THE INADEQUATE STUDY OF SOCIAL CHOICE THEORY

AND ITS WORLD-WIDE CONSEQUENCES

欢迎

Peter Emerson

The de Borda Institute

德博达研究所

ZIMBABWE

President Mugabe:

Elections: first-past-the-post

Governance: majority vote

EGYPT

Constitutional Referendum

Yes 77.3%

No 22.7%

(41% turnout)

MAJORITARIANISM(majority rule by majority vote)

The (simple or weighted) majority vote is the most inaccurate measure of collective opinion ever invented.

CLOSED

QUESTIONS

SEMI-OPEN

QUESTIONS

OPEN

QUESTIONS

↑All

prefs

Borda

BC / MBC

non

Major-

C AV = alternative vote

BC = Borda Count

IRV = instant run-off

MBC = modified Borda count

STV = single transferable vote

Condorcet

(Copeland)

M

A

J

O

R

I

T

A

R

I

A

N

OSome

Approval

voting

U prefs Serial voting

Sweden*

AV = IRV = STV

N 1st

prefs

only

Weighted majority

SA, UN

Consociational

NI, Belgium

2-round voting

Norway**

T Simple majority

Ireland, UK

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 → →

DECISION-MAKING

‘DEMOCRATIC’ (?) DICTATORS

OPTIONSVoters and their preferences

i j k l m n p

A 1 1 1 4 4 4 4B 2 3 3 1 2 3 3C 3 2 2 2 1 2 2D 4 4 4 3 3 1 1

A VOTERS’ PROFILE

OPTIONSVoters and their preferences

i j k l m n p

A 1 1 1 4 4 4 4B 2 3 3 1 2 3 3C 3 2 2 2 1 2 2D 4 4 4 3 3 1 1

A VOTERS’ PROFILE

OPTIONSVoters and their preferences

i j k l m n p

A 1 1 1 4 4 4 4B 2 3 3 1 2 3 3C 3 2 2 2 1 2 2D 4 4 4 3 3 1 1

A VOTERS’ PROFILE

OPTIONSVoters and their preferences

MBCCon-dor-cet

i j k l m n p

A 1 1 1 4 4 4 4 16 0B 2 3 3 1 2 3 3 18 2C 3 2 2 2 1 2 2 21 3D 4 4 4 3 3 1 1 15 1

A VOTERS’ PROFILE

MethodologySocial Choice

and Social Ranking

Examples of use in:

1st 2nd 3rd 4th Decision-making Elections

Plurality vote A D B/C

UK (where it is called FPP)

KenyaTwo-round system

D A - - New Zealand (referendums)

Norway (in parliament)

FranceCôte d'Ivoire

AV B A - - AustraliaBC/MBC C B A D SloveniaCondorcet C B D A -

‘DEMOCRATIC’ RESULTS

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 2nd 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 2nd choice 1 pt).

He who votes for 3 options gives his favourite 3 pts, (his 2nd choice 2 pts and his 3rd 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 2nd choice 1 pt).

He who votes for 3 options gives his favourite 3 pts, (his 2nd choice 2 pts and his 3rd choice 1 pt).

She who votes for all 5 options gives her favourite 5 pts, (her 2nd choice 4 pts, and so on).

PARTIAL VOTING IN AN MBC

If you vote for:

Number of options

1 2 3 4 5

your 1ST pref gets: 1 pt 2 pts 3 pts 4 pts 5 pts

your 2ND pref gets: 1 pt 2 pts 3 pts 4 pts

your 3RD pref gets: 1 pt 2 pts 3 pts

your 4TH pref gets: 1 pt 2 pts

your 5TH pref gets: 1 pt

BORDA COUNT (BC)

A full vote = n, n-1 … 2, 1

MODIFIED BORDA COUNT (MBC)

A full vote = n, n-1 … 2, 1

A partial vote = m, m-1 … 2, 1

CLOSED

QUESTIONS

SEMI-OPEN

QUESTIONS

OPEN

QUESTIONS

↑All

prefs

Borda

BC / MBC

non

Major-

C AV = alternative vote

BC = Borda Count

IRV = instant run-off

MBC = modified Borda count

STV = single transferable vote

Condorcet

(Copeland)

M

A

J

O

R

I

T

A

R

I

A

N

OSome

Approval

voting

U prefs Serial voting

Sweden*

AV = IRV = STV

N 1st

prefs

only

Weighted majority

SA, UN

Consociational

NI, Belgium

2-round voting

Norway**

T Simple majority

Ireland, UK

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 → →

DECISION-MAKING