Status inequality and social stratification cause much social ill. So why do status hierarchies pervade societies and social groups? One possible explanation lies in the individual desire for status. A recent review found the desire for status is a fundamental human motive – people seek to receive respect and deference from others. We found converging evidence that this desire is competitive in nature; people not only desire to be respected, they desire to be accorded more respect and deference than others. In a laboratory experiment, participants (n = 226) felt better when they alone had high status than when everyone had equal status. In a national survey, participants (n = 715) preferred having higher status than others, even if it meant that everyone had lower status on an absolute level. Status hierarchies might be ubiquitous in part because people are unsatisfied with egalitarianism and pursue positions of superior (and unequal) status.