When Shimon Peres' supporters ran out of conventional arms in the battle against Amir Peretz, they brought out their Judgment Day weapon: "Picture Amir Peretz sitting in the White House and having a talk with President Bush about the road map," they said mockingly.

Now, in the wake of the sweet victory, Peretz's camp can snort. If Peretz becomes prime minister, they say, he will fold up the map and save the expense of traveling to Washington. He has promised them that the day after he steps into the Prime Minister's Office, he will invite Palestinian Authority Chairman Mahmoud Abbas for direct negotiations on a final-status agreement - no more unilateral withdrawals, an end to the season of dictates, an end to belligerence, an end to conditioning the continuation of the peace process on "the dismantling of the terror infrastructures."

Sharon believes that the Palestinians are raised on the milk of Israel hatred, and that they will not rest until the country is wiped out. Therefore, a peace treaty with them is of no value whatsoever, and Israel is left with no alternative but to subdue the enemy by force, until it capitulates and makes do with the little it is offered.

Peretz, on the other hand, began his discourse with members of the Palestine Liberation Organization in the Gaza Strip more than 20 years ago in his capacity as Sderot mayor when meetings with the Palestinians were not yet in fashion. By the way, his wife, Ahlama, recently completed a course for mediators for meetings between Jews and Arabs.

The Peretz family believes that their neighbors also have much to gain from peace and much to lose from its absence. In others words, they believe that the Arabs are no less rational than the Jews, and that the unemployed individual from the Balata refugee camp, like the unemployed individual from Sderot, will support a leadership and policy that will offer him a livelihood, ensure a good education for his children, and fight against those elements that threaten to harm his life and welfare.

Peretz views peace not only as a value unto itself, but also as an essential condition for growth and improvement of the individual's lot. Peretz believes that human life is sevenfold more important than a few kilometers in the West Bank or the Golan Heights. As far as he is concerned, the occupation corrupts the occupier, and the territories are more damaging than beneficial.

Were it up to Peretz, he would present Abbas with an offer he could not refuse, and renew talks with Syria at the point at which Ehud Barak broke them off.

All said, Peretz is far from being naive. He knows that the public is in love with the separation fence, stuck on the "united Jerusalem" slogan, and fearful of the right of return for Palestinian refugees. As a result, he will make do with amending the route of the fence in order to minimize its effect on the lives of the Palestinians; for Jerusalem, he will propose religious autonomy without dividing the city; and when it comes to the refugees, he will seek solutions outside of Israel's borders, with a few exceptions based on family reunification.