How to resolve the ongoing government formation impasse-how about a Matrix Vote on it?

Screenshot 2020-04-07 at 21.14.25

(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.”

Both words are ’de Borda’!  However, both require a little explanation.
‘Preferendum’ was coined at a meeting of the European Greens in Dover in 1984; (yes, I’m getting older); the matrix vote, my invention, dates from 1978; (and older).  Prototypes of both voting procedures were used at the New Ireland Group’s People’s Convention of 1986: over 200 participants, everything from SF to Unionist, (no DUP but) UUP, UDA and even Ulster Clubs!)-8 years before the cease-fire!  And a consensus was found!
(i) We prefer to call Preferenda the Modified Borda Count MBC., There are however, umpteen ways a multi-option ballot may be conducted and counted, and so the word means different things to different people; so we use either “Borda preferendum” or, better still, MBC (and not BC which, of course, is subject to Arrovian vulnerabilities like irrelevant alternatives and things).
{In elections, the Quota Borda System QBS is the best.  But PR-STV is also very good, so we’ll leave QBS till later.  Suffice to say that QBS was invented by Professor Sir Michael Dummett and first used by de Borda for Mediation in NI.
(ii) I could have called the Matrix vote the Emerson vote, however,  I felt at the time that the name ‘matrix vote’ would give it a greater chance of being considered.  Basically, the MBC is more accurate — and therefore more democratic  —  than any binary vote.  So it should be the democratic norm.  But the MBC is also non-majoritarian — at best, it identifies the option with the highest average preference… and of course, an average involves everyone who votes, not just a majority of them.  So, with the MBC, [binary] majority rule goes out the window!  Instead, every democracy could enjoy all-party power-sharing coalition governments.  And no longer would the world have to bear the consequences of so much power being given to just single individuals, be they Trump, Bolsonaro, Netanyahu, Modi, Erdogan… or Johnson.   So let’s have ‘preferential majority rule’ where governance is of the all-party coalition variety, and policy decisions are subject to MBC voting.


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



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


The Cabinet   Minister of…. (the departments chosen in 2.ii above).
Prefs Name PM A B C D E F G H I J K L M N


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 15th preference nominee.


Table 2          A Completed Ballot

The Cabinet   Minister of…. (the departments chosen in 2.ii above).
Prefs Name PM A B C D E F G H I J K L M N
1st Ms i         P2       P1       P3    
2nd Mr t       P1 P2         P3          
…. …. P1   P2         P3              
…. ….             P1   P2            
15th Ms p                       P1      



2.5       The count first identifies the 15 most popular TDs, initially on a PR-STV analysis of each candidate’s 1st 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

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