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VOTING THEORY: DECISION-MAKING
In th following profile, 12 voters – Messrs. i to u cast their prefereences on five different options,
A.B, C, D and E.
So which option - A, B, C, D or E - best represents the collective will of the twelve voters?
2
5OPTIO
NS
12 voters and their preferencesi j k l m n p q r s t u
A
1 1 1 1 - 5 5 5 3 5 4 4
B
2 4 - 3 1 1 4 3 5 3 3 2
C 3 3 - 4 2 2 1 4 2 2 2 -
D 4 5 2 2 3 3 2 1 1 4 5 3
E 5 2 3 - - 4 3 2 4 1 1 1
VOTING THEORY - A VOTERS’ PROFILE
5OPTIO
NS
12 voters and their preferencesRESULTS
i j k l m n p q r s t u
A
1 1 1 1 - 5 5 5 3 5 4 4 4
B
2 4 - 3 1 1 4 3 5 3 3 2 2
C 3 3 - 4 2 2 1 4 2 2 2 - 1D 4 5 2 2 3 3 2 1 1 4 5 3 2
E 5 2 3 - - 4 3 2 4 1 1 1 3
MAJORITY/PLURALITY VOTING
5OPTIO
NS
12 voters and their preferencesRESULTS
i j k l m n p q r s t u
A
1 1 1 1 - 5 5 5 3 5 4 4 5
B
2 4 - 3 1 1 4 3 5 3 3 2 -
C 3 3 - 4 2 2 1 4 2 2 2 - -D 4 5 2 2 3 3 2 1 1 4 5 3 -
E 5 2 3 - - 4 3 2 4 1 1 1 6
TWO-ROUND SYSTEM (TRS)
5OPTIO
NS
12 voters and their preferencesRESULTS
i j k l m n p q r s t u
A
1 1 1 1 - 5 5 5 3 5 4 4 4
B
2 4 - 3 1 1 4 3 5 3 3 2 2
C 3 3 - 4 2 2 0 4 2 2 2 - 0D 4 5 2 2 3 3 2
(1)1 1 4 5 3 3
E 5 2 3 - - 4 3 2 4 1 1 1 3
A KNOCK-OUT (stage ii)
5OPTIO
NS
12 voters and their preferencesRESULTS
i j k l m n p q r s t u
A
1 1 1 1 - 5 5 5 3 5 4 4 4
B
2 4 - 3 0 0 4 3 5 3 3 2 0
C 3 3 - 4 2 2 0 4 2 2 2 - 0D 4 5 2 2 3
(1)3(1)
2(1)
1 1 4 5 3 5
E 5 2 3 - - 4 3 2 4 1 1 1 3
A KNOCK-OUT (stage iii)
5OPTIO
NS
12 voters and their preferencesRESULTS
i j k l m n p q r s t u
A
1 1 1 1 - 5 5 5 3 5 4(1)
4 5
B
2 4 - 3 0 0 4 3 5 3 3 2 0
C 3 3 - 4 2 2 0 4 2 2 2 - 0D 4 5 2 2 3
(1)3(1)
2(1)
1 1 4(1)
5 3(1)
7
E 5 2 3 - - 4 3 2 4 0 0 0 0
A KNOCK-OUT (stage iv)
5OPTIO
NS
12 voters and their preferencesRESULTS
i j k l m n p q r s t u
A
15
15
15
15--
51
51
51
33
51
42
42 31
B
24
42--
33
15
15
42
33
51
33
33
24 35
C 33
33--
42
24
24
15
42
24
24
24-- 35
D 42
51
24
24
33
33
24
15
15
42
51
33 37
E 51
24
33----
42
33
24
42
15
15
15 34
POINTS BORDA COUNT, BC
5OPTIO
NS
12 voters and their preferencesRESULTS
i j k l m n p q r s t u
A
15
15
13
14
--
51
51
51
33
51
42
41 27
B
24
42
--
32
13
15
42
33
51
33
33
23 31
C 33
33
--
41
22
24
15
42
24
24
24
-- 32
D 42
51
22
23
31
33
24
15
15
42
51
32 31
E 51
24
31
--
--
42
33
24
42
15
15
14 31
POINTS MODIFIED BORDA COUNT, MBC
10
5OPTIO
NS
12 voters and their preferencesResults Winsi j k l m n p q r s t u
A
1 1 1 1 - 5 5 5 3 5 4 4 5
B
2 4 - 3 1 1 4 3 5 3 3 2 7 1
C 3 3 - 4 2 2 1 4 2 2 2 -D 4 5 2 2 3 3 2 1 1 4 5 3
E 5 2 3 - - 4 3 2 4 1 1 1
LEAGUE - A:B
11
5OPTIO
NS
12 voters and their preferencesResults Winsi j k l m n p q r s t u
A
1 1 1 1 - 5 5 5 3 5 4 4
B
2 4 - 3 1 1 4 3 5 3 3 2 1
C 3 3 - 4 2 2 1 4 2 2 2 - 6 0.5D 4 5 2 2 3 3 2 1 1 4 5 3
E 5 2 3 - - 4 3 2 4 1 1 1 6 0.5
LEAGUE - A:B, C:E
12
5OPTIO
NS
12 voters and their preferencesResults Winsi j k l m n p q r s t u
A
1 1 1 1 - 5 5 5 3 5 4 4
B
2 4 - 3 1 1 4 3 5 3 3 2 7 2
C 3 3 - 4 2 2 1 4 2 2 2 - 0.5D 4 5 2 2 3 3 2 1 1 4 5 3 5
E 5 2 3 - - 4 3 2 4 1 1 1 0.5
LEAGUE - A:B, C:E, B:D
13
5OPTIO
NS
12 voters and their preferencesResults Winsi j k l m n p q r s t u
A
1 1 1 1 - 5 5 5 3 5 4 4 -
B
2 4 - 3 1 1 4 3 5 3 3 2 3
C 3 3 - 4 2 2 1 4 2 2 2 - 2.5D 4 5 2 2 3 3 2 1 1 4 5 3 8 2
E 5 2 3 - - 4 3 2 4 1 1 1 4 2.5
LEAGUE - A:B, A:C, A:D, A:EB:C, B:D, B:E C:D, C:E D:E
MethodologySocial Ranking Examples of use in:
1st 2nd 3rd 4th 5th Decision-making Elections
Majority/Plurality vote
A E B/D - C Finland(referendums)
UK Kenya
Two-round System
E A - - - New Zealand Norway (parliament)
FranceIvory Coast
Knock-outAlternative vote
D A - - - Australia
BC D B/C - E A Dublin NauruSlovenia
MBC C B/D/E - - A - -
LeagueCondorcet
B C/E - D A - -
DIFFERENT ‘DEMOCRATIC’ RESULTS
CLOSED
QUESTIONS
SEMI-OPEN
QUESTIONS
OPEN
QUESTIONS
↑All
Prefs
DECISION-MAKING Borda
BC / MBC
C BC = Borda Count
MBC = modified Borda count
NI = Northern Ireland
UK = United Kingdom
UN = United Nations
Condorcet
(League)
OSome
1. Approval Vote
2. Alternative Vote
(knock-out)
U prefs Serial voting
Sweden*
N 1st
prefs
only
Weighted majority
UN
Consociational
NI, Belgium
2-round voting
Norway**
T Simple majority
Ireland, UK, Taiwan
Twin Majority
Switzerland
Plurality
New Zealand
* a series of majority votes
** 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 → →