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 → →

Peter Emerson

爱 默生 彼得Питер Эмерсон

The de Borda Institute

德博达 研究所Инситут им. де Борда

Promoting inclusive voting procedures

推广具有包容性的投票系统www.deborda.org