During my lifetime, Third Party candidates (for national office) have at best been spoilers (e.g., Perot in 1992; Nader in 2000).
But if a third party -- Green Party, Libertarian Party, or what have you -- took a significant number of seats in the House and/or Senate, so that no party had a majority, and they all had comparable levels of clout, how would that change politics in America? Would it be more or less likely that significant policy changes could be effected?