The Economic and Social Review, Vol. 16, No. I, October 1984, pp. 1-18
Chance in Preferential Voting Systems:
An Unacceptable Element in Irish Electoral
JOHN
COAKLEY
GERALD 0
The National
NEILL
Institute for Higher Education,
Limerick
Abstract: T h e single transferable vote system o f p r o p o r t i o n a l representation as operated in elections to D a i l
fiireann
is one o f the most sophisticated electoral systems, m a x i m i s i n g the capacity o f the voter to determine
the o u t c o m e of a n election a n d allowing m u l t i - d i m e n s i o n a l representation o f party political a n d other
interests. Its most significant drawback is the fact that it retains a n element o f chance in certain circumstances,
although this has been reduced to insignificance in the c o m p a r a b l e electoral systems o f T a s m a n i a , N o r t h e r n
I r e l a n d a n d the Irish Senate. T h e r a n d o m element may o c c u r as a consequence o f surplus distribution. I f the
surplus votes of an elected candidate are fewer than the n u m b e r o f transferable votes in the parcel being
examined, I r i s h electoral law provides, in effect, for a r a n d o m selection of papers to pass to continuing
candidates. F u r t h e r preferences o n these papers may affect the final outcome o f the election. T h i s p r o b l e m
c o u l d be overcome by amendment o f the electoral f o r m u l a , but in an electoral system where the formula is
already very complicated this w o u l d place a heavy extra b u r d e n o n the agencies responsible for the election
count. T e c h n o l o g i c a l development may, however, allow introduction o f the computer in elections, a n d this
c o u l d permit the elimination not merely o f the r a n d o m element but also o f certain other arbitrary provisions
that violate the n o r m s o f social choice theory.
I
I
INTRODUCTION
f o n e assumes t h a t t h e p r i m a r y o b j e c t o f a n y e l e c t o r a l system is t o p r o d u c e
a p a r l i a m e n t t h a t is r e p r e s e n t a t i v e
o f those w h o vote f o r it, then
the
y a r d s t i c k b y w h i c h a p a r t i c u l a r system is assessed m u s t b e its c a p a c i t y t o r e f l e c t
voters'
preferences.
Few w o u l d
dispute
the inadequacy
o f the
traditional
p l u r a l i t y ( " s t r a i g h t v o t e " ) system i n t h i s respect. I n c o u n t r i e s w h e r e t h i s system
is u s e d (such as t h e U n i t e d K i n g d o m , C a n a d a , t h e U n i t e d States a n d N e w
Z e a l a n d ) m a n y c a n d i d a t e s are e l e c t e d o n a m i n o r i t y v o t e a n d t h e results at
' W e are indebted to J o e Buckley, A l a n Hegarty a n d G o r d o n Lessels for c o m m e n t s o n an earlier draft.
1
n a t i o n a l level are typically n o n - p r o p o r t i o n a l . A t t e m p t s t o r e m o v e the m o r e
o u t s t a n d i n g a n o m a l i e s o f t h i s system w i t h i n s i n g l e - m e m b e r c o n s t i t u e n c i e s ,
s u c h as t h e t w o - b a l l o t system (France) o r t h e a l t e r n a t i v e v o t e system ( A u s t r a l i a ,
a n d a d v o c a t e d b y t h e F i a n n a F a i l a n n u a l c o n f e r e n c e o f 1984 f o r t h e R e p u b l i c o f
Ireland),
i m p r o v e t h e p o s i t i o n at c o n s t i t u e n c y l e v e l b y e n s u r i n g t h a t
the
w i n n i n g c a n d i d a t e has a m a j o r i t y o f t h e v o t e l o c a l l y b u t t y p i c a l l y g i v e a n o n proportional
r e s u l t at
n a t i o n a l l e v e l . L i s t - b a s e d systems o f p r o p o r t i o n a l
r e p r e s e n t a t i o n , h o w e v e r , e n s u r e n o t o n l y t h a t seats a r e d i s t r i b u t e d i n m u l t i ­
m e m b e r c o n s t i t u e n c i e s o n a q u o t a basis b u t also n o r m a l l y g i v e a p r o p o r t i o n a l
r e s u l t at n a t i o n a l l e v e l .
T h e l i s t s y s t e m o f p r o p o r t i o n a l r e p r e s e n t a t i o n is t h e o n e i n g e n e r a l use i n
w e s t e r n d e m o c r a c i e s . M u c h m o r e u n u s u a l is t h e s i n g l e t r a n s f e r a b l e v o t e (S'TV)
f o r m : t h i s is u s e d t o elect t h e l o w e r h o u s e o f p a r l i a m e n t i n o n l y t w o s o v e r e i g n
states ( I r e l a n d a n d M a l t a ) b u t i t is also u s e d i n d i r e c t e l e c t i o n s t o t h e A u s t r a l i a n
Senate a n d t o t w o s u b o r d i n a t e c h a m b e r s : t h e H o u s e o f A s s e m b l y o f T a s m a n i a
and
the
N o r t h e r n Ireland
Assembly. Despite
its
cumbersome
counting
procedures
a n d c e r t a i n o t h e r d r a w b a c k s , t h e S T V system m a y b e seen as
possessing
two
significant
advantages
over
list
systems
of proportional
r e p r e s e n t a t i o n . I n the first place, i t m a x i m i s e s the p o w e r o f the i n d i v i d u a l voter.
T h e v o t e r is e n t i t l e d t o r a n k a l l c a n d i d a t e s l i s t e d o n t h e b a l l o t p a p e r ; i n t h e
m o s t l i b e r a l list systems he has a l i m i t e d n u m b e r o f votes o f e q u a l v a l u e w h i c h
he can concentrate o n o n e o r m o r e candidates, b u t m o r e typically c u m u l a t i o n
o f t h i s k i n d is n o t p e r m i t t e d a n d t h e v o t e r m a y n o t v o t e f o r c a n d i d a t e s o f m o r e
than
one
party.
Secondly,
S T V - t y p e systems
seek t o
promote
a
multi­
d i m e n s i o n a l f o r m o f p r o p o r t i o n a l r e p r e s e n t a t i o n , u n l i k e u n i - d i m e n s i o n a l list
systems w h i c h seek t o secure t h e p r o p o r t i o n a l r e p r e s e n t a t i o n o n l y o f p a r t y
p o l i t i c a l loyalties. W i t h the STV, the voter m a y r a n k candidates i n terms n o t
merely
o f party but
also
o f r e g i o n a l , social, c u l t u r a l ,
gender
or
other
preferences.
