One of the few Libertarian candidates to be elected to a state legislature, Marrou served in the Alaska House of Representatives for one term, from 1985 to 1987. He was the party's vice-presidential nominee in the 1988 election, garnering 432,179 votes (0.5%) on a ticket with Ron Paul, and its presidential nominee in the 1992 election, receiving 291,627 votes (0.28%).