DECISION-MAKING
The de Borda Institute
www.deborda.org
www.decision-maker.org
MAJORITY RULE
MAJORITARIANISM = ….........................
Микайл Сергеeвич, Вам нужен …...................
MAJORITY RULE
MAJORITARIANISM = БОЛЬШЕВИЗМ
Микайл Сергеeвич, Вам нужен большевизм
ЗАПАДНЫЕ БОЛЬШЕВИКИ
ELECTED DICTATORS
• Gamsakhurdia
ЗАПАДНЫЕ БОЛЬШЕВИКИ
ELECTED DICTATORS
• Gamsakhurdia
• Erdoğan
• Putin
• Trump
• Bashar al-Assad
MAJORITY RULE…
A CAUSE OF WAR
Always: Israel/Palestine
1940s/50s India/Pakistan
1970s/80s Northern Ireland
1990s The Caucasus, The Balkans
Rwanda
2000s Syria, Yemen…
Kenya
2010s Ukraine
THE BALKANS
“All the wars in the former Yugoslavia started with
a referendum.”
Oslobodjenje,
Sarajevo’s famous newspaper
7.2.1999
The same quotation now applies to Ukraine.
MAJORITY RULE or POWER-SHARING
50% + 1
The winner gets everything, the loser gets nothing!
2004 Yushchenko v Yanukovich
Ющенко v Янукович
2010 Yanukovich v Timoshenko
Янукович v Тимошенко
CURRENT FORMS OF GOVERNANCE
Parliament
The People
GovernmentOpposition
CRAZY COALITIONS
• UK Conservative Party + Democratic
Unionist Party
• Austria Centre-right party + Extreme-right party
• Israel Likud with very extremist Jewish Home
• Turkey Coalition with the Kurds?
• Israel Coalition with Arab List?
SWITZERLAND
AND THE ‘MAGIC FORMULA’
Federal Council
7 persons, elected by parliament on a magic
formula from the four main parties.
2:2:2:1
MY TALK
1. Majority voting (on only two options) is
inaccurate. It should be replaced by preferential
voting (on many options).
2. So majority rule should be replaced by all-party
power-sharing.
I. A critique of majority voting.
II. The right of self-determination.
III. Preferential points voting.
IV. (Briefly) all-party coalitions.
I. A CRITIQUE OF MAJORITY VOTING
Majority Voting
• Option A or option B?
• Option A, yes-or-no?
NORMAL DISTRIBUTION CURVE
Figure
1 -- Standard Normal Distribution
SMALL TALLAVERAGE
NORMAL DISTRIBUTION CURVE
Figure
1 -- Standard Normal Distribution
LEFT-WING RIGHT-WINGAVERAGE
GEORGE WASHINGTON
The two-party system of politics
“has perpetrated the most horrid
enormities [and] is itself a frightful
despotism.”
Farewell address, 1796.
A MINIMUM PLURALIST SOCIETY…
3 PERSONS WITH 3 OPINIONS
Three people
Ms i Mr j Ms k
Three options
A B C
Ale Beer Cider
3 PERSONS AND THEIR 1st PREFERENCES
Ms i Mr j Ms k
A B C
3 PERSONS AND THEIR 1st, 2nd and 3rd PREFERENCES
Ms i Mr j Ms k
1st A B C
2nd B C A
3rd C A B
ORDER OF VOTING
A
versus = A
B versus = C
C
ORDER OF VOTING
C
versus = C
A versus = B
B
ORDER OF VOTING
B
versus = B
C versus = A
A
ORDER OF VOTING
A
versus = A
B versus = C
C
B
versus = B
C versus = A
A
C
versus = C
A versus = B
B
PARADOX OF VOTING
MAJORITY RULE IN A PLURALIST SOCIETY?
A > B > C > A ….
THE SIMPLEST DEBATE
A MOTION: Paint the door red.
ONE AMENDMENT: Delete the word ‘red’
and insert ‘blue’.
A = A red door
B = A blue door
C = The status quo: a green door.
BOSNIA
1990 elections:
Moslem:Orthodox:Catholic = 40:30:20
40 + 30 > 20
40 + 20 > 30
30 + 20 > 40
40 + 20 = a majority = war
. 40 versus 20 = another war
MANIPULATION: THE ROLE OF THE CHAIR
Ms i Mr j Ms k
D D D
A A A
A = ale
D = draught
DIVIDE AND RULE
Ms i Mr j Ms k
D B C
A C D
B D A
C A B
A = ale
B = beer
C = cider
D = draught
A > B > C > D > A…
D
versus = C
C
A > B > C > D > A…
D
versus = C
C versus = B
B
A > B > C > D > A…
D
versus = C
C versus = B
B versus = A
A
‘DEMOCRATIC DICTATORS’
PLACE Date AUTHOR ISSUE FOR TURN
OUT
FRANCE 1800 NAPOLEON BE CONSUL 99% 43%
CHILE 1818 O’HIGGINS BE SUPREMO 100% -
RUSSIA 1903 LENIN BOLSHEVISM 49% -
GERMANY 1936
HITLER
FUHRER 98% 98%
AUSTRIA 1938 ANSCHLUSS 99% 99%
IRAN
1953 MOSSADEGH SOCIALISM 99% -
1963 SHAH REVOLUTION 99% 91%
1979 KHOMEINI ISLAMIC 99% 65%
THE QUESTION IS THE ANSWER
PLACE Date AUTHOR ISSUE FOR TURN
OUT
NORTHERN
IRELAND
1973 TED HEATH
(BRITISH PM)
THE BORDER 99% 59%
NAGORNO-
KARABAKH
199I - INDEPENDENT 99% 82%
KOSOVA 1991 RUGOVA INDEPENDENT 99% 87%
Republica
Srpska
1991 KARADŽIĆ STAY IN
YUGOSLAVIA
98% 85%
ABKHAZIA 1999 ARDZINBA INDEPENDENT 97% 88%
IRAQ
1995
SADDAM
HUSSEIN
HIMSELF 99.9 99.5
2002 HIMSELF 100% 100%
II. SELF-DETERMINATION
“All peoples have the right of self-determination.”