S o m e o f t h e p r a c t i c a l costs o f t h e f l e x i b i l i t y a n d s o p h i s t i c a t i o n o f t h e S T V
system as a p p l i e d i n I r e l a n d are o b v i o u s : a m a r g i n a l l y m o r e d i f f i c u l t a c t i v i t y f o r
t h e v o t e r , a s u b s t a n t i a l l y m o r e c o m p l e x p r o c e d u r e f o r t h e r e t u r n i n g officer a n d
a
practical
limit
on
constituency
size,
which,
in
the
absence
of
any
2
c o m p e n s a t o r y m e c h a n i s m , t e n d s t o lessen p r o p o r t i o n a l i t y . A m o r e c o v e r t , b u t
no
less
significant,
cost
is
the
intrusion
of a
random
element
in
the
3
d e t e r m i n a t i o n o f the o u t c o m e o f an election i n certain circumstances .
1. I n the United K i n g d o m , for instance, 64 per cent of M P s elected in the February 1974 G e n e r a l E l e c t i o n
were returned o n a minority vote (i.e., m o r e voters opted for rival candidates than for them); a n d although
the T o r i e s "lost" the most recent British G e n e r a l E l e c t i o n in 1983 (in that their share of the poll, already a
minority, d r o p p e d to 42.4 per cent from 43.9 p e r c e n t in 1979) their share o f seats increased from 53.5 p e r c e n t
to 61.1 per cent, a n d M r s T h a t c h e r took the view that she h a d been given a mandate to govern.
2. F o r a review that covers also the broader political consequences o f this type of system see G a l l a g h e r (1984).
3. T h e original standard w o r k o n the subject drew attention to this p r o b l e m at a n early stage ( H u m p h r e y s ,
1911), as does the best recent review o f the S T V f o r m of p r o p o r t i o n a l representation ( L a k e m a n , 1974, pp.
139-144).
T h e e l e m e n t o f c h a n c e c a n n o t b e e l i m i n a t e d f r o m e l e c t o r a l contests. U n d e r
t h e p l u r a l i t y o r m a j o r i t y systems c a n d i d a t e s m a y t i e ; u n d e r l i s t systems, votes
f o r t w o p a r t y lists m a y b e e q u a l , a n d w i t h i n each l i s t t w o o r m o r e
candidates
m a y each b e e q u a l l y e n t i t l e d t o a seat. I n m a n y instances, t h e t i e - b r e a k i n g
mechanism
is a n
arbitrary rather
than
a random
one.
Electoral law i n
c o n t i n e n t a l E u r o p e , f o r i n s t a n c e , s o m e t i m e s p r e s c r i b e s t h a t t h e eldest o f t w o o r
m o r e c a n d i d a t e s w h o t i e b e e l e c t e d . I t is o u r o b j e c t i n t h i s p a p e r t o s h o w t h a t i n
t h e I r i s h e l e c t o r a l system t h e r e exists a s i g n i f i c a n t r a n d o m e l e m e n t o v e r a n d
above
this o m n i p r e s e n t
possibility o f a tied vote between candidates;
to
e x a m i n e t h e p r o b a b i l i t y o f t h e o u t c o m e o f a n e l e c t i o n b e i n g affected b y c h a n c e ;
a n d to e x p l o r e the possibility o f r e s o l v i n g this difficulty a n d o f e l i m i n a t i n g
certain other arbitrary procedures
might
find
i n t h e I r i s h e l e c t o r a l system t h a t p u r i s t s
objectionable.
I I R A N D O M E L E M E N T S I N T H E I R I S H E L E C T O R A L SYSTEM
U n d e r t h e S T V f o r m o f p r o p o r t i o n a l r e p r e s e n t a t i o n as o p e r a t e d i n I r e l a n d
f o r g e n e r a l e l e c t i o n s t o t h e D a i l , t h e r e a r e t h r e e o c c a s i o n s w h e r e ties b e t w e e n
candidates m a y take place a n d w h e r e the electoral l a w p r o v i d e s f o r r a n d o m
4
selection .
(1) O n a n y c o u n t , t w o o r m o r e c a n d i d a t e s m a y e x c e e d t h e q u o t a b y t h e same
a m o u n t . I n s u c h a n event, t h e s u r p l u s w h i c h is f i r s t d i s t r i b u t e d is t h a t o f t h e
c a n d i d a t e w i t h t h e l a r g e s t n u m b e r o f first p r e f e r e n c e v o t e s . I f t h e c a n d i d a t e s
h a v e t h e same n u m b e r , t h e n t h e first c o u n t at w h i c h t h e y h a d a n
unequal
n u m b e r o f votes is u s e d , t h e s u r p l u s o f t h e c a n d i d a t e w i t h t h e largest n u m b e r
b e i n g d i s t r i b u t e d first. I f t h e n u m b e r s o f votes a r e e q u a l o n a l l c o u n t s , t h e n t h e
r e t u r n i n g officer determines b y l o t w h i c h surplus w i l l be d i s t r i b u t e d
(2)
O n a n y c o u n t at w h i c h n o c a n d i d a t e reaches t h e q u o t a , t w o o r
candidates
m a y have
the lowest n u m b e r
first.
more
o f v o t e s . I n s u c h a n event,
the
c a n d i d a t e t o b e e l i m i n a t e d is t h e o n e w i t h t h e l o w e s t n u m b e r o f first p r e f e r e n c e
votes o r , i f these are e q u a l , t h e c a n d i d a t e w i t h t h e l o w e s t n u m b e r o f votes at t h e
first
c o u n t at w h i c h t h e n u m b e r o f votes are u n e q u a l . I f t h e n u m b e r s o f votes
are e q u a l o n a l l c o u n t s , t h e n t h e r e t u r n i n g o f f i c e r d e t e r m i n e s b y l o t w h i c h
c a n d i d a t e w i l l b e e l i m i n a t e d . T h i s p r o v i s i o n o b v i o u s l y g o v e r n s p r o c e d u r e at t h e
last c o u n t , w h e n t w o c a n d i d a t e s m a y t i e .
