(above an example of possible Matrix ballot paper used to determine cabinet formation)

By Peter Emerson of the the De Borda institute

Because of Covid-19 we need not only to “totally re-imagine economics,” (to quote the Irish Times -Sat 28th), but also to “totally re-imagine politics.” In a recent Irish Times edition, Prof. Sam McClonkey further writes, “We can use consensus promoting tools such as preferendums and matrix voting.”

But how does the Matrix system work that Prof. McClonkey mentioned?

THE MATRIX VOTE

1          THE PROCESS

The procedure is as follows:

1. Each Party publishes its proposals for cabinet, naming the 15^[1] ministerial posts and perhaps including procedures like rotating Taoisigh.
2. Next, all TDs cast their preferences on this list, to see which option has the highest average preference. This preference points voting is called a Modified Borda Count, MBC (as used by the Greens when electing the NEC, for example).

• Parties may then declare their nominees for the named ministries, and the bigger ones will almost certainly wish to do so. And finally,

1. Maybe two or three days later, allowing time for Party and Independent TDs to conduct negotiations, etc, the TDs use a matrix vote, electronically, (but with a paper back-up).

2          THE VOTE

2.1       The d’Hondt process in Stormont chooses WHO but not WHAT.

2.2       With a matrix vote, the TDs may choose, in their order of preference, both WHO and WHAT, i.e., who is to do what job.  So the ballot paper has two-dimensions.  It looks like this:

Table I          The Ballot

2.3       Each TD chooses (up to) 15 nominees; lists them in order of preference in the shaded column; and then prioritises up to three ministries in which he/she would like each of these nominees to serve: P₁, P₂ and P₃.  A full valid vote will have a P₁ in each column and a P₁ in each row – they are shown below in green tint; (there are no requirements for how many P₂ and P₃ priorities are in each row/column).

2.4       In voting, therefore, a TD might well wish to award his/her top preferences with three or at least two priorities.  But there’s not much point in giving a P₂ or P₃ to a 15^th preference nominee.

Table 2          A Completed Ballot

2.5       The count first identifies the 15 most popular TDs, initially on a PR-STV analysis of each candidate’s 1^st preferences, (their P₁’s).  Then, in an MBC analysis, again initially on the basis of the candidates’ P₁ scores, we examine the matrix to see which of these 15 should serve in which post.  Doubtless, all three groups of FF, SF and FG TDs will probably want (or be whipped) to give a top priority, P₁, for one of theirs to be the Taoiseach; they may; but if a TD’s nominee doesn’t win the P₁ post, the preference goes to the TD’s P₂ nominee… and the count continues from the top score in the matrix, downwards.

2.6       In the event of a tie for any one posting, the appointment is given to the more popular candidate; in the highly unlikely event that there is still a tie, precedence is given to the more ‘popular’ ministry, (doubtless, for example, more P₁’s will be given to the post of Taoiseach and the Ministry of Finance than, say, to the Department of Sport).

2.7       The matrix vote is PR.  So a party with about 25% of the Dáil seats will get about 25% of the 15 seats in Cabinet: at least 3, possibly 4.  Indeed, because the matrix vote encourages each party to nominate (a) only as many candidates as it thinks it can get elected – in this regard, it is very similar to PR-STV –  and (b) only for those posts where it has a decent chance, the whole process becomes quite manageable.  Furthermore, because the MBC (on which the matrix vote is based) encourages every TD to submit a full ballot of all 15 preferences, the procedure incentivises every TD to cross the party divide.  This, we would argue, is a prerequisite of good power-sharing.

2.8       The whole process of electing a government could be done in just a few days: one day for deciding on the ministries – how many and which ones; one for the possible nominations; two days for hustings and negotiations; and one day for the matrix vote.

2.9       It is a proven technology, although not yet used by any national government.  Suffice to say here that whenever it has been used, in Belfast, Dublin, Maynooth, Berlin, Vienna and Tianjin, it has always worked: the outcome has always been proportional, and most of those chosen were generally regarded as being suitable for the subsequent appointment.

^[1]           For the moment at least, let all concerned accept the constitutional limit of 15.  In the current emergency, a different number or distribution of portfolios might be chosen.

Peter Emerson of the De Borda Institute