Wollman was the chairman of the
Spink County Democratic Party. He ran for the
South Dakota State Senate in 1966, but lost to
Herb Heidepreim. Wollman ran again in 1968 and won a rematch against Heidepreim. He was re-elected in 1970. After the 1970 election, he was elected as
minority leader. He was first elected
lieutenant governor in 1974, on a ticket with
Governor Richard F. Kneip. In 1978, Wollman ran for the Democratic nomination for governor. He lost the primary election to State Senator
Roger D. McKellips on June 8. Governor Kneip resigned to accept an appointment as
United States Ambassador to Singapore, and Wollman succeeded him as governor on July 24, 1978. Wollman was sworn in as governor by his brother,
Roger Leland Wollman, who was serving at the time as Chief Justice of the
South Dakota Supreme Court. Wollman served as governor until January 1, 1979. While he was in office, he worked to speed the repeal of the state property tax and increase the budget for higher education. He was succeeded by
Republican Bill Janklow (who defeated McKellips in the general election). Wollman remained interested in politics, saying that he did not want to run for governor in 1982, but was looking into running for the
United States Senate in the
1984 election. He decided instead to run for his old seat in the state senate in 1984 with an eye on running for governor in the
1986 election. He lost to
Mary McClure, the incumbent Republican, in the election. ==Personal life and death==