(3) O n a n y c o u n t w h e r e a s u r p l u s is b e i n g d i s t r i b u t e d a n d w h e r e t h e s u r p l u s is
less t h a n t h e n u m b e r o f t r a n s f e r a b l e p a p e r s , a n o t h e r m o r e c o m m o n b u t m o r e
t r i v i a l p r o b l e m m a y arise. T h e s u r p l u s votes a r e a l l o c a t e d i n p r o p o r t i o n t o t h e
d i s t r i b u t i o n o f n e x t a v a i l a b l e preferences i n t h e p a r c e l o f votes last r e c e i v e d b y
t h e e l e c t e d c a n d i d a t e (i.e., a l l o f his p a p e r s i f h e has b e e n e l e c t e d o n t h e
first
4. T h e electoral regulations to w h i c h we refer were adopted by the Electoral A c t , 1923 (No. 12 o f 1923). Rules
for the counting o f votes as a m e n d e d by subsequent legislation are appended to the official reports o n general
elections; see, for instance, I r e l a n d (1983), pp. 59-64.
c o u n t , o r a l l o f t h e t r a n s f e r r e d p a p e r s t h a t t o o k h i m o v e r t h e q u o t a i f h e has
b e e n e l e c t e d s u b s e q u e n t l y ) . Since t h e n u m b e r o f v o t e s t o b e t r a n s f e r r e d t o a
given c o n t i n u i n g candidate
is n o t n o r m a l l y a n i n t e g e r , t h e e l e c t i o n r u l e s
p r o v i d e t h a t as m a n y f r a c t i o n s as necessary ( i n o r d e r o f size) b e m a d e u p t o
w h o l e n u m b e r s t o e n s u r e t h a t t h e f u l l n u m b e r o f transfers takes p l a c e , t h e
r e m a i n i n g f r a c t i o n s b e i n g d i s r e g a r d e d . I f a t i e o c c u r s b e t w e e n t h e last f r a c t i o n s ,
t h a t c a n d i d a t e is c h o s e n w h o h a d t h e l a r g e s t n u m b e r o f votes o n t h e f i r s t o r o n
t h e e a r l i e s t s u b s e q u e n t c o u n t ; i f these a l l t i e , t h e r e t u r n i n g o f f i c e r d e t e r m i n e s b y
l o t w h i c h f r a c t i o n s h a l l b e c o m e a u n i t . A s a n e x a m p l e : i f a s u r p l u s o f 35 votes is
t o be d i s t r i b u t e d between f o u r candidates, A , B , C a n d D , i n the p r o p o r t i o n s
10:5:3:2, t h e n t h e c a n d i d a t e s a r e e n t i t l e d r e s p e c t i v e l y t o 17.50, 8.75,5.25 a n d 3.50
votes. Since t h e i n t e g e r p o r t i o n s o f these n u m b e r s a m o u n t o n l y t o 33, t h e t w o
r e m a i n i n g v o t e s g o t o B ( w h o s e f r a c t i o n a l p o r t i o n is t h e largest) a n d t o e i t h e r A
o r D ( w h o s e f r a c t i o n a l p o r t i o n s are n e x t largest, b u t tie) as d e t e r m i n e d b y
preferences o n earlier c o u n t s o r b y l o t .
S e l e c t i o n b y l o t , as i n t h e t h r e e k i n d s o f c o n t e x t o u t l i n e d a b o v e , is a r a r e
event, b u t c h a n c e f r e q u e n t l y p l a y s a p a r t i n d e t e r m i n i n g w h o is t o b e a D a i l
member.
This
happens
in
certain
circumstances
following
a
surplus
d i s t r i b u t i o n . W h e n a s u r p l u s is d i s t r i b u t e d , t h e exercise is n o t m e r e l y n o t i o n a l :
p h y s i c a l b a l l o t p a p e r s are t r a n s f e r r e d . B u t since t h e s u r p l u s is u s u a l l y less t h a n
t h e n u m b e r o f t r a n s f e r a b l e p a p e r s , n o t a l l p a p e r s m a y b e u s e d ; h e n c e , t h e r e is a
p r o b l e m o f s e l e c t i o n . T h e e l e c t o r a l r u l e s p r o v i d e t h a t t h e p a p e r s t h a t a r e to b e
transferred
physically be p i c k e d f r o m
the t o p o f the existing bundles
of
transferable papers, w h i c h , given the Electoral Act's p r o v i s i o n f o r a n i n i t i a l
5
m i x i n g o f b a l l o t p a p e r s , effectively gives a random selection . T h e s i g n i f i c a n c e o f t h i s
is t h a t t h e c o m p o s i t i o n o f t h e t r a n s f e r r e d b u n d l e s m i g h t h a v e a c r u c i a l effect o n
the o u t c o m e o f the election. O n e b u n d l e m i g h t , f o r instance, take
c a n d i d a t e o v e r t h e q u o t a . I n t h a t case t h e n e w l y - e l e c t e d c a n d i d a t e ' s
would
be
allocated
i n p r o p o r t i o n to
preferences in the randomly-composed
the
distribution
o f next
another
surplus
avaikble
bundle which brought him to the quota; w e r e t h i s
b u n d l e to be c o m p o s e d differently (which, given a different initial m i x i n g , i t
c o u l d ) t h e n his surplus w o u l d be transferred i n a different m a n n e r . T o illustrate
t h i s p o i n t a n d t o u n d e r l i n e its s i g n i f i c a n c e , w e d e s c r i b e b e l o w w h a t h a p p e n e d
o n o n e such occasion.
I l l V I C T O R Y BY C H A N C E : A N E X A M P L E F R O M T H E N O V E M B E R
GENERAL
1982
ELECTION
W e take h e r e t h e e x a m p l e o f t h e e l e c t i o n i n S l i g o - L e i t r i m i n t h e N o v e m b e r
1982 G e n e r a l E l e c t i o n , w h e n o n e c a n d i d a t e , Ray M a c S h a r r y , defeated a n o t h e r ,
5. T h e p r o v i s i o n for m i x i n g ballot papers dates from the Ballot Act o f 1872 a n d was initially intended to
ensure that the identity o f voters could not be inferred.
J o h n E l l i s , f o r t h e last seat by chance i n t h e sense t h a t t h e l a t t e r ' s v i c t o r y w o u l d
n o t h a v e b e e n i n c o m p a t i b l e w i t h w h a t is k n o w n o f t h e v o t e r s ' wishes. W e
r e p r o d u c e t h e r e s u l t s i n T a b l e 1. T h e c o n s t i t u e n c y was t o r e t u r n f o u r d e p u t i e s ,
a n d Joe M c C a r t i n (FG) a n d T e d N e a l o n (FG) were elected o n the t h i r d a n d
f o u r t h counts, respectively, f o l l o w i n g the e l i m i n a t i o n o f f o u r o t h e r candidates.
O n t h e f o u r t h c o u n t , a t w h i c h N e a l o n was e l e c t e d o n M c C a r t i n ' s s u r p l u s , t h r e e
F i a n n a F a i l c a n d i d a t e s r e m a i n e d : M a t t h e w B r e n n a n w i t h 9,004 votes, J o h n E l l i s
w i t h 8,753 a n d R a y M a c S h a r r y w i t h 8,752. T h e s u b s e q u e n t d i s t r i b u t i o n o f
N e a l o n ' s s u r p l u s p u t B r e n n a n c l e a r l y i n t h e l e a d , g i v i n g h i m 278 e x t r a votes,
b u t b y g i v i n g M a c S h a r r y a n e x t r a 126 t o E l l i s ' s 38 p u t t h e l a t t e r i n t o b o t t o m
p o s i t i o n , so t h a t h i s f e l l o w - p a r t y m e m b e r s
were declared elected
without
r e a c h i n g the q u o t a . Yet, f r o m the p u b l i s h e d results, i t appears that Ellis c o u l d
h a v e w o n t h e seat w i t h a l e a d o f 693 votes o v e r M a c S h a r r y .
