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A blog: " De Borda abroad."  From Belfast to Beijing and beyond... and back. Starting in Vienna with the TEDx talk, I go by bus and/or train for more debates in Belgrade, Sarajevo, Istanbul, Tbilisi, Yerevan and Tehran, before flying - sorry about that - to Urumqi in Xīnjiāng, followed by more debates in Beijing, Tianjin, Hong Kong and Taiwan... but not in Pyongyang. Then back via Mongolia (where I was an election observer last year) and Moscow (where I worked in the '80s).

I have my little fold-up Brompton with me - surely the best way of exploring any new city! So I fly hardly at all; I go by train, boat or bus if possible, and then cycle wherever in each new venue; and all with just one plastic water bottle... or that was the intention!

The story is on:  https://debordaabroad.wordpress.com/2017/09/07/de-borda-abroad/


Inclusive voting app 



(Currently under re-construction.)


The Hospital for Incurable Protestants

The Mémoire of a Collapsed Catholic

 This is the story of a pacifist in a conflict zone, in Northern Ireland and the Balkans.  Only in e-format, but only £5.15.  Available from Amazon.



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The de Borda Institute aims to promote the use of inclusive voting procedures on all contentious questions of social choice.

This applies specifically to decision-making, be it for the electorate in regional/national polls, for their elected representatives in councils and parliaments, for members of a local community group, for members of a company board, for members of a co-operative, and so on.




The director alongside the statue of Jean-Charles de Borda, capitaine et savant, in l’École Navale in Brest, 24.9.2010. Photo by Gwenaelle Bichelot. 

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Welcome to the home page of the de Borda Institute, a Northern Ireland-based international organisation (an NGO) which aims to promote the use of inclusive voting procedures on all contentious questions of social choice. For more information use the menu options above or feel free to contact the organisation's headquarters. If you want to check the meaning of any of the terms used, then by all means have a look at this glossary.

As shown in these attachments, there are many voting procedures for use in decision-making and even more electoral systems.  This is because, in decision-making, there is usually only one outcome; but with some electoral systems, as in any proportional ones, there can be several winners.  Sometimes, for any one voters' profile - that is, the set of all their preferences - the outcome of any count may well depend on the voting procedure used.  In this very simple example of a few voters voting on just four options, and in these two hypothetical examples on five, (word document) or (power-point) in which a few cast their preferences on five options, the profiles are analysed according to different methodologies, and the winner could be any one of all the options.  Yet all of these methodologies are called democratic!  Extraordinary!

FAQ on > Voting Systems > What is a Matrix Vote?

Search the FAQ for entries containing:

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
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 25, 2017 by Deborda