government and a leadership rotation, some reports suggest that it may come with legislation aimed at preventing the premature demise of such a coalition before each man has served his time as PM, possibly by requiring the support of 80 of the 120 MKs to bring down the government.

3. Anonymous sources close to Rivlin told Channel 13 that the president has not made up his mind who to charge first with the task of building a coalition. “He does not have a name in his head,” the TV station quoted an unnamed source as saying.

The president has until Wednesday, October 2 to make a choice — which happens to be the same day as Netanyahu’s hearing pending indictment. Rivlin could choose one of the two to form a government as early as this Wednesday or Thursday, the TV report said, but would be perfectly prepared to wait another week, enabling them to reflect on his unity appeal during the two-day Rosh Hashanah holiday, which begins Sunday.

4. If Netanyahu and Gantz cannot agree between themselves on a process of coalition building, Rivlin will indeed face a complex choice. Neither would-be prime minister has majority support or a clear path to a coalition. Fifty-five MKs (from Likud, Shas, United Torah Judaism and Yemina) have recommended Netanyahu as prime minister, compared to 54 for Gantz (from Blue and White, Labor-Gesher, the Democratic Camp, and 10 of the 13 Arab MKs from the Joint List). By that measure, Rivlin could opt to give Netanyahu the first shot at mustering a majority. But Blue and White party has 33 seats, compared to 31 for Likud. So that favors Gantz.

In 1984, when elections also produced political deadlock, the Labor Alignment had 44 seats to Likud’s 41, and the Alignment’s leader Shimon Peres took the first two years as prime minister, before the role rotated to Likud’s Shamir.

5. While both Netanyahu and Gantz have professed to seeking a unity arrangement, Netanyahu and his ultra-Orthodox and right-wing allies have also agreed to negotiate as a single bloc, prompting Blue and White to dismiss his unity overtures as disingenuous spin. Gantz, for his part, while seeking to partner with Likud, has said he will do so only when it has ditched Netanyahu.

Gantz also initiated a meeting earlier Monday with Liberman, and is said in some unsourced Hebrew media reports to be so closely coordinated with the Yisrael Beytenu leader as to have already begun discussing the distribution of ministerial posts. Netanyahu blames Liberman for precipitating these elections, by refusing to join his coalition after April’s vote, and now routinely disparages his former ally as a man of the left. And Liberman has said he will not sit in a coalition with the ultra-Orthodox parties to whom Netanyahu is bound.

If Rivlin can somehow cut through those and other complexities, and foster a Netanyahu-Gantz partnership, he will be a true political magician.

6. Adding to the scale of the president’s task is the fact that he has a famously difficult relationship with Netanyahu. Rivlin is a former Likud MK and Knesset speaker whom Netanyahu sought to prevent becoming president, and who has repeatedly, if implicitly, criticized Netanyahu for his divisive political tactics. The “bad blood” between the two runs so thick, one political analyst noted in a TV report Monday night, that Netanyahu will be inclined “to think of any proposal from Rivlin as aimed to bring about the end of his career.”

7. TV reports as the triumvirate met on Monday raised all kinds of speculative notions about how a Netanyahu-Gantz rotation of the prime ministership might work, including one under which Netanyahu would serve as prime minister first, with the obligation to step down if he is indicted in any of the corruption cases against him. But such thinking assumes their readiness to defy expectation and agree to a partnership.

It is far more likely that for all of Rivlin’s efforts, each will still insist on trying to build a government without the other, though they themselves may not yet have decided whether it is smarter to take the first shot at such an effort, or hold back and wait for their rival to, hopefully, fail.

Thus Rivlin, forced to make his Solomonic decision, may be choosing between two candidates who may not have figured out if they even want to be chosen.