Table 1: Results of general election, November 1982, in Sligo-Leitrim
Valid poll:
Number of seats:
Quota:
Candidate
Total
Count 3
(Lavin elim­
inated)
Count 4
(McCartin's
surpl,us)
Count 5
(Nealon's
surplus)
Trans­ Total
fers
Trans­ Total
fers
Trans­ Total
fers
- 36
-
_
+278
+ 38
-
+ 126
1,832
8,167
8,552
562
180
4,317
8,242
7,897
6,682
-1832
+ 345
+ 160
- 562
- 180
+ 241
+ 277
+ 676
+ 544
_
_
8,512
8,712
+ 456
+ 34
8,968
8,746
4,558
-4,558
8,519
8,573
7,226
+2,213
+ 130
+ 1,662
-10,732
--1,445
9,287
8,703
8,888
+ 49
+ 1,353
8,752
10,241
-954
8,878
9,287
-
+ 331
331
394
394
+512
906
46,431
-
46,431
-
-
46,431
Bree (-)
Brennan (FF)
Ellis (FF)
Finan (Lab)
Gorman (N-P)
Lavin (FG)
McCartin (FG)
MacSharry (FF)
Nealon (FG)
Non­
transferable
Count 2
(Bree, Finan,
Gorman elim­
inated)
Trans­ Total
fers
Count 1
46,431
4
9,287
+
—
63
-
46,431
+
+
7
9,004
8,753
46,431
—
9,282
8,791
9,287
Elected: M c C a r t i n ( C o u n t 3)
N e a l o n ( C o u n t 4)
B r e n n a n ( C o u n t 5)
M a c S h a r r y ( C o u n t 5)
Source: I r e l a n d , 1983, p. 44.
T o c l a r i f y t h i s p o i n t , w e l o o k i n m o r e d e t a i l i n T a b l e 2 at t h e last t h r e e c o u n t s .
T h i s t a b l e is b a s e d o n t h e a s s u m p t i o n t h a t a n y c o u n t m a y b e seen as c o m p r i s i n g
three
components:
(1) t h e s e l e c t i o n o f a p a r c e l o f p a p e r s f o r d i s t r i b u t i o n o n t h a t c o u n t a n d the
s o r t i n g o f these p a p e r s a c c o r d i n g t o n e x t a v a i l a b l e p r e f e r e n c e s ;
(2) t h e a t t r i b u t i o n o f votes t o c o n t i n u i n g c a n d i d a t e s a n d t h e p h y s i c a l a l l o c a t i o n
o f b a l l o t papers to each; a n d
(3) t h e c a l c u l a t i o n o f t h e n e w a g g r e g a t e v o t e f o r each c a n d i d a t e a n d d e c l a r a t i o n
o f the result o f that count.
Table 2: Last three counts in Sligo-Leitrim, general election, November 1982
Continuing
Candidate
Brennan (FF)
Ellis (FF)
McCartin (FG)
MacSharry (FF)
Nealon (FG)
Non-trans­
ferable
Count 3
(Lavin's votes)
Total
Papers Votes
in
attri­
votes
parcel
buted
Count 4
(McCartin's surplus)
Total
Papers Votes
votes
in
attri­
parcel buted
Count 5
(Nealon's surplus)
Total
Papers Votes
attri­
votes
in
parcel buted
456
34
2,213
130
1,662
456
34
2,213
130
1,662
8,968
8,746
10,732
8,703
8,888
53
11
-2,213
73
2,007
36
7
-1,445
49
1,353
9,004
8,753
9,287
8,752
10,241
126
-1,353
126
-954
-
9,282
8,791
9,287
8,878
9,287
63
63
394
69
0
394
911
512
906
278
38
-
278
38
Notes: Q u o t a = 9,287; four vacancies to be filled.
Source: I r e l a n d , 1983, p. 44, a n d information supplied by the office o f the R e t u r n i n g Officer for SligoLeitrim.
T h e t h r e e c o l u m n s u n d e r t h e h e a d i n g o f each c o u n t i n T a b l e 2 r e f e r t o these
t h r e e processes; t h e o f f i c i a l results r e p o r t t h e c o n t e n t s o f C o l u m n s (2) a n d (3),
e x c e p t f o r t h e f i r s t c o u n t , w h e r e these a r e i d e n t i c a l . I n cases w h e r e t h e p a r c e l i n
q u e s t i o n is m a d e u p o f p a p e r s o f a n e l i m i n a t e d c a n d i d a t e (as i n t h e t h i r d c o u n t
i n T a b l e 2), C o l u m n (1) is i d e n t i c a l t o C o l u m n (2). I n cases w h e r e t h e p a r c e l
consists o f votes r e c e i v e d b y a c a n d i d a t e d e e m e d e l e c t e d a n d w h e r e t h e r e p o r t e d
n u m b e r o f n o n - t r a n s f e r a b l e votes is g r e a t e r t h a n z e r o (as i n t h e f i f t h c o u n t ) , t h e
c o n t e n t s o f C o l u m n (1) m a y b e i n f e r r e d f r o m C o l u m n (2). I n cases w h e r e (the
p a r c e l consists o f votes r e c e i v e d b y a c a n d i d a t e d e e m e d e l e c t e d a n d w h e r e no
n o n - t r a n s f e r a b l e votes a r e r e p o r t e d (as i n t h e f o u r t h c o u n t ) , t h e c o n t e n t s o f
C o l u m n (1) c a n o n l y b e o b t a i n e d f r o m
the r e t u r n i n g officer; they are n o t
published.