USA President Woodrow Wilson
A MAJORITY
OF THE WHOLE
BIG
A MAJORITY OF THE MINORITY
SMALL
A MAJORITY OF THE MINORITY
OF THE MINORITY
TINY
MATRIOSHKA NATIONALISM
BIG SMALL TINY
UK IRELAND NORTHERN IRELAND
SCOTLAND ORKNEY ISLANDS
SOVIET
UNION
or
RUSSIA
GEORGIA ABHAZIA
SOUTH OSSETIA
ADJARA
AZERBAIJAN NAGORNO-KARABAKH
MOLDOVA TRANS-DNESTR
CRIMEA
UKRAINE DONETSK
KRASNOARMIISK RAION ?
CHECHNYA
TARTARSKAYA?
YUGOSLAVIA
CROATIA KRAJINA
BOSNIA REPUBLIKA-SRPSKA
HERZEG-BOSNA
SERBIA KOSOVA
PREŠEVO VALLEY ?
. KIRKUK
IRAQ
. KIRKUK
IRAQ
. KIRKUK
IRAQ
. KIRKUK
IRAQ
III. A MORE INCLUSIVE VOTING PROCEDURE
Multi-option voting
Preferential voting
SWEDEN – 1955
Which side of the road shall we drive on?
• Left
• Right
• Blank
SWEDEN – 1955
Which side of the road shall we drive on?
• Left 82.9%
• Right 15.5%
• Blank 1.6%
CLOSED
QUESTIONS
SEMI-OPEN
QUESTIONS
OPEN
QUESTIONS
↑All
Prefs
DECISION-MAKING Preferential
points voting
C AV = alternative vote
PPV = preferential points voting
TRS = two-round system
Condorcet
OSome
U prefs AV
N 1st
prefs
only
Weighted majority
EU
Power-sharing
NI, Bosnia
2-round system
TRS Norway*
T Simple majority
Everywhere
Double Majority
Switzerland
Plurality
Denmark
* a first-
round
plurality
and then a
majority
vote
1 of 2
options
1 of some
options
1 or some of
some options
1or some or all
of all options
1st preference only Preferential
BINARY MULTI-OPTIONAL
VOTERS’ CHOICE → →
AVERAGE HEIGHT
Option A < 1 m 60
Option B ≥ 1 m 60
Option C ≥ 1 m 70
Option D ≥ 1 m 80
Option E ≥ 1 m 90
A VOTERS’ PROFILE ON FOUR OPTIONS
A, B, C and D
14 voters
5 4 3 2
1st Preference A C D B
2nd Preference B B B D
3rd Preference C D C C
4th Preference D A A A
PLURALITY VOTE
A 5, C 4, D 3, B 2
14 voters
5 4 3 2
1st Preference A C D B
2nd Preference B B B D
3rd Preference C D C C
4th Preference D A A A
TWO-ROUND SYSTEM (TRS)
1st round: A 5, C 4, D 3, B 2
2nd round: A 5, C 9
14 voters
5 4 3 2
1st Preference A C D B
2nd Preference B B B D
3rd Preference C D C C
4th Preference D A A A
ALTERNATIVE VOTE (AV, IRV, PV or STV)
1st round: A 5, C 4, D 3, B 2
2nd round: A 5, C 4, D 5
3rd round: A 5, D 9
14 voters
5 4 3 2
1st Preference A C D B
2nd Preference B B B D
3rd Preference C D C C
4th Preference D A A A
BORDA COUNT (BC)
PREFERENTIAL POINTS VOTING
A 29, B 44, C 36, D 31
14 voters
5 4 3 2
1st Pref (4 points) A C D B
2nd Pref (3 points) B B B D
3rd Pref (2 points) C D C C
4th Pref (1 point) D A A A
PREFERENTIAL POINTS VOTING
A 29, B 44, C 36, D 31
14 voters
5 4 3 2
1st Pref (4 points) A 20 C 16 D 12 B 8
2nd Pref (3 points) B 15 B 12 B 9 D 6
3rd Pref (2 points) C 10 D 8 C 6 C 4
4th Pref (1 point) D 5 A 4 A 3 A 2
THE WINNERS!
