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Based on reference group and cognitive bias considerations, we advance a theory, explicated via a computer simulation, to explain (1) people's perceptions of how equalitarian the class system is, (2) where people place themselves in the class system, (3) where people place others' occupations, and (4) people's estimates of the pay of different occupations. Using a new set of diagrammatic and verbal questions on class, we test our hypotheses on large, representative national samples in Australia (N = 6,177) and Hungary (N = 2,606). A full-information maximum-likelihood analysis strongly supports the hypotheses.