I t w i l l b e clear t h a t o n t h e t h i r d c o u n t M c C a r t i n was t a k e n o v e r t h e q u o t a b y a
p a r c e l o f 2,213 p a p e r s f r o m L a v i n , l e a v i n g h i m w i t h a s u r p l u s v o t e o f 1,445. T h e
a c t u a l d i s t r i b u t i o n o f n e x t preferences a m o n g c o n t i n u i n g c a n d i d a t e s i n t h e f u l l
p a r c e l was n e x t a s c e r t a i n e d ; o f t h e 2,144 t r a n s f e r a b l e votes i n t h e M c C a r t i n
p a r c e l , 2,007 w e n t t o N e a l o n , f o r i n s t a n c e , 73 t o M a c S h a r r y , a n d so o n . Since
M c C a r t i n ' s a c t u a l s u r p l u s was o n l y 1,445, h o w e v e r , t h e v a l u e o f each o f these
e l e m e n t s h a d t o b e r e d u c e d p r o p o r t i o n a t e l y (each was t o b e m u l t i p l i e d b y t h e
r a t i o o f the surplus t o the n u m b e r o f transferable votes, 1,445/2,144 = 0.67). I n
N e a l o n ' s case t h e n e w figure was 1,353, i n M a c S h a r r y ' s 49, a n d so o n . N e a l o n ' s
1,353
b a l l o t papers were taken f r o m
MacSharry's
preferences
from
his sub-parcel
the t o p o f his sub-parcel
o f 73, a n d
so
on. The
o f 2,007,
next
available
o n these 1,353 p a p e r s a c t u a l l y selected f o r p h y s i c a l t r a n s f e r i n
N e a l o n ' s case h a v e b e e n c l e a r l y e s t a b l i s h e d , b u t a d i f f e r e n t s e l e c t i o n o f p a p e r s
f r o m his b u n d l e o f 2,007 m i g h t h a v e g i v e n a d i f f e r e n t r e s u l t , as i l l u s t r a t e d i n
T a b l e 3. T h e n e x t a v a i l a b l e preferences o n t h e 654 p a p e r s t h a t r e m a i n e d i n t h e
p a r c e l t h a t t o o k N e a l o n o v e r t h e q u o t a c a n n o t b e e s t a b l i s h e d , b u t i f (as is
p o s s i b l e b u t h i g h l y u n l i k e l y ) a l l o f these w e n t t o E l l i s a n d i f , m o r e o v e r (as is also
p o s s i b l e b u t also v e r y u n l i k e l y ) , these p a p e r s h a d a c t u a l l y b e e n selected f o r
physical transfer w h i l e B r e n n a n a n d M a c S h a r r y received n o f u r t h e r papers,
t h e n t h e o u t c o m e w o u l d h a v e b e e n as i n t h e e x t r e m e r i g h t - h a n d c o l u m n o f
T a b l e 3. T h e o r d e r o f e l e c t i o n w o u l d h a v e b e e n E l l i s - B r e n n a n r a t h e r t h a n
Brennan-MacSharry.
It will
be
clear
that
while
this
exact
outcome
is
t h e o r e t i c a l l y p o s s i b l e b u t i n p r a c t i c e e x t r e m e l y u n l i k e l y , a less e x t r e m e b i a s i n
Ellis's f a v o u r ( w h i c h w o u l d b e m u c h less i m p r o b a b l e ) c o u l d s t i l l leave h i m w i t h
a seat.
Table 3: Possible outcome on distribution of surplus onfifth count in Sligo-Leitrim, general election, November
1982
Next
available
preference
Not known
Brennan
Ellis
MacSharry
Non-transferable
Total
Actual
distribution
of Nealon's
parcel on
fifth count
Other possible
selection
Actual selection made on
fifth count
Papers
654
278
38
126
911
2007
Votes
Result
—
_
_
278
38
126
911
1353
278
38
126
512
954
9,282
8,791
8,878
906
-
Papers
Votes
Result
_
_
0
692
0
661
1353
0
692
0
262
954
—
9,004
9,445
8,752
656
-
O n e c o u l d , o f c o u r s e , p i c k o t h e r e x t r e m e cases: o n e c o u l d a s s u m e t h a t a l l o f
t h e transfers i n t h e " u n k n o w n " b u n d l e passed t o B r e n n a n a n d t h a t t h e t w o
other c o n t i n u i n g candidates
r e c e i v e d n o f u r t h e r preferences,
or one
could
make a s i m i l a r l y favourable a s s u m p t i o n a b o u t M a c S h a r r y . I n theory, then, the
range o f possible results i n the S l i g o - L e i t r i m e l e c t i o n includes the f o l l o w i n g
t h r e e e x t r e m e e x a m p l e s i n t h e case o f t h e last t w o vacancies (the figures i n
p a r e n t h e s e s i n d i c a t e t h e results
o f t h e last c o u n t , e l e c t e d c a n d i d a t e s
i n i t a l i c s a n d " N T " refers t o n o n - t r a n s f e r a b l e v o t e s ) :
Brennan (9,936), Ellis (8,753), M a c S h a r r y (8,752), N T = 416
Ellis (9,445), Brennan (9,004), M a c S h a r r y (8,752), N T = 656
MacSharry (9,532), Brennan (9,004), E l l i s (8,753),
N T = 568
are
IV T H E ROLE OF PROBABILITY I N DETERMINING
ELECTION
OUTCOMES
I t w i l l b e c l e a r f r o m t h e last s e c t i o n t h a t t h e r e is a possibility u n d e r
Irish
e l e c t o r a l l a w t h a t , even i f t h e i n t e r v e n t i o n o f c o u n t i n g o r c a l c u l a t i o n e r r o r s is
d i s c o u n t e d , a r e p e a t o f t h e process o f i n i t i a l m i x i n g , c o u n t i n g a n d d i s t r i b u t i n g
o f b a l l o t papers f r o m start to finish m a y result i n :
(1) a d i f f e r e n t n u m b e r o f votes u l t i m a t e l y b e i n g a t t r i b u t e d t o each c a n d i d a t e ;
a n d i n s o m e cases
(2) a d i f f e r e n t o u t c o m e f o r t h e e l e c t i o n , i n t h a t a " d e f e a t e d " a n d a " s u c c e s s f u l "
candidate m a y exchange
places.
Table 4: Elements in an election by single
transferable vote ainmulti-member constituency
Count 1
Candidate l
R
Candidate 2
R
Candidate M
R
2 1 S21 T21
R
ml S i T
m
Non-trans­
ferable
R
Total
Note:
l i Sii T n
R
01
Soi
...
Count 2
R
m l
TQI
R
R,S,T,
1 2
S T
2 2
S
m2
S
R
1 2
1 2
2 2
T 2
S
T 2
m
• ••
T
0 2 02 0 2
R
lnSi Ti
n
R
2
m 2
Count N
2 $2 "^2
S
n
T
2n 2n 2n
R
mnS
R
S
u n
0 n
m n
T
R S T
n
n
T
m n
0 n
n
Rjj = Number of papers counted
Sjj = Number of votes attributed
Ty = Aggregate or cumulative number of votes attributed.
