He was the leader of The Liberal Party from 1982 to 1986 and again from 1992 to 1996. From 1970 to 1972 he was the leader of the party's youth organization (Unge Venstre).
Despite becoming an experienced Minister of Justice, Dørum himself had a run-in with the law in his youth. He participated in a non-violent civil disobedience protest in Mardøla, Norway in 1970. Protesting against the government turning several waterfalls into powerplants, he was carried away by police together with other prominent protestors like philosopher Arne Næss. This marked the first time civil disobedience was used to protect the environment.
Dørum is known as a very grounded person, and unlike most politicians his age he does not take himself very seriously. For decades he has been a huge fan of The Lord of the Rings books and made headlines when he showed up for the premiere of The Lord of the Rings: The Return of the King wearing a hobbits robe, much to the amusement of its star Viggo Mortensen. He later donned the same outfit again in an outdoor Lord of the Rings concert in Frognerparken in Oslo in 2005.
He lives in Oslo, is married, and has two children.