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³ Party identification may be useful if proposals have been referred to the people by the legislature.

⁴ Being closer to the median voter is not always beneficial. For example, protections for minorities may move policy away from what the median voter wants. This article assumes that so long as the courts protect minority rights, direct democracy ought to enact the will of the majority: failure to do so will as likely benefit powerful special interests as endangered minorities. In any case, the empirical results of this article stand or fall independently of their normative import.

⁵ Appendix A, published with the online version of this article by Cambridge University Press at doi:10.1017/S0032247409990520, contains formal proofs.

⁶ Arizona, Arkansas, California, Colorado, Idaho, Massachussetts, Michigan, Missouri, Nebraska, Nevada, North Dakota, Ohio, Utah. Mississippi uses this system unless the counter-initiative is sponsored by the legislature, in which case the Washington State system is used. Oklahoma uses this system but specifies that if both measures fail but one gets more than a third of votes cast, it is voted on alone at the next election. See the list of state constitutions at http://www.iandrinstitute.org, downloaded December 2005.

⁷ Supreme Court of California, Taxpayers to Limit Campaign Spending v. Fair Political Practices. Commission, 51 Cal.3d 744 [No. S012016. Supreme Court of California. Nov 1, 1990].

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²³ Proposals on the other side of the status quo from the median voter would never pass, and so could not threaten a proposal that might pass.

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²⁵ A formal proof is available on request. Proofs of Propositions 1 and 2 are given in Appendix A of the website version of this article published online by Cambridge University Press, 2010, doi:10.1017/S0032247409990520.

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²⁷ A model of individually rational voting demonstrating this is available from the author on request.

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³⁰ These regressions are summarized in Appendix B of the website version of this article published online by Cambridge University Press, 2010, doi:10.1017/S0032247409990520. Full results are available from the author on request.

³¹ No measure of voter information was available in 1990.

³² Lacy, and Niou, , ‘A Problem with Referendums’.Google Scholar