Fink was elected to the Alaska House of Representatives in 1966, and became Speaker of the House in 1973. In 1975, he resigned in protest of a new law that would have required him to release a list of his insurance clients.[3]
In 1987, Fink was elected Mayor of Anchorage in the wake of a dramatic drop in the price of oil, which devastated the local economy. During his term in office, he advocated the sale of ATU, the municipal telephone utility.[5] He received national attention for his stance on gay rights when he vetoed a 1993 municipal ordinance that would protect city employees from discrimination on the basis of sexual orientation.[6] The same year, he called for the cancellation of funding for Pomo Afro Homos, a local theater group that included works with homosexual themes in their repertoire.[7] In both cases, he was overridden by the Anchorage Assembly. In 1997, after sitting out one term, Fink returned to politics to mount an unsuccessful challenge to incumbent Republican mayor Rick Mystrom.