The three Libertarian U.S. House nominees in the nation (in races with both a Republican and a Democrat) who received the highest shares of the vote in 2012 were in Arizona, Mississippi and Kansas. Powell Gammill, in the Arizona 9th district, polled 6.64% (16,620 votes). Ron Williams, in the Mississippi 4th district, polled 6.30% (17,982 votes). He is an experienced campaigner and had run for Governor in the 2011 Republican primary. In Kansas, Libertarian nominee Thomas Jefferson, running in the 4th district, polled 6.20% of the vote (16,058 votes).
Kansas also had the strongest Libertarian showing for a U.S. House race that lacked one major party. As noted earlier, in the Kansas 3rd district, Libertarian Joel Balam polled 31.55% (92,675 votes), the highest showing ever for a Libertarian in any U.S. House race. He almost carried Wyandotte County, which contains Kansas City. Thanks to Krystyna Lesiak for catching the original error in this post; the error was the failure to mention the Arizona race.