Here's a simple proposal for a top-two-like mechanism for primaries, copied from an answer of mine on Quora<http://www.quora.com/Politics-of-the-U-S/How-would-you-redesign-the-top-two-primary-system/answer/Jameson-Quinn> :
The simplest good solution would be "*Top 2+1 approval*". That is: - a primary using approval voting - the top two advance to the general election, plus the top vote-getter outside that party if they're both from the same party - then a general election using approval voting. Why is this good? In the US today, primaries serve two purposes. They help general-election voters focus their attention, so they can take a deeper look at the serious candidates and ignore the less-serious ones; and they help avoid problems with vote-splitting. But vote-splitting is scarcely a problem in a decent voting system; the only reason it's so important is that we use a stupid voting system<http://www.quora.com/Politics-of-the-U-S/What-is-the-root-problem-in-US-politics/answer/Jameson-Quinn>, plurality voting. By using approval voting in the general election, we could handle two strong candidates from the same party. Only the first purpose, focusing attention, would be needed. And the specifics of 2+1 make this even safer. Say that three candidates go to the general election: X1, X2, and Y, in descending order of approvals in the primary. The pathology to avoid is vote-splitting: a case where a majority of voters support party X, but Y wins because the X votes are split between X1 and X2. But there is a simple and palatable strategy for party-X voters to avoid that: since X1 was stronger in the first round, any party-X voter who can bear to approve X1 should do so, approving X2 only if they prefer them. As long as X1 gets approvals from everyone who approved X1 in the primary, plus all party-X voters who approved neither X1 nor X2, then the pathology is almost certainly impossible. And that still leaves room for the X2-only voters in the primary to continue to vote X2-only. So the winner will probably be X1, possibly X2 if they get enough party-Y votes to pass X1, and possibly Y if there was actually a majority of party-Y supporters that was masked by vote-splitting in the first round. Note that, although this system is built to allow only two parties in the general election, that does not mean it would perpetuate two-party domination. A leftist district could easily have Democrat(s) and Green in the general, and a conservative district could easily have Republican(s) and Libertarian. And if the "minor" party actually had more support, they would go on to win the seat. Certainly you could propose complex systems that could be better than this proposal in some ways. For instance, you could use a proportional representation system such as Bucklin Transferrable Voting (BTV) for the first round. But this proposal is a simple balance of the requirements: nonpartisan voting, a balance of candidates and parties in the general election, yet focused attention on a few strong candidates.
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