The article examines demands for gender parity in political representation and the ways in which they respond to the frequent charges of essentialism implicit to such demands. The first part addresses arguments that have tried to avoid evoking the difference between men and women by simply appealing to justice between sexes. It will be argued that, besides the inability to stay within universalistic discourse, they have failed to account for the normative expectations of democratic process as well. The second part explores the ways in which different normative models of democracy – liberal, republican and deliberative – have shaped the arguments for gender parity and how these relate to the issue of women’s difference. Although arguments made on the premises of each model assume the difference between men and women, they have, to the various degree, proven to be successful in avoiding the trap of essentialism.