After Alaska greatly increased its revenue from the development of oil, Randolph advocated the repeal of the state income tax.

The effort was successful, with Alaska being one of only two states where residents pay neither an income nor a sales tax—the other being New Hampshire.

He moved to Fairbanks in 1964 and founded a State Farm Insurance agency, becoming its top sales agent in the nation in 1965.

[2] Running as a Libertarian in 1978 Randolph finished fifth out of 17 candidates, taking one of the six State House seats in District 20.

[3] He was re-elected in 1980, coming in first out of 18 candidates, with his fellow Libertarian Ken Fanning taking 4th and giving the Alaska LP two of the six seats in District 20.