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This paper considers a population divided into two significantly-sized groups regarding the preferences its members have about a single public good. The public good equilibrium amount is that of the majority group in such a way that it is far from the Pareto-efficient one. This allows us to characterize a social loss function, which depends on the inter-group heterogeneity and the relative size of each group, parameters which also compound the degree of polarization. Our main conclusion is that, in general, higher levels of polarization do not imply higher social losses. This happens whenever the higher polarization is associated with higher inter-group heterogeneity, and the change in the amount of the public good in equilibrium implied is low enough.