Deschouwer and Van Parijs (2009) argue that the political philosophy underlying their proposal for a federal electoral district in Belgium (known as the Pavia Group proposal) is based on the belief that intelligent institutional engineering can provide concrete solutions for linguistically heterogeneous polities such as Belgium or the European Union. The proposal consists of creating a single federal electoral district in Belgium, from which 15 of the 150 federal parliamentarians would be elected according to a proportional representation (PR) formula. Every citizen, thus, could cast two votes: one within his/her electoral district (as today), and one within the single federal district. The system of open party lists would allow citizens to vote not only for a party but also for single candidates from the same party list. Its authors hope that this proposal would provide incentives to politicians and the media to cross linguistic boundaries. For their part, voters would have an incentive to vote for candidates from a language group other than their own. If implemented, this proposal would clearly move Belgium away from the present consociational model (Lijphart 2004), and towards the logic of the so-called “integrative school” (Horowitz 2002). In this paper, I will first briefly evaluate the Pavia Group proposal by drawing attention to the disadvantages of one of its features, the reserved seats for language groups: (a) the legitimacy problem, and (b) the problem of non-territorial quotas. I will then illustrate this problem by discussing two examples from Switzerland in which a single electoral district has been either implemented or envisaged. Finally, I will propose three amendments to the proposal.