Will the Libertarian Party ever win a seat in the House or Senate?

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Libertarian demographics rarely find themselves packed in a single geographic area, especially one that would affect the very large  house districts. Even well established classical liberals in other parties very rarely win single member seats, and mostly rely on lists and preference deals. There are (as far as I know) three parties which rely on the libertarian moniker (In Australia, Costa Rica and Denmark) and all of them rely on PR.

the Green Party has a much higher likelihood of winning single member seats, because their demographics pack together. And indeed they have managed to win SM seats across the rest of the Anglosphere, and Germany; after intensive and long term campaigning. (Like really long-term in some cases)

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I could see Alaska going for a Libertarian House member if the Dems didn't contest a seat, the Libertarian ran a great campaign and had lots of money, and Don Young falls to a huge corruption scandal.

Alaska? The state entirely dependent on state handouts and subsidies? The state whose main desire in a federal politician someone who says to the Treasury "gib money pls" as often as possible? The state who constantly confounds Washington conventional wisdom by voting for economic populist items? That Alaska?

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Yes, but I feel there is a natural ceiling in that state. Too many natives, a large federal government presence, too many small rural areas that rely on subsidies. Which is a problem in general for rural libertarians. On paper, people think that people who live far away from the government wouldn't care for it, but for the most part rural areas do not want the full Libertarian treatment. I'm not surprised Alaska has a high Lib. vote, but that seems more likely a protest against the dominant Republican Party which is known to be fairly corrupt.

Rural areas probably could have a seperate party catering to them, but it certainly wouldn't resemble the libertarians.

Where the Danish libertarians (I don't have much info on Costa Rican demographics) flourish is in opposing environments. Young, urban, single and working in the high income private sector. It's a specific demographic and the issue for the libertarians is that these guys are (like the lone rural libertarians) drowned by left-leaning neighbours in single member demographics.