An absensce of outrage dominated voter sentiment this week as incumbent mayors in Los Angeles and Madison, Wis., easily turned back challengers who had conducted emotional campaigns against them.

In Los Angeles a Democratic state senator who had professional assistance from Republicans had hoped to force Mayor Tom Bradley into a run-off. But Bradley, a black in a city where blacks provide less than a sixth of the vote, won 60 per cent of the vote in a 12-candidate field.

His main challenger. Alan Robbins, received 27 per cent, far less than his expectations. Robbins had attempted to exploit fears of court-ordered crosstown school busing in Los Angeles, which is under a state Supreme Court school desegregation order.

In Madison, incumbent Mayor Paul Soglin won more than 60 per cent of the vote against Republican alderman Nino Amato, 25, who contended that Soglin's reputation as a "radical" who had twice traveled to Cuba damaged the city's reputation.

And in St. Louis, where there was no incumbent, Democratic State Sen. James Conway won nearly two-thirds of the vote against a Republican challenger and a black write-in campaign waged by Rep. William Clay. Conway, a businessman, had broad-based support from business, organized labor and municipal leaders.

In none of these cities did the campaigns of the challengers catch fire. Bradley was portrayed as being insensitiv eto the fears of white voters in the San Fernando Valley, who are concerned that their children may be bused 30 miles away to school. Conway was depicted 35 being insufficiently sensitive to the needs of the black community.

When the votes were counted, however, Bradley had carried the San Fernando Valley and Conway most of the black section of St. Louis.

Voter turnout was low, slightly more than 40 per cent in both Los Angeles and St. Louis. This also would seem to indicate that the voters are not in rebillious mood.

Bradley analyzed the election as indicating that race is not an important issue for most Los Angeles voters.

"I'm delighted with the outcome," he said. "It reaffirms what the people said in 1973, that they wanted to elect a mayor on the basis of qualifications, competence of programs and ideas."

The 59-year-old Bradley mocked Robbins' campaign by blowing on a "rape whistle," which Robbins distributed by the thousands to emphasize his role in drafting rape legislation in Sacramento.

But the idea that Bradley, former police lieutenant, was in any way soft on crime never appealed to Los Angeles voters. Bradley defused the busing issue by saying that he opposed "massive crosstown busing" but would carry out any court order.

Actually, the Los Angeles mayor has little authority to deal with crime or none at all to deal with busing. Education matters are controlled by an independently elected school board and the mayor, under the city's non-partisan city council form of government, has little independent power.

Within the severe limitations of the office, Bradley has emerged as a quiet and popular public official who has wide credence for a claim he made yesterday that "we tried to serve all areas of the city equally and justly." tr for add four.

Bradley's victory yesterday established him as a potential statewide political candidate. Two blacks in California already hold statewide office.

In another mayoralty election Tuesday, write-in candidate Al Veys, a grocer, pulled an upset in Omaha and will face city council member Betty Abbott in a May 10 runoff.

A May 17 runoff congressional election is scheduled in Washington State's 7th district to fill the seat vacated by Brock Adams, now secretary of transportation in the Carter administration.

Environmentalist Marvin Durning won the Democratic nomination in a field of 17 candidates. State Sen. Jack Cunningham won the Republican nomination against seven opponents.

Atlanta City Council President Wyche Fowler won the Georgia 5th Congressional District seat, succeeding Andrew Young, the U.S. ammbassador to the United Nations. Hewas immediately sworn in and flew to Washington in time to join the House for its 10-day Easter recess.

Fowler, who is white, defeated black civil rights activist John R. Lewis in an election where voting divided largely along racial lines. Fowler, who won 62 per cent of the vote, carried the white suburbs, while Lewis ran ahead in the largely black inner city.