One of twelve Libertarians to be elected to a state legislature, Marrou served in the Alaska House of Representatives for one term, from 1984 to 1986.
He was the party's vice-presidential nominee in the 1988 election; on the ballot in 46 states and the District of Columbia, U.S. Congressman Ron Paul and Marrou placed third in the popular vote with 432,179 votes (0.5%), behind Bush-Quayle and Dukakis-Bentsen. Paul and Marrou were kept off the ballot in Missouri, and received votes there only when written in, due to what the St. Louis Post-Dispatch called a "technicality".
In the 1992 election, Marrou was the party's presidential nominee, receiving 291,627 votes (0.28%).