Large-scale societies are impossible to perceive directly.Unsurprisingly, lay demographic estimates are wildlyinaccurate. How should we interpret these errors? Mostaccounts assume these errors are evidence of topic-specificbiases and prejudices. (e.g., “People overestimateimmigration because immigrants threaten the status quo.”)But this glosses over the distortions that are introducedwhenever underlying perceptions are translated into explicitnumerical estimates. For instance, estimates are typicallyhedged, or ‘rescaled,’ toward an expected value — aperfectly rational strategy when information is uncertain.We show that uncertainty-based rescaling accounts for mosterror in individual demographic estimates. Residual errorswere not even always in the same direction; populations thatappeared to have been over-estimated (e.g., Asian-Americans) now appear to be under-estimated. The amountof rescaling engaged in by an individual was proportional totheir uncertainty (about politics or about numbers).Perceptions of society are surprisingly good; thepsychophysics of estimation gets in the way.