Can a Jewish liberal congressman who looks like chicken-king Frank Perdue become mayor of New York? Or will the next mayor be a former congresswoman made over for an upcoming Good Househeeping magazine article into "Brand New Bella?"

Those are only two of the possibilities. If you like pulling levers in voting booths you could do worse than be a New York Democrat this month.

After a campaign in which seven Democratic candidates for mayor scoured New York's streets and beaches all summer for voters hands to shake, the voters will strike back Thursday and elimate at least five of the aspirants.

It appears certain, however, that New Yorkers will not give and candidate 40 per cent of the vote so there will be 11-day runoff campaign between the top two finishers and the city's Democrats will go back to the voting booths to make their final primary choice Sept. 19.

Four of the candidates entered the final week before the first vote with a chance to stay alive, according to a welter of polls and freely offered opinions.

Mayor Abraham Beame, Bella Abzug. Rep. Edward Koch - who hopes to do as well his campaign as Perdue has done with his capons - and New York Secrectary of State Mario Cuomo are all given a chance to make the runoff.

Koch's candidacy has sured only in the last two weeks and many predict he will be the finals with the flamboyant and anti-establishment Abzug who has led in the polls from the start but been slipping steadily.

Despite the repeated disasters which have afflicted the city during his adminstration. Beame cannot be counted out because of his labor and traditional political clubhouse backing. Cuomo has Gov. Hugh Carey behind him (and, sometimes in front of him seeming to tug along as his candidacy sometimes appears relucant.

It is interesting that in a city where politicians used to have to furrow their brows and give public evidence of serious concerns over the widening gap between rich and poor the biggest issue with voters this year appears to be the death penalty.

The passions over reviving electroution are so strong that the candidates are constantly asked their positions although the mayor doesn't determine how criminals are punished.

One candidate, Koch, doesn't have to be asked his opinion. He is happy to tell all listners that he supports the death penalty. Execution is a deerrent and his in keeping with the Judeo-Christian heritage. Koch explains, and "society has the right to show its sense of outrage."

Cuomo has attacked Koch for practicing "the politics of death." Carey, Cuomo's backer, recently vetoed a bill that would have reimposed the death penalty in New York.

In his eagerness to bolster the lack-luster Cuomo campaign. Carey somewhat undermined the authority of his position this week when he said he would reconsider his death penalty stand - but only if New Yorkers elected Cucomo.

The first reaction from Cuomo - who strongly opposes the death penalty - when reporters brought him news of Carey's offer was to quip that he was reconsidering his position on Carey.

Cuomo has built something of a reputation for witty irreverence about his patron and his campaign and for a refusal to take cheap shots. "It's not that simple," Cuomo says frequently.

"Ask Mario a question and he says he'll appoint a commission to study it," Koch jibes. "That campaign is Cuomotose."

The Koch-Cuomo relationship has a history. Essentially they divide the same constituency - the "I-Don't-Want-Beame-Again-But-I'm-Not-Ready-Vote-For-Abzug" white voters.

A key figure in the history is David Garth, the campaign media expert whom many credit with getting John Lindsay elected. Garth has done a series of television commercials for Koch so effective in presenting Koch as the straightfoward candidate of integrity that it is uncanny to listen to citizens respond when Koch asks them during his walking tours why they like him.

"Because you're honest and straightforward," they reply one after another as though Garth or Koch had fed them the line.

The history goes like this.

Garth wanted to work for Cuomo, but Cuomo told him he wasn't running. Garth went to work for Koch. Koch asked Gov. Carey for support. Carey turned him down and twisted Cuomo's arm until Cuomo entered the race despite public statements that he didn't want to be mayor. Carey asked Garth to desert Koch for Cuomo. Garth refused.

Cuomo was to preempt the right wing vote by being the white Catholic ethnic candidate, may of his supporters thought. But Cuomo doesn't like campaigning and his refusal to be a demagogue left him with the appearance of being indecisive.

"I will do many things to be mayor, but I won't lie," he said often. When a man told Cuomo that he shoould change his position and advocate capital punishment or lose a lot of votes, Cuomo replied, "so I'll lose."

While Cuomo refused to play the role of Archie Bunker candidate, Koch's support of the death penalty in a city absorbed by the "Son of Sam" murders, his call to bring in the National Guard to prevent looting during the July blackout and his opposition to allowing policemen or firemen to strike, have allowed him to ride into the law-and-order position Cuomo's backers had thought they had marked out for their man.

Cuomo accuses Koch who once had the reputation of being the classic liberal of opportunism, saying Koch changed his stand to suit the city's mood." "You've moved so far to the right you're a speck on the horizon," Cuomo told him during one debate.

Koch counters that his criterion is not whether a position is liberal or conservative, but whether it's sensible.

Eleven days of a Koch-Cuomo run-off would be a rough scramble, but would not pose as stark a choice as the more likely Koch-Abzug or Abzug-Became pairings.

If she makes the runoff, Abzug will be opposed by the many entrenched interests in the city which cannot afford to have her win because the essence of her campaign is that they are New York's villains. These interests include municipal unions, real estate developers, bankers, old-line Democratic pliticians and New York's other power brokers.

Will people have the nerve to make a change? That's the one, clear issue, Abzug's campaign manager Terry O'Connell said.

O'Connell knows that Abzug makes people uncomfortable and that people generally vote for a candidate with whom they feel comfortable. It's a tough choice for the people to make, O'Connell said.

The conventional wisdom throughout the campaign has been that Abzug would get into the runoff but lose in the second round. Enough New Yorkers admire her to place Abzug first or second in a crowded field, this reasoning goes, but enough fear or dislike her to deny her victory in a two-person contest.

New York's political establishment can't stand her. "She is hated by the right people," the Village Voice newspaper said in endorsing Abzug.

One thing is certain about Abzug. Win or lose.Good Housekeeping will go on sale Sept. 15 with a photograph of "Brand New Bella" - 25 pounds ligher, with a new hairdo and makeup.

Became, 71, had been fighting a series of unlikely enemies in his campaign to win reelection. The blackout gave him Consolidated Edison as a foe and now he punches daily at the Security and Exchange Commission which issued a report last week accusing Became of misleading New Yorkers about the gravity of the city's fiscal crisis in 1974 and 1975.

Any runoff with Became in it would have the handling of that crisis as a major issue.

The death penalty would also stay alive as an issue. Became switched to support of execution in mid-campaign and has used his new stand in his speeches as often as Koch has.

Cuomo calls Became's switch pandering. Became accuses Cuomo of being more concerned about criminal defense than about the victims of crime.

Abzug (and others) accuse Cuomo of being the government's puppet. All of the challengers (including U.S. Rep Herman Badillo, Manhattan Borough President Percy Sutton and businessman Joel Harnett who are though to have no chance of victory) deprecate Beame's record. All of the men attack Abzug for her support of policemen's and firemen's right to strike.