In Ward 3, the area west of Rock Creek Park that produced some of the most vigorous campaigning in the city's first home rule election four years ago, political activity in this year's council election is decidedly low-key.

Incumbent Polly Shackleton, a Democrat seeking a seond term, is spending half of August on vacation in Vermont.

Her only opponent in the Sept. 12 primary, attorney Joel Joseph, still hasn't issued any campaign leaflets. His few campaign buttons are leftovers from 1974 when he finished fourth out of five candidates in the ward's Democratic council primary.

Among Republicans, who make up about a quarter of ward's registered voters, only one candidate, Alexander Cartner, an IBM service representative, has filed nominating petitions.

Cartner said he had had no previous involvement in political or civic organizations and before he filed, he was unknown by the ward's Republican committee members who had spent almost six months searching unsuccessfully for a candidate of their own.

Albert Rosenfield, the 1974 GOP candidate who garnered 37 percent of the vote, has switched his registration to Democratic, and is campaigning hard for Mayor Walter Washington.

"I told Polly Shackleton the other night," Rosenfield said recently, "'Don't knock yourself out this time. Just stay home in your rocking chair. You have it in your bag.'"

"We're not taking anything for granted," said David Grinnel, Shackleton's campaign chairman, "but this time we're not mounting a major campaign. Four years from now, if Mrs. Shackleton retires, I'm sure there will be a very active race beacuse there are a lot of very young people here who are just itching to jump in, but this time they decided not to waste any of their money, time and effort."

Actually, at age 68 Shackleton doesn't own a rocking chair, and although she speaks less than many council members, her attendance record at council meetings is almost perfect, and she shows up often at community meetings as well. With help from volunteers, she runs a busy constituent service office in Chevy Chase, D.C. She also has found time to appear in a Democratic Party musical review dressed like Eleanor Roosevelt, whom she resembles somewhat physically and whose strong liberalism she shares.

Although Shackleton's family was much less wealthy than the Roosevelts, her father Adolph Ehrlich, was president of a Boston department store, and she still draws income from family trusts.

Ward 3, which includes Georgetown, Cleveland Park, Chevy Chase and all other neighborhoods west of Rock Creek Park, is 95 percent white - a proportion that has remained steady for decades even though the rest of Washington has become about 85 percent black.

Since the early 1970s, the ward's real estate prices have soared, turning comparatively modest neighborhoods such as Glover Park and the Palisades into trendy settlements of young professionals, where "cheap" homes cost $100,000. Average family income is by far the highest for any part of the city, and at about $27,000 exceeds that in Fairfax and Montgomery counties.

The ward also pays high taxes. With only about one-eighth of the city's populations, its residents paid 36 percent of all D.C. income taxes in 1976 and accounted for about one-third of residential property tax collections.

The ward, however, makes relatively little use of city services. Only about half of the children living in the ward attend public schools. They account for less than 5 percent of Washington's public school enrollment.

For the past three and a half years, Shackleton has served on a council which, even with slight changes in membership, has always been composed of 11 Democrats, one Republican and one Statehood Party member; 11 blacks and two whites.Shackleton has known most of them well - either from her three years on the city's first appointed council in the late 1960s or from more than 20 years' activity in local Democratic politics and civic causes.

Shackleton has been part of the voting majority on most major council measures: budgets and taxes, rent control and restrictions on condominium conversions, laws to discourage real estate speculation and to set aside 25 percent of city contracts for black and other minority-owned firms. She has often worked closely with at-large council member Marion Barry, although she has made no public endorsement in the race for mayor in which Barry is facing Mayor Washington and council chairman Sterling Tucker and several others.

Recently, though, Shackleton voted against two measures that Barry favored - allowing workers to continue collecting D.C. unemployment compensation even if they quit their jobs voluntarily, and an $18.5 million public jobs program from teen-agers. On two issues she has taken the most conspicuous public lead by criticizing the D.C. Department of Human Resources when it was headed by Joseph P. Yeldell, who is now under indictment for bribery and conspiracy, and by lobbying for limiting massage parlors and pornographic bookstores in residential areas.

In an interview recently, Shackleton said that one of her main concerns now is "overdevelopment that really destroys established neighborhoods and communities."

