He backed the full legalization of abortion and the repeal of laws that criminalized drug use, prostitution and homosexuality. He attacked campaign donation limits and assailed the Republican star Ronald Reagan as a hypocrite who represented “no change whatsoever from Jimmy Carter and the Democrats.”

It was 1980, and the candidate was David H. Koch, a 40-year-old bachelor living in a rent-stabilized apartment in New York City. Mr. Koch, the vice-presidential nominee for the Libertarian Party, and his older brother Charles, one of the party’s leading funders, were mounting a long-shot assault on the fracturing American political establishment.

The Kochs had invested hundreds of thousands of dollars in the burgeoning libertarian movement. In the waning days of the 1970s, in the wake of Watergate, Vietnam and a counterculture challenging traditional social mores, they set out to test just how many Americans would embrace what was then a radical brand of politics.

It was the first and only bid for high office by a Koch family member. But much of what occurred in that quixotic campaign shaped what the Kochs have become today — a formidable political and ideological force determined to remake American politics, driven by opposition to government power and hostility to restrictions on money in campaigns.