Being one of 700,000 Palestinians refugees from the 1948 upheaval that created the state of Israel deeply affected Abbas's outlook on life.
After half a century in exile, Abbas is a pragmatist -- eager to end his people's pain.
Abbas is also one of the few Palestinian leaders to have deeply studied Israeli history and politics. In 1993, he was a key player in the Oslo peace accords between the Palestinians and Israel.
Last month, he called the intifada, or uprising, against Israel a mistake that must end.
But for Abbas, the statement was nothing new.
"We will do our best and we will use all of our means to end the armed intifada, and we will succeed," Abbas said on 4 June 2003. "The armed intifada has to end, and we have to use peaceful means to end the [Israeli] occupation and to end the suffering of Palestinians and Israelis and build the Palestinian state."
Abbas's comments came while speaking in Aqaba, Jordan, alongside U.S. President George W. Bush and Israeli Prime Minister Ariel Sharon. As the Palestinians' first prime minister, Abbas had just committed his government to the "road map" peace plan drawn up by the United States, European Union, United Nations, and Russia.
But it was not to be.
Three months later, Abbas resigned. He accused Arafat of undermining him by refusing to hand over control of Palestinian security to rein in militants. And he said Israel had failed to respect its road-map commitments.
Abbas had reluctantly taken office. The United States saw Arafat as tainted by ties to terrorism and had demanded new leadership as a condition to begin work on the road map.
Here's Bush after his return from Aqaba in 2003.
"The Palestinian people must know that by accepting a peaceful government, by embracing the prime ministership of Abu Mazen, that there's a better day ahead for them when it comes to making a living," Bush said.
Yet, when he resigned, Abbas also blamed the United States for not pressuring Israel to take constructive steps to foster peace and bolster his fledgling Palestinian government.
Abbas had since kept a low profile. But Arafat's death in November thrust him back into the spotlight.
He was elected to replace Arafat as chairman of the Palestinian Liberation Organization and was then chosen by Arafat's Fatah movement to be its presidential candidate.
In his campaign, the suit-and-tie Abbas has sought to depict himself as the rightful heir to the uniformed Arafat, revered as the heroic leader of the Palestinian struggle.
That has not been an easy task for a lawyer who, as Palestinian academic Mahdi Hamdi notes, has never carried a gun, fought a battle, run for election -- and "has been known as a sulking, as a reluctant person."
But Abbas has done his best to attract the support of all Palestinians, including militants whose backing he will need to stop violence during future peace talks.
Last week, Abbas allowed himself to be carried triumphantly by militants in Gaza and responded with inflammatory rhetoric after Israel troops killed several Palestinians there.
"We are praying for the souls of our martyrs who were killed today by the shells of the Zionist enemy in Beit Lahiya," Abbas said.
Israeli and U.S. officials both criticized that statement.
But Israel knows that what matters is not what Abbas says before the election -- but what he does after it. Following Abbas's "Zionist enemy" comment, Israeli Prime Minister Ariel Sharon said he hopes to meet with him soon after the vote.
Throughout his campaign, Abbas has stood firm on the major negotiating points of the Palestinian cause -- a state within pre-1967 borders with its capital in east Jerusalem and the "right of return" for refugees and their descendants, who now total 4 million.
That last point is unacceptable to Israel. But starting points are one thing; final positions another.
Abbas's only return to his now-Jewish village overlooking the Sea of Galilee was done secretly in 1994. As a lifelong refugee, he appears to know the value of compromise.
The key will be whether he can persuade militants to lay down their arms. Israeli Foreign Minister Silvan Shalom made that point recently.
"The only chance for the success of any future talks between Israel and the Palestinians is if the terrorist option is removed from the equation," Shalom said.
To achieve that, Abbas must convince militants he can win concessions, such as an end to the occupation of Palestinian areas.
Abbas's chief election rival, meanwhile, is Mustafa Barghouti.
A physician trained in the Soviet Union, Barghouti took part in the 1991 Madrid peace talks. He also holds a master's degree from Stanford University and heads the Union of Palestinian Medical Relief Committees, a nongovernmental organization that provides health care to 1 million Palestinians.
Israeli police today briefly detained Barghouti when he tried to enter the Temple Mount, a Jerusalem shrine holy to Muslims and Jews. Here he is speaking to police.
"You are arresting a presidential candidate that has a permit to be in Jerusalem," Barghouti said. "I gave you the permit. I gave you the permit that shows that I can enter Jerusalem and I can come to Jerusalem. I am coming here to pray in the [Al-Aqsa] mosque."
It was the third time in a month that Israeli police had detained Barghouti, who is a distant relative of Marwan Barghouti, a popular grass-roots leader of the uprising who is serving five life terms in an Israeli prison.
Overall, Mustafa Barghouti is expected to win 20 percent of the vote. Last week, he said he had the support of the Popular Front for the Liberation of Palestine, a militant group.
The popular militant group Hamas says it will not take part in the vote, but media reports say their leaders may tell supporters to vote for Barghouti.