JERUSALEM — Yasser Arafat may cast the most important vote in determining who is the next prime minister of Israel.

If Ehud Barak is to win re-election, he must persuade Arafat to end the current violence and to sign a draft peace accord before Israelis go to the polls, probably in May.

If the leader fails to bring Arafat on board — and the odds at this time are that he will fail, given the Palestinians’ present and recent inflexibility — it is unlikely Barak can defeat the presumptive Likud candidate, Benjamin Netanyahu. The former prime minister currently leads Barak by 20 percentage points in public opinion polls.

After acceding Tuesday night to the Knesset’s obvious desire for early elections, Barak made it clear that vigorous diplomatic efforts would continue during the coming months of a “lame-duck government.”

Representatives of Barak’s One Israel bloc and the opposition Likud met briefly Wednesday to determine an election date. In a turnabout, hawkish opposition leader Ariel Sharon — whose visit to the Temple Mount over two months ago marked the onset of a wave of violence being dubbed the new intifada — said he was willing to hold new coalition talks if Barak offers up the invitation.

However, Barak had rejected that idea just one day earlier, based on Sharon’s condition that if a unity government formed, it would have veto powers over the prime minister’s peace maneuvers.

To Barak’s advantage, the early elections bill still awaits two more readings, giving Barak several more weeks to scramble together a political strategy.

In a television interview, Barak bemoaned the Palestinian rejection of ideas put forward by Israel and the Americans at July’s Camp David summit and in subsequent diplomatic contacts.

But, he added, “it may not be over.”

Barak insisted his diplomatic efforts would continue alongside the Israel Defense Force’s efforts to contain and reduce Palestinian violence.

Israeli military sources reported a sharp decline Tuesday in the number and intensity of violent incidents in the West Bank and Gaza Strip, possibly due to the holy month of Ramadan, when Muslims fast from dawn to dusk.

If the reduction was orchestrated by Arafat and was intended to help Barak out of his parliamentary predicament, it plainly came too late.

But there is no doubt that the Palestinians are closely following Israel’s intricate political drama. And they will have to recognize the fact that their behavior — on the “war” front and in the peace talks — could directly and critically influence the outcome of Israel’s domestic contest.

The confluence of domestic and diplomatic circumstances could therefore become a catalyst, driving Israel and the Palestinian Authority toward a comprehensive or partial agreement before the election deadline draws near.

On the other hand, some skeptics contend the Palestinians are not genuinely interested in a peace agreement and would prefer to face a harder-line Likud government that would take the international blame if peace talks founder.

In any case, events between Israelis and Palestinians on the ground could prove to have a negative and even dangerous impact during the pre-election period.

Barak seemed aware of this danger in his televised interview, when he vowed that the army, under his direction, would not “play to the gallery” by overreacting to violent Palestinian provocations.

Too often, Barak said, Israeli governments pandering to the public’s natural urge for revenge have ordered the army to overreact to Arab violence, only to regret the harmful effects to Israel’s international standing and overall strategic strength.

As the election campaign moves forward, Barak will come under greater temptation to strike back ever harder after Palestinian acts of terror or violence because he cannot afford to be perceived by sections of the electorate as soft and hesitant.

For its part, the Likud will be tempted to criticize Barak for softness and hesitancy, and to demand ever-harsher military measures.

The election probably will take place in May, or at the earliest, before Passover, April 7, as Sharon would have it, but who will the candidates be?

Barak announced Tuesday that he would run as the Labor candidate. He appeared to share the widespread assumption that Netanyahu will be back to head the Likud, noting that he had beaten Netanyahu before and would beat him again.

But Barak’s candidacy is not a foregone conclusion, however unconventional and messy it is for a party to dislodge a sitting prime minister and party leader.

Foreign Minister Shlomo Ben-Ami, for one, certainly sees himself as prime ministerial material.

There may yet be other candidates.

Israel Radio reported Tuesday night that the speaker of the Knesset, Avraham Burg, would also contend for the Labor leadership.

Burg has been something of a dissident figure in Labor since Barak’s May 1999 election victory, when Barak ignored Burg’s great popularity within the party and declined to offer him a Cabinet seat.

Burg then ran for the largely ceremonial role of Knesset speaker, defeating an effort by Barak to block him.

As speaker, Burg has shied away from the hurly-burly of party politics, steering clear of public controversy. But he has not neglected his standing in the party, taking care to visit party branches around the country and keep up contact with the thousands of field workers and activists who are the backbone of any political movement.

As a yarmulke-wearing man whose late father was leader of the National Religious Party, Burg has appeal among traditional and some moderate-Orthodox voters.

Furthermore, as a consistent dove — he was a leader of Peace Now in his younger years — he is well liked on the left.

Such a resume might allow Burg to unite diverse Labor factions behind his banner. He also is a charismatic public speaker and a tough and experienced political infighter, skills he would need against Netanyahu.

Yet his dovish views also could become a liability if Palestinian violence continues and the public clamors for a strong response.

In the Likud, chairman Sharon shows little willingness to vacate the party leadership for the more popular Netanyahu.

To the contrary, Sharon is to be heard disparaging Netanyahu in private conversations.

Indeed, much of the failed negotiation between Sharon and Barak on the creation of a national unity government was predicated on their joint desire to keep Netanyahu out — so much so that political wags joked that Sharon might prefer to serve as Barak’s No. 2 rather than as Netanyahu’s.

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