A way to overcome bickering and polarization?

Do you live in a jurisdiction dominated by one political party? Vince Carroll writes a provocative post in today's Denver Post in which he points out that one-third of Colorado's voters are not members of either the Democrat or Republican parties. Yet,

to participate in June's primary, which determines who appears on November's ballot, they first have to register as a Democrat or Republican.

Carroll writes that California has adopted a primary system in which all candidates run against each other, then the top two vote-getters run against each other in the fall election.

Would that be a better idea?