Speaking as a Californian, direct democracy via initiatives and referenda has basically allowed people to do an end run around the state legislature, and made it possible for the legislature to fob off difficult decisions onto the citizenry instead of doing their damn job. I wouldn't want to eliminate it, but I'd prefer that it be harder to get an initiative or referendum on the ballot, and make it impossible for the legislature to do so. Brexit is a shining example of everything that is wrong with direct democracy.

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