Shackleton's own home is just a short block off Wisconsin Avenue NW in Georgetown, and she has joined citizens' groups in opposing new stores, offices and apartments, not only in Georgetown, but also in Friendship Heights, around Tenley Circle and at McLean Gardens.

"I think there certainly should be development, but it should be placed in areas that are more appropriate, such as downtown," Shackleton said. "From my point of view, I support the residents. I don't think they should be driven out by intrusions in their communities."

Her opponent Joseph, who is 30, said he agrees with most of what Shackleton says and with most of her votes on the City Council. But he added, "She'll vote the right way, but she's not going to generate any new proposition's a matter of activism, of getting results and also having new ideas, and that's where I think we differ."

Born in Cleveland, Joseph went to Northwestern University, where he took an active part in demonstrations against the Vietnam War and registered as a conscientious objector to military service. At Georgetown Law School, from which he graduated in 1973, he became involved in health and environmental issues. He now makes a living as a lawyer - about $15,000 last year - chiefly by handling cases for nonprofit groups.

Several years ago, Joseph won a lawsuit forcing D.C. Transit Co. to cover abandoned trolley tracks. Recently, he has filed suits to limit noise from airplanes - his small house on Foxhall Road is in a flight path to National Airport, to ban smoking in most federal offices and to allow federal workers to campaign for local Democrats and Republicans in D.C. elections.

"Mrs. Shackleton has been given a chance for more than three years to deal with our main problem: air pollution, congestion and condominium conversion," Joseph said. "They've not been relieved but aggravated. We need something more."

Joseph said that the city's rent control program has been "ineffective," and has "forced landlords to convert to condominiums. "Right now, rent control is probably a necessary evil," he added, "but we should exempt luxury apartments."

To limit condominium conversions, which have spread rapidly in the ward despite current restrictions. Joseph favors a city law requiring that a majority of tenants in an apartment building approve conversion before it can take place.

Joseph also proposes a limit on property taxes, somewhat similar to California's Proposition 13. He said assessments should be rolled back to 1976 levels and future increases limited to 2 percent a year until houses are sold. The loss in revenue, Joseph said, could be made up partly by raiding taxed on parking and gasoline and also by trimming about 2 percent from the budgets of most city agencies.

Republican Cartner said that his main interest is stopping the rise in property taxes, although he is less specific than Joseph about how to do it.

Several weeks ago, the City Council, including Shackleton, voted to cut property tax. The vote, Cartner remarked, was "just an election year maneuver. They've had three and a half years to toy with this, and until now things have just gone up, up, up."

One new source of revenue, Cartner suggests, is a city lottery. Most important, Cartner added, is to cut city government spending by making the departments efficient and properly managed so that "city services can be run like a business."

Cartner, 46, was born in Washington and graduated from Eastern High School. He served in the Navy for four years, and has worked 11 years for IBM. He moved to his present home in American University Park in 1966. Cartner is married and has no children.

When he grew up, Cartner said, city services such as schools, trash collection and street cleaning were much better than they are now.

"I've watched this new government for the past few years," he said, "and I don't like what I see. The expenses of the District of Columbia are exorbitant for the size of the city. They're getting beyond the reach of the taxpayer."

Cartner said that when he noticed no other Republicans had filed in the race against Shackleton, he picked up nominating petitions about two weeks before the deadline and collected 150 signatures himself. He still has no campaign manager or treasurer and no firm idea of what amount he might spend.

Cartner is alone on the Republican ballot and, at this point, the only opposition could come from write-in votes. By law the names of all party candidates are required to appear on the primary ballot.

So far Joseph has raised about $1,000, half of it from his family, and said he hopes to spend $10,000. Shackleton said that she has raised about $4,000 already and probably won't need much more.

Last March, Shackleton was the first council member to announce that she would run for reelection. She filed petitions with 4,193 signatures, more than any candidate in any ward race. Her support committee of about 250 includes her two closest rivals in the 1974 primary - Kay McGarth and Mary Lela Sherburne - as well as a long list of other Democrats. Among them are such notables as former Supreme Court Justice Abe Fortas; Bess Abell, press secretary to Joan Mondale; lawyer Joseph Rauh, Jr.; and Robert B. Washington, Jr., chairman of the D.C. Democratic Central Committee.

Both Cartner and Joseph said they have compiled no lists of endorsements yet.