I t r e m a i n s t o d e f i n e these t w o events m o r e p r e c i s e l y a n d t o l o o k at t h e probability
o f e i t h e r e v e n t i n g i v e n c o n d i t i o n s . T o b e g i n , t h e process o f c o u n t i n g votes i n a
p a r t i c u l a r c o n s t i t u e n c y m a y b e e n v i s a g e d as f o l l o w i n g t h e l i n e s i n d i c a t e d i n
T a b l e 4. I n t h i s t a b l e R , Sy a n d T y r e p r e s e n t , r e s p e c t i v e l y , t h e t h r e e c o l u m n s o f
y
T a b l e 2 : t h e n u m b e r o f b a l l o t p a p e r s c o u n t e d , t h e n u m b e r o f votes a l l o c a t e d
a n d t h e a g g r e g a t e n u m b e r o f votes f o r c a n d i d a t e I o n c o u n t J , w h e r e there a r e
M
c a n d i d a t e s a n d N c o u n t s . T h e p e n u l t i m a t e r o w refers t o n o n - t r a n s f e r a b l e
p a p e r s , w h e r e R j r e p r e s e n t s the t o t a l n u m b e r o f n o n - t r a n s f e r a b l e
0
o c c u r r i n g o n each c o u n t a n d S
oj
papers
a n d T j represent, respectively, the r e p o r t e d
0
n u m b e r o f n o n - t r a n s f e r a b l e votes n o t effective a n d t h e a g g r e g a t e n u m b e r o f
n o n - t r a n s f e r a b l e votes o n each c o u n t . T h e b o t t o m r o w r e p r e s e n t s t h e c o l u m n
t o t a l s . O n t h e first c o u n t a l l b a l l o t p a p e r s are c o u n t e d , g i v i n g t h e t o t a l p o l l ( R , ) ;
i n v a l i d p a p e r s are s e p a r a t e d o u t ( R ) a n d t h e n u m b e r o f v a l i d p a p e r s a t t r i b u t e d
0 1
t o t h e v a r i o u s c a n d i d a t e s is c o u n t e d ( R : i = i , M ) . T h e v a l i d votes a r e t h e n
n
a l l o c a t e d t o t h e a p p r o p r i a t e c a n d i d a t e s a n d t h e o u t c o m e o f t h e first c o u n t is
known
(T = S
n
;1
= R
( T = T j = S, = R , - R
0 1
n
: i=i,M);
the
total
valid
poll,
T,
is
known
) a n d t h e q u o t a , Q , is c a l c u l a t e d :
Q ^ = ( T / ( U + 1 ) ) + 1, i g n o r i n g a n y r e m a i n d e r ,
(1)
w h e r e U is t h e n u m b e r o f seats t o b e f i l l e d . O n s u b s e q u e n t c o u n t s e i t h e r a
s u r p l u s is d i s t r i b u t e d o r t h e votes o f o n e o r m o r e e l i m i n a t e d c a n d i d a t e s
are
d i s t r i b u t e d . I n t h e f o r m e r cases, t h e s u r p l u s V- is c a l c u l a t e d :
V
•
where T
k J
_
h
T
j= M-h-Q.
*
(2)
represents the aggregrate v o t e o f elected candidate K o n c o u n t J - H
the c o u n t o n w h i c h he attained the q u o t a . T h e b a l l o t papers e x a m i n e d are those
i n t h e p a r c e l t h a t t o o k K o v e r t h e q u o t a , so t h a t :
Rj = S _
kJ
(3)
h
I n t h e l a t t e r cases, t h e b a l l o t p a p e r s e x a m i n e d a r e t h o s e o f t h e e l i m i n a t e d
c a n d i d a t e s , so t h a t :
Rj=T
(4)
i < H l
w h e r e t h e s u m m a t i o n is o v e r a l l c a n d i d a t e s e l i m i n a t e d o n t h e p r e v i o u s c o u n t . I t
w i l l be n o t i c e d that T a b l e 4 resembles
a n o r t h o d o x r e s u l t sheet f o r a D a i l
constituency i n a general election, except that i n the latter the f u l l
details
r e g a r d i n g t h e d i s t r i b u t i o n o f p a p e r s at e a c h c o u n t (R^) are n o t g i v e n .
T h e r a n d o m e l e m e n t i n t r u d e s , as w e h a v e i n d i c a t e d , i n c e r t a i n instances o f
s u r p l u s d i s t r i b u t i o n . T h e p r o c e d u r e f o r d i s t r i b u t i n g s u r p l u s V j o n c o u n t J is as
f o l l o w s : Rj is p a r t i t i o n e d i n t o its c o m p o n e n t p a r t s a c c o r d i n g t o n e x t a v a i l a b l e
preferences f o r c o n t i n u i n g candidates, a n d the n u m b e r o f transferable papers,
Pj, is c a l c u l a t e d , w h e r e :
Pj = R j - R o j -
(5)
T h e n e x t step d e p e n d s o n w h e t h e r o r n o t Pj exceeds t h e s u r p l u s , V J ; t h u s ,
i f Pj > V j ,
t h e n Sg = Ry * ( V / P j )
ifP <Vj,
t h e n Sij = Ry
and S j = o
(6)
0
j
and S
oj
= Vj-Pj.
(7)
I n t h e f o r m e r case, b a l l o t p a p e r s a r e selected a t r a n d o m f r o m Ry t o m a k e u p Sy;
i n t h e l a t t e r case t h e y are selected a t r a n d o m f r o m R j t o m a k e u p S j. T h e l a t t e r
0
case is o f n o
further
interest,
since
the papers
0
thus
transferred
are
not
s u b s e q u e n t l y u s e d . I n t h e f o r m e r case, h o w e v e r , i t is i m p o r t a n t t h a t t h e s a m p l e
d r a w n reflects a c c u r a t e l y t h e c o n t e n t s o f t h e b u n d l e f r o m w h i c h i t was t a k e n . ( I n
o t h e r w o r d s , the d i s t r i b u t i o n o f n e x t available preferences
for continuing
c a n d i d a t e s i n S- m u s t b e e x a c t l y p r o p o r t i o n a l t o t h a t i n Ry.)
W e n o w t u r n t o l o o k at t h e probability o f e l e c t i o n s b e i n g affected b y c h a n c e . I n
t h e g e n e r a l case w e r e q u i r e t h a t t h e p r o b a b i l i t y b e e q u a l t o o n e t h a t , i n t h e case
of
any sub-parcel
o f p a p e r s passed t o a c a n d i d a t e
as p a r t o f a
surplus
d i s t r i b u t i o n , t h e p r o p o r t i o n o f f u r t h e r preferences f o r c o n t i n u i n g c a n d i d a t e s
b e e x a c t l y e q u a l t o t h a t i n t h e p a r c e l f r o m w h i c h i t was d r a w n . I f a p a r c e l o f N
votes takes a c a n d i d a t e o v e r t h e q u o t a , l e a v i n g h i m w i t h a s u r p l u s o f M , a n d i f
t h e p a r c e l c o n t a i n s n p a p e r s t h a t t r a n s f e r l a t e r t o c a n d i d a t e X , w h a t is t h e
p r o b a b i l i t y t h a t M p a p e r s selected at r a n d o m f r o m t h i s p a r c e l w i l l c o n t a i n
e x a c t l y m p a p e r s t h a t t r a n s f e r l a t e r t o c a n d i d a t e X ? ( T o satisfy t h e c r i t e r i o n o f
fairness, o f c o u r s e , w e r e q u i r e t h a t m b e t h e n e a r e s t i n t e g e r t o ( n / N ) * M . ) T h i s
p r o b a b i l i t y m a y b e d e f i n e d as f o l l o w s :
where
( J
m
d e n o t e s m i t e m s selected f r o m M i t e m s . I n T a b l e 5 w e t a b u l a t e t h e
p r o b a b i l i t i e s f o r t h e case w h e r e m / M = 0.5. T o give a c o n c r e t e e x a m p l e , T a b l e 5
tells us t h a t i f 20 p a p e r s are p i c k e d a t r a n d o m f r o m a p a r c e l o f 100 ( i n 50 o f
w h i c h t h e n e x t a v a i l a b l e p r e f e r e n c e goes t o c a n d i d a t e X ) , t h e p r o b a b i l i t y is v e r y
s m a l l t h a t X w i l l get his d u e s h a r e ( o f 10 n e x t p r e f e r e n c e s ) ; m o r e s p e c i f i c a l l y , t h e
p r o b a b i l i t y is 0.1969, o r r o u g h l y o n e i n
five.
