When a public problem is perceived to be poorly addressed by current policy, it is often the case that credible alternative policies are proposed to both the status quo’s left and right. Specially designed national surveys show that in circumstances like these, many Americans’ preferences are not single-peaked on the standard left-right dimension. Rather, they simply want the government to “do something” about the problem and therefore prefer both liberal and conservative policies to the moderate status quo. This produces individual and collective preferences that are double-peaked with respect to the left-right dimension. Double-peakedness is less prevalent on issues where no consensus exists regarding policy goals, and it increases when exogenous events raise the public’s concern about the seriousness of a policy problem.