A or B or C or D
Plurality Two-
round
AV or
STV
PPV
A 5 5 5 29
B 2 - - 44
C 4 9 - 36
D 3 - 9 31
….
PREFERENTIAL POINTS VOTING
He who votes for 1 option gives his favourite 1 point.
. PARTIAL VOTING IN PREFERENTIAL POINTS VOTING
He who votes for 1 option gives his favourite 1 point.
She who votes for 2 options gives her favourite 2 points (and her
2nd choice 1 point).
. PARTIAL VOTING IN PREFERENTIAL POINTS VOTING
He who votes for 1 option gives his favourite 1 point.
She who votes for 2 options gives her favourite 2 points (and her 2nd choice 1 point).
He who votes for 3 options gives his favourite 3 points, (his 2nd
choice 2 points and his 3rd choice 1 point).
PARTIAL VOTING IN PREFERENTIAL POINTS VOTING
If you vote for:
Number of options
1 2 3 4 5
your 1ST preference
gets:1
point
2
points
3
points
4
points
5
points
your 2ND preference
gets:_ 1
point
2
points
3
points
4
points
your 3RD preference
gets:_ _ 1
point
2
points
3
points
your 4TH preference
gets:_ _ _ 1
point
2
points
your 5TH preference
gets:_ _ _ _ 1
points
0
1
2
3
4
5
6
A-40% B-45% C-50% D-55% E-60%
MrJ
LOGICAL PREFERENCES
Mr J - E, D, C, B, A
0
1
2
3
4
5
6
A-40% B-45% C-50% D-55% E-60%
MrJ
MsK
LOGICAL PREFERENCES
Mr J - E, D, C, B, A
Ms K - B, A, C, D, E
0
1
2
3
4
5
6
A-40% B-45% C-50% D-55% E-60%
MrJ
MsK
MsL
LOGICAL PREFERENCES
Mr J - E, D, C, B, A
Ms K - B, A, C, D, E
Ms L - B, C, D, A, E
0
1
2
3
4
5
6
A-40% B-45% C-50% D-55% E-60%
MrJ
MsK
MsL
MrM
ILLOGICAL PREFERENCES
Mr M - D, B, E, A, C
0
1
2
3
4
5
6
A-40% B-45% C-50% D-55% E-60%
MrJ
MsK
MsL
LOGICAL PREFERENCES
Mr J - E, D, C, B, A
Ms K - B, A, C, D, E
Ms L - B, C, D, A, E
COLLECTIVE
SET OF PREFERENCES
Mr J (1, 2, 3, 4, 5)
+ Ms K (4, 5, 3, 2, 1)
+ Ms L (2, 5, 4, 3, 1)
= All (7, 12, 10, 9, 7)
THE COLLECTIVE WILL
3 LOGICAL PREFERENCESMr J = 1 - 2 - 3 - 4 - 5
Ms K = 4 - 5 - 3 - 2 - 1
Ms L = 2 - 5 - 4 - 3 - 1
All = 07-12-10-09-07
0
2
4
6
8
10
12
14
A - 40% B - 45% C - 50% D - 55% E - 60%
J
K
L
All
CLOSED
QUESTIONS
SEMI-OPEN
QUESTIONS
OPEN
QUESTIONS
↑All
Prefs
DECISION-MAKING Preferential
points voting
C AV = alternative vote
BC = Borda Count
MBC = Modified Borda Count = PPV
PPV = preferential points voting = MBC
TRS = two-round system
Condorcet
OSome
Approval
voting
U prefs AV
N 1st
prefs
only
Weighted majority
EU, Finland
Power-sharing
NI, Belgium
2-round system
TRS Norway*
T Simple majority
Ireland, UK, all
Twin Majority
Switzerland
Plurality
Denmark
* a first-
round
plurality
and then, if
need be, a
majority
vote
1 of 2
options
1 of some
options
1 or some of
some options
1or some or all
of all options
1st preference only Preferential
BINARY MULTI-OPTIONAL
VOTERS’ CHOICE → →
CURRENT FORMS OF GOVERNANCE
Parliament
The People
GovernmentOpposition
16
32
64
128
256
512
2000 ’01 ’02 ’03 ’04 ’05 ’06 ’07 ’08 ’09 2010 ’11 ’12 ’13 ’14 ’15 16 17
Austria
Belgium
Finland
Germany
Ireland
Netherlands
Spain
SMALL CIRCLE Minority, one partyDIAMOND Minority coalitionBIG CIRCLE Majority, one partyTRIANGLE Majority coalitionSQUARE Grand coalition
LINE Undecided
REPRESENTATION
Government
Parliament
The People
IV. ALL-PARTY COALITIONS
The people elect the parliament,
the electoral system is proportional and preferential.
The parliament elects:
(i) the government; and
(ii) its referees;
again, the electoral system is proportional and preferential.
For non-urgent decisions:
all parties can make proposals
the referees choose the options for the ballot
and decisions are taken by a preferential points system.