This document discusses different methods of decision-making, voting systems, and electoral systems. It compares closed questions that only allow one choice versus more open questions that allow preferences. It also explains how the Borda count and modified Borda count systems allocate points for partial votes depending on the number of options voted for. Finally, it provides an overview of electoral systems and how they fall along a spectrum from only allowing votes for single candidates to fully open proportional representation systems.

1. Peter Emerson
The de Borda Institute
August 8 2013, Wood Quay Venue, Dublin @ogpconsultirl #ogpIRL

2. SOCIAL CHOICES
and
SOCIAL RANKINGS
The de Borda Institute
www.deborda.org

3. DECISION-MAKING
Questions
MEDIATION open, multi-optional
POLITICS closed, majority votes

4. MAJORITARIANISM
The (simple or weighted)
two-option majority vote is
the most inaccurate measure
of collective opinion ever
invented

5. CLOSED
QUESTIONS
SEMI-OPEN
QUESTIONS
OPEN
QUESTIONS
↑ All
Prefs
DECISION-MAKING Borda
BC / MBC
C AV = alternative vote
BC = Borda Count
IRV = instant run-off
MBC = modified Borda count
STV = single transferable vote
Condorcet
(Copeland)
O
Some
Approval
voting
U prefs Serial voting
Sweden*
AV = IRV =
STV
N 1st
prefs
only
Weighted majority
EU, SA, UN
Consociational
NI, Belgium
2-round voting
Norway**
T Simple majority
Ireland, UK, etc.
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 → →

6. PARTIAL VOTING IN A 5-OPTION MBC
• He who votes for 1 option gives his favourite
1 pt.

7. PARTIAL VOTING IN A 5-OPTION 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).

8. PARTIAL VOTING IN A 5-OPTION 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).

9. PARTIAL VOTING IN A 5-OPTION MBC
If you vote for: Number of options
1 2 3 4 5
your 1ST pref gets: 1pt 2pts 3pts 4pts 5pts
your 2ND pref gets: 1pt 2pts 3pts 4pts
your 3RD pref gets: 1pt 2pts 3pts
your 4TH pref gets: 1pt 2pts
your 5TH pref gets: 1pt

10. 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

11. CLOSED
QUESTIONS
SEMI-OPEN
QUESTIONS
OPEN
QUESTIONS
↑ All
Prefs
DECISION-MAKING Borda
BC / MBC
C AV = alternative vote
BC = Borda Count
IRV = instant run-off
MBC = modified Borda count
STV = single transferable vote
Condorcet
(Copeland)
O
Some
Approval
voting
U prefs Serial voting
Sweden*
AV = IRV =
STV
N 1st
prefs
only
Weighted majority
SA
Consociational
NI, Belgium
2-round voting
Norway**
T Simple majority
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 → →

12. THRESHOLD THRESHOLD THRESHOLD THRESHOLD
HIGH LOW HIGH LOW HIGH LOW HIGH LOW
↑
C
O
U
N
T
All
prefs
E L E C T O R A L S Y S T E M S QBS + top-up
AMS = additional member system
AV = (STV) = alternative vote FPP = first-past-the-post
MBC = modified Borda count MMP = multi-member proportional
QBS
BC/MBC
Condorcet
lots
some
prefs
few
QBS =quota Borda system
S(N)TV = single (non-) transferable vote
PR-List
Swiss
PR-STV
Ireland
N Ireland
Approval Voting
AV
Australia
PR-List
Belgium
2-round
France
Bosnia ’90
Mixed FPP + PR
Croatia ’92-’95 MMP – Germany, NZ
1st
prefs
FPP
UK
Kenya
PR-list
closed
Israel, Iraq
Bosnia ’96
Kosovo*
AMS
FPP
Lebanon
SNTV
Afghan-
istan
PR-list
Holland
Bosnia ’00
* with set-
aside.
1 party only 1 candidate
of 1 party
1 or some candidates of
1 or some parties
1, some or all
candidates of any or all
parties
V O T E R S ' C H O I C E →