Among those advocating the use of particular electoral mechanisms to reduce the prospects for conflict and strengthen democracy in societies that are deeply divided in ethnic or religious terms, there are two main approaches, one associated with Arend Lijphart, one with Donald Horowitz. Lijphart advocates using electoral rules such as list PR that strengthen the power of ethnically or religiously defined political elites in the context of implementing power-sharing mechanisms at the elite level that institutionalize norms such as proportional allocation and mutual veto across ethnies. Horowitz advocates using a preferential voting method, the alternative vote (AV), within constituencies that are multi-ethnic in character, to allow for voting across ethnic lines and to increase the likelihood of electing candidates whose perceived obligations are wider than their own ethnic group and/or to foster the creation of coalitions that are multi-ethnic in character. The main focus of this essay is the reformulation of Horowitz's approach in terms of ideas adapted from the neo-Downsian literature on median voter models. We illustrate Horowitz's approach with illustrations inspired by the predominantly biracial political competition in Fiji between native Fijians and those of Indian descent.