Policymakers seeking to limit climate change have many policy options to choose from, but in general, those popular with the public will be easier to enact and sustain. What then makes policies more or less popular? We propose that perceptions of policies’ consequences shape their relative popularity, and those perceptions are widely shared. We tested this theory in a study of 54 climate policies across 75 societies in all world regions (n = 14,053). Societies differ in overall support, yet they show close agreement about policies’ consequences, most importantly whether they are effective, fair, and low-cost. Together these perceived consequences predict which policies are globally popular (predictive R2 = 0.78 in leave-one-out cross-validation). An embedded experiment supports a causal interpretation: expert statements shift support to the extent that they shift perceived consequences. The experiment also reveals a communication dilemma: negative statements about consequences reduce support everywhere, whereas positive statements backfire in societies where institutional quality is low.