In deeds mediation, questions are open; in politics, then, why are they closed? The de Borda Institute

MAJORITARIANISM “Democracy rests upon the principles of majority rule.” “Democracy rests upon the principles of majority rule.” “Democracy works on the basis of a decision by the majority.” “Democracy works on the basis of a decision by the majority.” “Democracy is based on majority decision.” “Democracy is based on majority decision.”

SWEDEN – 1955 Referendum: which side of the road shall we drive on? Right15.5% Right15.5% Left82.9% Left82.9% Blank 1.6% Blank 1.6%

SELF-DETERMINATION “All peoples have the right to self- determination. By virtue of that right they freely determine their political status…” Article 1.1, The International Covenant on Civil and Political Rights

DEMOCRATIC DICTATORS

THE QUESTION IS THE ANSWER

CANADA – QUEBEC THE ‘NEVER-END-UM’ ForAgainstTurnout %59.6%85.6% %55.4%82.8% %50.6%93.5%

NORTHERN IRELAND Border poll – 1972 Population: roughly 60% Protestant, 40% Catholic Turnout59% yes97%

A MAJORITY OF THE WHOLE

A MAJORITY OF THE MINORITY OF THE WHOLE

A MAJORITY OF THE MINORITY OF THE MINORITY OF THE WHOLE

RUSSIAN DOLLS

YUGOSLAVIA

THE CAUCASUS

RWANDA “Rubanda Nyamwinshi” the majority people

POLL TAX Poll TaxTory Property TaxLabour Local Income TaxLib-Dems Land taxGreens The rates (status quo)

OLYMPICS London London Madrid Madrid Moscow Moscow New York New York Paris Paris

NORMAL DISTRIBUTION CURVE Distribution. Figure 1 -- Standard Normal Distribution

Table I A group of2may exercise a majority veto in a society of 3. That group of3may then exercise a majority veto in a society of 5; – ’’ –5 9; – ’’ –9 17; – ’’ –17– ’’ –33; – ’’ –33– ’’ –65; – ’’ –65– ’’ –129; – ’’ –129– ’’ –257; – ’’ –257– ’’ –513; and that group of513– ’’ –1025. TABLE 1

Ifa countrywants to be independenT then, if a majority of the wholevotes in favo ur, it may. UKYugo- slavia but ifa minoritywants to opt out, and if a majority of that minority– ” –IrelandSerbia but ifa minority of the minority – ” –a majority of that minority of the minority – ” –N IrelandKosova but ifa minority of the minority of the minority – ” –a majority of that minority of the minority of the minority – ” –W BelfastNorth Mitrovica but ifa minority of the minority of the minority of the minority – ” –a majority of the minority of the minority of the minority of the minority – ” – but if….– ” –….– ” – but if17– ” –9 but if9– ” –5 but if5– ” –3 but if3– ” –2 TABLE II

MAJORITARIANISM “Democracy is based on majority decision. It is the most important instrument for finding peaceful solutions to conflicts.” “Democracy is based on majority decision. It is the most important instrument for finding peaceful solutions to conflicts.”UNESCO

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

THE WILL OF THE PEOPLE Closed questionsyes-or-no for-or-againstwin-or-lose (i.e., some people) Open - i.e., multi-option – questions yes 1 st, (and 2 nd, and 3 rd …) win-win (i.e., all people).

A PLURAL DEMOCRACY Collective wisdom, or unanimity Collective wisdom, or unanimity Common consensus Common consensus Best possible compromise Best possible compromise

AVERAGE PREFERENCE SCORE ON A 5-OPTION BALLOT IF EVERYONE GIVES A CERTAIN OPTION THEIR THAT OPTION WILL GET AN AVERAGE PREFERENCE SCORE OF 1 ST PREFERENCE 1 (THE MAXIMUM) 2 ND PREFERENCE 2 3 RD PREFERENCE 3 (THE MEAN) 4 TH PREFERENCE 4 5 TH PREFERENCE 5 (THE MINIMUM)

A VOTERS’ PROFILE 1 ST 2 ND 3 RD 4 TH 5 TH AveragePreferendeScore A B C D E

A VOTERS’ PROFILE 1 ST 2 ND 3 RD 4 TH 5 TH AveragePreferendeScore A B C D E

A VOTERS’ PROFILE 1 ST 2 ND 3 RD 4 TH 5 TH AveragePreferendeScore A B C D E

A VOTERS’ PROFILE 1 ST 2 ND 3 RD 4 TH 5 TH AveragePreferendeScore A-7-8-c.3 B-8-7-c.3 C D E

A PLURAL DEMOCRACY Collective wisdom, or unanimity1-1.5 Collective wisdom, or unanimity1-1.5 Common consensus1.5-2 Common consensus1.5-2 Best possible compromise2-2.5 Best possible compromise2-2.5

LEVEL OF CONSENSUS ON A 5-OPTION BALLOT IF OPTION D, SAY GETS THE HIGHEST AVERGAE PREFERENCE SCORE OF OPTION D WILL REPRESENT THE 1 – 1.5 UNANIMOUS VIEWPOINT 1.5 – 2 COMMON CONSENSUS 2 – 2.5 BEST POSSIBLE COMPROMISE

CONSENSUS COEFFICIENT The consensus coefficient, C, of option A, is C A ; where S A is the MBC score of option A, where V is the valid vote, and where n is the number of options, C A is given by: C A = S A / V.n

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

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

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).

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).

PARTIAL VOTING IN AN MBC If you vote for: Number of options 1234 your 1 ST pref gets: 1 pt 2pts 3 pts 4 pts your 2 ND pref gets: 1 pt 2pts 3 pts your 3 RD pref gets: 1 pt 2pts your 4 TH pref gets: 1 pt

CLOSEDOPEN THRESHOLD HIGHLOWHIGHLOWHIGHLOWHIGHLOW COUNTCOUNT All prefs QBS + top-up E L E C T O R A L S Y S T E M S QBS BC/MBC Condorcet some prefs PR-STV Ireland PR-List Swiss Approval Voting AV Australia 2-round France Mixed FPP + PR Croatia MMP - Germany 1 st prefs FPP UK PR-list closed Israel AMSFPP PR-list Holland Lebanon 1 party only1 candidate of 1 party 1 or some candidates of 1 or some parties 1, some or all candidates of any or all parties V O T E R S ' C H O I C E

QBS - THE QUOTA BORDA SYSTEM in a 4-seater constituency All candidates gaining the quota are elected. All candidates gaining the quota are elected. All pairs of candidates gaining 2 quotas are elected. All pairs of candidates gaining 2 quotas are elected. ________________________________________________________ ________________________________________________________ All pairs gaining 1 quota elect 1 candidate, (the one with the higher MBC score). All pairs gaining 1 quota elect 1 candidate, (the one with the higher MBC score). All remaining seats go to those candidates with the highest MBC scores. All remaining seats go to those candidates with the highest MBC scores.

THE MATRIX VOTE