Right‐wing authoritarianism (RWA) and social dominance orientation (SDO) are widely used constructs in research on social and political attitudes. This study examined their hierarchical and correlative structure (across sexes, generations and rater perspectives), as well as how genetic and environmental factors may contribute to individual differences in them (using different rater perspectives and nuclear twin family data). We found a substantive common aspect (beyond shared artificial variance arising from socially desirable responding) underlying both RWA and SDO: aggression against subordinate groups. We discussed how this aspect could help to explain the commonly reported correlation between the two concepts in Western countries. Estimates of genetic and environmental components in RWA and SDO based on self‐reports were quite comparable with those based on peer reports. When controlling for error variance and taking assortative mating into account, individual differences in RWA were primarily due to genetic contributions including genotype–environment correlation, whereas variance in SDO was largely attributable to environmental sources shared and not shared by twins. The findings are discussed in terms of the utility of RWA and SDO as basic constructs to describe individual differences in social attitudes and with respect to the different patterns of genetic and environmental influences that underlie them. Copyright © 2016 European Association of Personality Psychology