FAQ on > Voting Systems > A Matrix Vote?
The matrix vote is used whenever a certain body - a parliament, an assembly, or any business, trades union, political party or community 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.
If it's (an Irish) parliamentary election, the ballot paper would look like this, and the instructions like this. Or if it was an Executive election in the Northern Ireland Assembly, it would be based on these lines. And if it's an AGM, then the ballot paper is like this, and again, the instructions like this.
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. In the case of a parliament/assembly electing an all-party coalition cabinet, it allows the MP to cast his/her preferences, not only for those whom he/she wants 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.
| Portfolio | Preferences | |||||
| 1st | 2nd | 3rd | 4th | 5th | 6th | |
| PM | ||||||
| Deputy PM | ||||||
| Minister of A | ||||||
| Minister of B | ||||||
| Minister of C | ||||||
| Minister of D | ||||||
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 his/her party colleagues, but to cast any lower preferences for MPs of other parties. In other words, the matrix vote encourages cross-party voting, an essential ingredient of power-sharing.
| Portfolio | Preferences | |||||
| 1st | 2nd | 3rd | 4th | 5th | 6th | |
| PM | Freda | |||||
| Deputy PM | Jill | |||||
| Minister of A | Joe | |||||
| Minister of B | Fred | |||||
| Minister of C | Phil | |||||
| Minister of D | Jo | |||||
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: elected candidates are appointed to ministerial posts in order of popularity, i.e., according to the individual person/post sums.
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. At best, it will ensure that, individually, each cabinet member is the best person for that job, (albeit in the consensus of parliament); and collectively, that every party is represented in due proportion.
Full details are in Designing an All-Inclusive Democracy, Springer, 2007.
Last updated on August 9, 2021 by Deborda
