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The matrix vote is used whenever a certain body - a parliament, an assembly, or an association at its AGM - wishes to elect a smaller number of persons to an equal number of perhaps very different posts, as is the case in an executive or a cabinet.

The matrix vote is proportional; it is based on a Quota Borda System, QBS, in which success depends on a quota of high preferences and/or a high score of points.  While QBS is a linear ballot, however, the matrix vote has a tabular format.  It allows the MP to cast his/her preferences, not only for those whom he/she wishes to see in cabinet, but also for the particular portfolio in which he/she wishes each of these nominees to serve.  In the example which follows, we will assume that the parliament has decided to elect a government of 6 ministers: a PM, a deputy, and four ministers.

All members of the parliament, except those who opt out, will be eligible for election to any ministerial post on the executive. In the election itself, then, all MPs state, in order of preference, which person should serve in which post.

Each MP considers whom he/she wishes to serve, and in what order of preference; then he/she decides in which ministerial post each should serve; and finally, he/she casts his vote, putting one name in each row, and one in each column.  An example is shown below.  The system is PR so, if party X has 40% of the seats in parliament, it can expect about 40% of the seats in government.  Thus any MP of party X would be well advised to cast 40% of his/her higher preferences for party colleagues, but to cast all of his/her lower preferences for those of other parties.  In other words, the matrix vote encourages cross-party voting, an essential ingredient of power-sharing.

The count proceeds as follows:

Stage I: all points awarded for each candidate in each post are totalled, as in a Modified Borda Count, MBC.

Stage II: the most popular candidates according to a QBS count are deemed elected but not yet appointed.

Stage III: a new matrix is drawn up, with both elected candidates and ministerial posts in order of popularity; again, this shows the individual person/post sums.

Stage IV: candidates are appointed in order of popularity according to the highest individual candidate/post sums in the matrix.

The outcome is bound to be a proportional, all-party, power-sharing, government of national unity, the collective consensus of all concerned.  It will specify just exactly who are the most popular candidates, and who will serve in which portfolio.

Full details are in Designing an All-Inclusive Democracy, Springer, 2007.

Last updated on March 1, 2010 by Deborda