Mr. Nusseibeh once advocated Palestinian voting, backing an Arab newspaper publisher who ran for mayor in 1987 but withdrew after his cars were burned and his home vandalized. Yet Mr. Nusseibeh himself has never voted here, either. And he said that the current Israeli-Palestinian peace talks, with the fate of Jerusalem among the contentious questions on the agenda, make people even more wary that voting could be seen as legitimizing Israel’s control of the city.

A Jerusalem Post article this month detailed a deep disengagement: many Arab residents did not know who was running, when Election Day was, or where the polling stations would be. Some mistakenly assumed an Israeli passport was required.

Alaa Obeid, 23, a student who briefly flirted with running for City Council this year on a new slate promoting the environment and women’s empowerment, said she and most other Palestinian residents rarely thought about why they did not vote. It is just not part of the culture, she said.

“In our society, it’s very important what the public thinks,” Ms. Obeid said, explaining why she decided against running. “If all these years, people have boycotted the elections, I might be in a place where there’s a risk to my future. I’ll be an outcast.”

A spokeswoman for Mr. Barkat said there had never been an Arab member of the Council. Nor are there Arab department heads in City Hall. The mayor’s part-time adviser on East Jerusalem is an observant Jew.

Mr. Barkat’s opponent in Tuesday’s balloting is Moshe Lion, a former director of the prime minister’s office who moved to Jerusalem from a Tel Aviv suburb to run and is backed by right-wing and ultra-Orthodox forces. Mr. Lion has accused the incumbent of threatening Israel’s sovereignty in the capital by giving “the extreme left” — Meir Margalit, a Council member from the peace-seeking Meretz Party — control of the East Jerusalem portfolio.

Mr. Margalit, an Israeli human-rights advocate who worked against the demolition of Arab homes before his election to the Council, has become this season’s most outspoken proponent of Palestinian participation. His slate includes an Arab-Israeli hospital technician, though polls show he is unlikely to make the cut. If Arab residents voted en masse like the ultra-Orthodox minority, Mr. Margalit said in an interview, they could win enough seats not only to demand better garbage pickup and more playgrounds, but to “change history” by blocking the Jewish settlement expansion that they say threatens their future capital and the two-state solution to the Israeli-Palestinian conflict.

“I would like to see them be more pragmatic,” Mr. Margalit said. “Ideology is a great thing, but in this specific context, ideology is not the main issue. The main issue is how to save East Jerusalem. In order to do it, they have to do it in the political arena.”