I n t h e case o f o t h e r
typical
selections t h e p r o b a b i l i t y o f a n a r i t h m e t i c a l l y j u s t r e s u l t is s i m i l a r l y l o w . T h e
v a l u e s i n t h i s t a b l e , i t s h o u l d b e p o i n t e d o u t , d e p e n d o n o n e a s s u m p t i o n t h a t is
r e l a t i v e l y f a v o u r a b l e t o t h e e l e c t o r a l system ( t h a t t h e r e are o n l y t w o p o s s i b l e
o u t c o m e s , preferences
passing o r n o t passing t o X ) a n d one
unfavourable
a s s u m p t i o n ( t h a t t h e r a t i o b e t w e e n these o u t c o m e s is 1:1). A s t h e n u m b e r o f
possible outcomes
increases, i n o t h e r w o r d s , t h e values f o r p r o b a b i l i t i e s
c o r r e s p o n d i n g t o t h o s e i n T a b l e 5 d r o p ; b u t as t h e r a t i o b e t w e e n
outcomes
changes t h e c o r r e s p o n d i n g values rise.
Table 5:' Probability of selecting m items of type X in a sample of size M drawn from a population of sir.e N
where there are n items of type X and m/M — n/N = 0.5
Size
Of
Popu­
lation
(N)
10
20
50
100
200
500
1000
2000
5000
10000
10
20
1.0000
.3437
.2748
.2593
.2525
.2486
.2473
.2467
.2463
.2462
1.0000
.2267
.1969
.1857
.1798
.1780
.1771
.1765
.1764
Size of sample (M)
50
100
-
-
1.0000
.1584
.1296
.1183
.1152
.1137
.1128
.1126
1.0000
.1124
.0890
.0839
.0817
.0804
.0800
-
1,000
2,000
200
500
-
-
-
-
-
1.0000
--
--
.0504
.0412
.0376
.0366
1.0000
.0357
.0282
.0266
1.0000
.0727
.0630
.0594
.0575
.0569
-
-1.0000
.0230
.0199
I t w i l l b e clear, t h e n , t h a t i n m o s t cases i t is o v e r w h e l m i n g l y i m p r o b a b l e t h a t
the
final
t a l l y o f votes w i l l b e " a c c u r a t e " i n c o n s t i t u e n c i e s w h e r e a p a r c e l o f
votes is f u r t h e r d i s t r i b u t e d u n d e r t h e c o n d i t i o n s d e s c r i b e d a b o v e . I n t h e S l i g o -
L e i t r i m case, f o r i n s t a n c e , i f o n e assumes t h a t N e a l o n ' s p a r c e l o f 2,007 votes
c o n t a i n s , say, 200 c o n t i n u i n g preferences f o r M a c S h a r r y , t h e p r o b a b i l i t y t h a t a
r a n d o m s e l e c t i o n o f 1,353 o f these w i l l c o n t a i n M a c S h a r r y ' s e x a c t d u e share o f
135 is v e r y s l i g h t . I t s h o u l d , h o w e v e r , b e p o i n t e d o u t t h a t a s t a t i s t i c a l l y
inaccurate result m a y n o t prejudice the o u t c o m e o f the election i n terms o f
who
w i n seats. T h e " v i c t o r y m a r g i n " o f t h e weakest w i n n i n g c a n d i d a t e m a y b e t a k e n
as i n d i c a t i n g a n a c c e p t a b l e e r r o r m a r g i n i n t h o s e cases w h e r e t h e r a n d o m
e l e m e n t is a f a c t o r , a n d T a b l e 5 c o u l d b e r e - c o m p u t e d f o r a n y g i v e n r a n g e o f
e r r o r . T o t a k e t h e e x a m p l e g i v e n a b o v e , i f i n s e l e c t i n g 20 p a p e r s f r o m a b u n d l e
of
100 ( o f w h i c h
50 g i v e c a n d i d a t e
X as
n e x t available preference)
the
r e q u i r e m e n t t h a t e x a c t l y 10 o f t h o s e c h o s e n also l i s t X n e x t is r e l a x e d t o a l l o w
a n e r r o r m a r g i n o f o n e o n e i t h e r side (i.e., 9, 10 o r 11 p a p e r s l i s t i n g X as n e x t
a v a i l a b l e p r e f e r e n c e w o u l d b e a c c e p t a b l e ) t h e chances o f a s a t i s f a c t o r y o u t c o m e
rise t o 0.5373, o r a p p r o x i m a t e l y 1 i n 2.
O n t h e o n e h a n d , t h e n , t h e d e g r e e o f a r i t h m e t i c a l a c c u r a c y w i l l t e n d t o f a l l as
t h e n u m b e r o f p a p e r s c h o s e n a t r a n d o m increases, a n d t h e l a t t e r w i l l t e n d t o
increase as t h e r a t i o o f v a l i d votes t o vacancies increases (the q u o t a w o u l d b e a
crude a p p r o x i m a t i o n o f this r a t i o ) . O n the o t h e r h a n d , the w i n n i n g m a r g i n o f
t h e last c a n d i d a t e elected w i l l also t e n d t o increase as t h e q u o t a increases. T h u s ,
a l t h o u g h t h e e r r o r i n t e r m s o f a b s o l u t e n u m b e r s o f votes increases as t h e q u o t a
increases, t h e e r r o r as a p e r c e n t a g e o f t h e q u o t a w i l l t e n d t o decrease a n d t h e
p r o b a b i l i t y o f t h e o u t c o m e o f a n e l e c t i o n b e i n g affected w i l l t e n d t o d i m i n i s h .
