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.
DECISION-MAKING
CLOSED
QUESTIONS
↑
C
All
prefs
O
Some
U
prefs
N
1st
prefs
only
T
* a series of
majority votes
** a first-round
plurality and
then a majority
vote
SEMI-OPEN
QUESTIONS
AV = alternative vote
BC = Borda Count
IRV = instant run-off
MBC = modified Borda count
STV = single transferable vote
Weighted
majority
SA, UN
Consociational
NI, Belgium
Simple majority
Ireland, UK
Twin Majority
Switzerland
1 of 2
options
Borda
BC / MBC
non
Major-
Condorcet
(Copeland)
M
A
J
O
R
I
T
A
R
I
A
N
Approval
voting
Serial voting
Sweden*
AV = IRV =
STV
2-round
voting
Norway**
Plurality
New Zealand
1 of some
options
1 or some of
some options
1st preference only
BINARY
OPEN
QUESTIONS
1or some or all
of all options
Preferential
MULTI-OPTIONAL
VOTERS’ CHOICE →
→
‘DEMOCRATIC’ (?) DICTATORS
COUNTRY
Date
AUTHOR
ISSUE
FOR
TURN
-OUT
FRANCE
1800 NAPOLEON
BE CONSUL
99%
43%
RUSSIA
1903 LENIN
BOLSHEVISM 49%
92%
ITALY
1929 MUSSOLINI
FASCISM
99%
96%
FUHRER
98%
98%
ANSCHLUSS
99%
99%
1963 SHAH
REVOLUTION 99%
91%
1979 KHOMEINI
ISLAMIC
96%
65%
LIBYA
1971 GADDAFI
HIS IDEAS
99%
-
IRAQ
2002 S. HUSSEIN
HIMSELF
100% 100%
GERMANY 1936
AUSTRIA 1938
IRAN
HITLER
A VOTERS’ PROFILE
Voters and their preferences
OPTIONS
A
B
C
D
i
1
2
3
4
j
1
3
2
4
k
1
3
2
4
l
4
1
2
3
m
4
2
1
3
n
4
3
2
1
p
4
3
2
1
A VOTERS’ PROFILE
Voters and their preferences
OPTIONS
A
B
C
D
i
1
2
3
4
j
1
3
2
4
k
1
3
2
4
l
4
1
2
3
m
4
2
1
3
n
4
3
2
1
p
4
3
2
1
A VOTERS’ PROFILE
Voters and their preferences
OPTIONS
A
B
C
D
i
1
2
3
4
j
1
3
2
4
k
1
3
2
4
l
4
1
2
3
m
4
2
1
3
n
4
3
2
1
p
4
3
2
1
A VOTERS’ PROFILE
Voters and their preferences
MBC
OPTIONS
A
B
C
D
i
j
k
l
m
n
p
1
2
3
4
1
3
2
4
1
3
2
4
4
1
2
3
4
2
1
3
4
3
2
1
4
3
2
1
16
18
21
15
Condorcet
0
2
3
1
‘DEMOCRATIC’ RESULTS
Methodology
Plurality vote
Two-round
system
AV
BC/MBC
Condorcet
Social Choice
and
Social Ranking
Examples of use in:
1st 2nd 3rd
A D B
/
C
D A -
4th
Decision-making
-
New Zealand
(referendums)
Norway (in parliament)
B
C
C
D
A
A
B
B
A
D
Elections
UK (where it is
called FPP)
Kenya
France
Côte d'Ivoire
Australia
Slovenia
-
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
Number of options
If you vote for:
your 1ST pref gets:
your 2ND pref gets:
your 3RD pref gets:
your 4TH pref gets:
your 5TH pref gets:
1
2
3
4
5
1 pt
2 pts
3 pts
4 pts
5 pts
1 pt
2 pts
3 pts
4 pts
1 pt
2 pts
3 pts
1 pt
2 pts
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
DECISION-MAKING
CLOSED
QUESTIONS
↑
C
All
prefs
O
Some
U
prefs
N
1st
prefs
only
T
* a series of
majority votes
** a first-round
plurality and
then a majority
vote
SEMI-OPEN
QUESTIONS
AV = alternative vote
BC = Borda Count
IRV = instant run-off
MBC = modified Borda count
STV = single transferable vote
Weighted
majority
SA, UN
Consociational
NI, Belgium
Simple majority
Ireland, UK
Twin Majority
Switzerland
1 of 2
options
Borda
BC / MBC
non
Major-
Condorcet
(Copeland)
M
A
J
O
R
I
T
A
R
I
A
N
Approval
voting
Serial voting
Sweden*
AV = IRV =
STV
2-round
voting
Norway**
Plurality
New Zealand
1 of some
options
1 or some of
some options
1st preference only
BINARY
OPEN
QUESTIONS
1or some or all
of all options
Preferential
MULTI-OPTIONAL
VOTERS’ CHOICE →
→