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There are many instances when a group of people might want to choose a committee, a fixed number of individuals to undertake a particular collective function. At their AGM or annual conference, residents in a community group, shareholders of a limited company, members of a trades union, and those of a political party, may all want to elect an executive: one person to be chair, another secretary, a third treasurer, etc. All these posts require different talents and all the individual office bearers undertake necessary but separate functions for the successful operation of that committee. In like manner, a parliament may choose to elect a government of national unity (GNU). The only voting procedure so far devised by which a given electorate—those concerned at an AGM or members of parliament (MPs)—may elect, not only those whom they wish to be in cabinet, but also the ministerial posts in which each of those chosen will then serve, is the matrix vote. This paper describes 1) an experiment held at the Political Studies Association of Ireland (PSAI), undergraduate conference in Dublin on 23rd June 2012 inwhich participants, role playing as members of the Irish parliament, elected a GNU; and 2) the matrix vote methodology, such that others may also employ this voting system. An obvious instance would be for the election of an all-party power-sharing executive in a post-conflict zone.