I believe the solution to the problems in Congress is to outlaw the gerrymandering of congressional election districts that occurs every 10 years after each census update. To ensure their re-election, the politicians redraw the district boundaries to include the most politically active members of the party then holding that seat.
The result is the representatives in Washington maintain their "pure red" or "Tea Party red" or "pure blue" ideological stance because they reflect the ideology of the majority of their constituents, ensuring their re-election, even when such a stance is detrimental to the U.S. as a whole.
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The Senate Democrats and Republicans may be able to come up with a compromise regarding the government shutdown and debt ceiling because each represents a whole state in which there is a variety of viewpoints. We don't redraw the state boundaries to conform to the census; we shouldn't redraw the congressional boundaries either. We should carve out square or rectangular districts, representing about equal numbers of people, without regard to voter registration or voting patterns. Representatives elected from such districts would be of more "moderate" views since they would have to appeal to the majority of a variety of voters with, probably, different viewpoints.
Jean M. Alberti