1. In mediation, the questions are open; In politics, they are closed! The de Borda Institute www.deborda.org

2. A SIMPLE MATRIX VOTE 1 st pref 2 nd pref 3 rd pref 4 th pref 5 th pref Centre Forward Left Wing Right Wing Back Goalie

3. THE MATRIX VOTE

4. Initials of candidates in order of preference 1 st 2 nd 3 rd 4 th 5 th 6 th 7 th 8 th 9 th 10 th Cabinet: Taoiseach Department of Finance Department of Foreign Affairs and Trade Department of Education and Skills Department of Jobs, Enterprise and Innovation Department of Defence Department of Justice and Equality Department of Health Department of Environment, Community, Local Govt Department of Arts Heritage and the Gaeltacht THE BALLOT PAPER

5. FORMING A GOVERNMENT Ireland0 UK5 days Iraq249 days Belgium541 days

6. THE BELFAST AGREEMENT “…the politics of Executive formation… has entrenched, encouraged, and even rewarded those who pursue… sectarian interests…” Rupert Taylor The injustice of consociationalism. In Consociational Theory.

7. DEMOCRATIC DICTATORS

8. THE QUESTION IS THE ANSWER

9. SWITZERLAND Collective presidency: the Swiss Federal Council Zauberformal 2:2:2:1

10. REPRESENTATION Government Parliament The People

11. DECISION-MAKING BC = Borda count MBC = modified Borda count

12. PLURALISM There are two defensible procedures for aggregating votes: the Condorcet rule and the Borda rule. The Condorcet rule selects the option (if one exists) that beats each other option in exhaustive pairwise comparisons. The Borda rule selects the option that on average stands highest in the voters’ rankings. Professor Iain McLean

13. Borda count A full vote=n, n-1 … 2, 1 Modified Borda Count A full vote = n, n-1 … 2, 1 A partial vote=m, m-1 … 2, 1

14. PARTIAL VOTING IN AN MBC t. He who votes for 1 option gives his favourite 1 pt.

15. PARTIAL VOTING IN AN MBC He who votes for 1 option gives his favourite 1 pt. She who votes for 2 options gives her favourite 2 pts (and her 2 nd choice 1 pt).

16. PARTIAL VOTING IN AN MBC He who votes for 1 option gives his favourite 1 pt. She who votes for 2 options gives her favourite 2 pts (and her 2 nd choice 1 pt). He who votes for 3 options gives his favourite 3 pts, (his 2 nd choice 2 pts and his 3 rd choice 1 pt).

17. PARTIAL VOTING IN AN MBC If you vote for: Number of options 12345 your 1 ST pref gets: 1 pt2pts3 pts4 pts5 pts your 2 ND pref gets: 1 pt2pts3 pts4 pts your 3 RD pref gets: 1 pt2pts3 pts your 4 TH pref gets: 1 pt2 pts your 5 TH pref gets: 1 pt

18. Initials of candidates in order of preference 1 st 2 nd 3 rd 4 th 5 th 6 th 7 th 8 th 9 th 10 th Cabinet: Taoiseach Department of Finance Department of Foreign Affairs and Trade Department of Education and Skills Department of Jobs, Enterprise and Innovation Department of Defence Department of Justice and Equality Department of Health Department of Environment, Community, Local Govt Department of Arts Heritage and the Gaeltacht THE BALLOT PAPER

19. Initials of candidates in order of preference 1 st 2 nd 3 rd 4 th 5 th 6 th 7 th 8 th 9 th 10 th Cabinet: JEANJEAN JIMJIM JANEJANE JOEJOE JOANJOAN JANJAN JAMESJAMES JOHNJOHN JOJO JILLJILL Taoiseach Department of Finance Department of Foreign Affairs and Trade Department of Education and Skills Department of Jobs, Enterprise and Innovation Department of Defence Department of Justice and Equality Department of Health Department of Environment, Community, Local Govt Department of Arts Heritage and the Gaeltacht THE BALLOT PAPER

20. Initials of candidates in order of preference 1 st 2 nd 3 rd 4 th 5 th 6 th 7 th 8 th 9 th 10 th Cabinet: JEANJEAN JIMJIM JANEJANE JOEJOE JOANJOAN JANJAN JAMESJAMES JOHNJOHN JOJO JILLJILL Taoiseach A Department of Finance A Department of Foreign Affairs and Trade A Department of Education and Skills A Department of Jobs, Enterprise and Innovation A Department of Defence A Department of Justice and Equality A Department of Health A Department of Environment, Community, Local Govt A Department of Arts Heritage and the GaeltachtA THE BALLOT PAPER

21. A MATRIX VOTE COUNT 1An election to choose the cabinet. Quota Borda System (QBS): the ten candidates with the highest number of top preferences and/or points. 2An election to appoint this cabinet to their various ministries. Modified Borda Count (MBC): ministers are appointed on the basis of the highest MBC sums for whatever ministry.

22. Initials of candidates in order of preference 1 st 2 nd 3 rd 4 th 5 th 6 th 7 th 8 th 9 th 10 th Cabinet: FDTPJMPOIMFSALRMCTOH Taoiseach 100 Department of Finance 90 Department of Foreign Affairs and Trade 2080 Department of Education and Skills 201030 Department of Jobs, Enterprise and Innovation 2010 Department of Defence 3050 Department of Justice and Equality 1040 Department of Health 1050 Department of Environment, Community, Local Govt 1020 Department of Arts Heritage and the Gaeltacht70 THE BALLOT PAPER

23. Initials of candidates in order of preference 1 st 2 nd 3 rd 4 th 5 th 6 th 7 th 8 th 9 th 10 th Cabinet: JEANJEAN JIMJIM JANEJANE JOEJOE JOANJOAN JANJAN JAMESJAMES JOHNJOHN JOJO JILLJILL Taoiseach A Department of Finance CA Department of Foreign Affairs and Trade BA Department of Education and Skills CBA Department of Jobs, Enterprise and Innovation BCBA Department of Defence A Department of Justice and Equality BA Department of Health CA Department of Environment, Community, Local Govt BCBA Department of Arts Heritage and the GaeltachtAC THE BALLOT PAPER

24. SHORT LIST OF POTENTIAL MINISTERS FINE GAEL (12)FIANNA FÁIL (3)SINN FÉIN (2) Richard BrutonRBMicheál MartinMMGerry Adams GA Simon CoveneySCÉamon Ó CuivEOCMary Lou McDonald MMD Lucinda CreightonLCWillie O’DeaWOD Jimmy DeenihanJD Frances FitzgeraldFF‘INDEPENDENTS’ (3) Phil HoganPHLABOURJoan Collins JC Enda KennyEKJoan BurtonJBJoe Higgins JH Nicky McFaddenNMFEamon GilmoreEGMaureen O’Sullivan MOS Michael NoonanMNBrendan HowlinBH James ReillyJRKathleen LynchKL Alan ShatterASRuairí QuinnRQ Leo VaradkarLVPat RabbittePR THE (SHORT) LIST OF CANDIDATES

25. THE CONSENSORS to adjudicate on just which of the suggested items of expenditure are to be allowed; to publicise a summary of just what the expenditures of €x or €y on such-and-such an item might do; to draw up and then maintain the list of options; to finalise this list of options into a ballot paper, if need be in short-list format; to count, analyse and identify the outcome of the subsequent vote.