V T H E O R I G I N OF T H E R A N D O M
ELEMENT
T h e r u l e s f o r c o u n t i n g votes i n I r i s h e l e c t i o n s h a v e l o n g r o o t s . T h e p r i n c i p l e
o n w h i c h t h e y w e r e b a s e d was i n v e n t e d i n 1855 b y a D a n i s h m a t h e m a t i c i a n , C.
G.
A n d r a e , a n d a p p l i e d to elections to the D a n i s h Rigsraad. A c c o r d i n g to
A n d r a e ' s system v o t e r s r a n k e d c a n d i d a t e s , t h e b a l l o t p a p e r s w e r e m i x e d i n a n
u r n a n d d r a w n o u t o n e b y o n e , a n d votes w e r e a t t r i b u t e d t o c a n d i d a t e s i n i t i a l l y
a c c o r d i n g t o first preferences. T h e r a n d o m e l e m e n t a p p e a r e d , h o w e v e r , w h e n
any candidate
reached
the electoral q u o t a :
h e was i m m e d i a t e l y d e c l a r e d
elected, a n d his n a m e was i g n o r e d i n a n y f u r t h e r b a l l o t p a p e r s (Sterne, 1871, p p .
233-237).
A
similar
independently, by an
system
was
simultaneously
Englishman, Thomas
devised,
Hare. Hare's
apparently
original
scheme
c o n t a i n e d a r a n d o m e l e m e n t i d e n t i c a l t o t h a t o f A n d r a e (see H a r e , 1859, p p .
186-200). I t s h o u l d be p o i n t e d o u t t h a t the r a n d o m e l e m e n t i n the o r i g i n a l
A n d r a e a n d H a r e systems was r a t h e r g r e a t : i t w o u l d affect any c o u n t o n w h i c h a
s u r p l u s was b e i n g d i s t r i b u t e d , a n d n o t m e r e l y c o u n t s s u b s e q u e n t t o a s u r p l u s
distribution.
T h i s system a r o u s e d
t h e i n t e r e s t o f s o m e i n t e l l e c t u a l s , b u t few f u r t h e r
a t t e m p t s at p r a c t i c a l a p p l i c a t i o n w e r e m a d e , a n d a l l o f these w e r e i n e x i s t i n g o r
f o r m e r B r i t i s h possessions. T h e
first
s u c h a t t e m p t was i n T a s m a n i a ,
where
H a r e ' s s y s t e m was i n t r o d u c e d b y t h e E l e c t o r a l A c t o f 1896 o n a l i m i t e d basis.
T h i s r e p r e s e n t e d t h e f i r s t stage i n t h e e l i m i n a t i o n o f t h e r a n d o m e l e m e n t . T h e
act i n c o r p o r a t e d a m o d i f i c a t i o n o f t h e c o u n t i n g r u l e s b y A t t o r n e y - G e n e r a l
Clark which
p r o v i d e d that
the surplus
votes
o f a n elected
candidate
be
d i s t r i b u t e d i n t h e same p r o p o r t i o n s as t h e d i s t r i b u t i o n o f n e x t preferences i n
t h e p a r c e l t h a t t o o k h i m o v e r t h e q u o t a ; b a l l o t p a p e r s w o u l d , h o w e v e r , i n effect
be
selected
at r a n d o m
f o r physical transfer
(Piesse, 1913, p p . 6 0 - 6 2 ) . I t s
i n n o v a t o r y status m e a n t t h a t t h i s system was i n t e n s i v e l y s t u d i e d . I n p a r t i c u l a r ,
t h e s u r v i v i n g r a n d o m e l e m e n t c a m e i n f o r m u c h c r i t i c i s m . T h e s e c o n d stage i n
its r e m o v a l i n v o l v e d a d o p t i o n o f t h e " G r e g o r y m e t h o d " , so c a l l e d after t h e
p e r s o n w h o i n v e n t e d i t i n 1880. T h i s was b u i l t i n t o t h e T a s m a n i a n E l e c t o r a l A c t
o f 1907, w h i c h e x t e n d e d t h e system t o t h e w h o l e m e m b e r s h i p o f t h e H o u s e o f
6
A s s e m b l y . T h e act p r o v i d e d t h a t , w h e n a s u r p l u s was t o b e d i s t r i b u t e d , all
b a l l o t p a p e r s i n t h e p a r c e l w h i c h b r o u g h t t h e successful c a n d i d a t e o v e r t h e
q u o t a b e f u r t h e r d i s t r i b u t e d , t h o u g h a t a p p r o p r i a t e l y r e d u c e d v a l u e (Piesse,
1913, p p . 6 7 - 7 1 ) . A f u r t h e r r e f i n e m e n t i n t r o d u c e d i n t h e e l e c t o r a l l a w o f t h e
S o u t h A f r i c a n Senate m a y b e i n t e r p r e t e d as a t h i r d stage i n t h e r e m o v a l o f t h e
r a n d o m e l e m e n t . T h i s s o u g h t t o a v o i d t h e loss o f v a l u e o w i n g t o d i s r e g a r d o f
fractions ( w h i c h c o u l d be o f considerable i m p o r t a n c e i n a s m a l l electorate)' b y
t r e a t i n g e a c h b a l l o t p a p e r as i f i t h a d t h e v a l u e 100 ( F l a n d i n , 1914, p p . 4 3 - 5 6 ) .
I n B r i t a i n itself, w h e r e e l e c t o r a l r e f o r m was m u c h s l o w e r t o take r o o t , t h e
sophistication
of
the
complication.
A
Royal
Gregory
method
Commission
of
was
felt
to
Enquiry
be
into
an
unnecessary
electoral
systems
e s t a b l i s h e d b y t h e B r i t i s h P a r l i a m e n t i n 1909 f e l t t h a t t h e a d d i t i o n a l a c c u r a c y
gained b y this r e f i n e m e n t " w o u l d n o t i n o u r o p i n i o n repay the extra l a b o u r
i n v o l v e d " ^ U n i t e d K i n g d o m , 1910). T h e r e g u l a t i o n s a d o p t e d f o r c e r t a i n l i m i t e d
purposes
and
advocated
by
the
Proportional
Representation
Society
consequently r e t a i n e d this r a n d o m element that r e m a i n e d i n the o r i g i n a l H a r e C l a r k r u l e s f o r s u r p l u s d i s t r i b u t i o n . I t h a d b e e n i n t e n d e d t h a t t h i s system b e
a d o p t e d f o r e l e c t i o n s t o t h e Senate a n d , i n s o m e c o n s t i t u e n c i e s , t o t h e H o u s e o f
C o m m o n s o f the I r i s h P a r l i a m e n t p r o p o s e d i n the G o v e r n m e n t o f I r e l a n d A c t ,
1914. T h e c o l l a p s e o f t h i s m e a s u r e m e a n t t h a t , a p a r t f r o m a " m o d e l e l e c t i o n "
c a r r i e d o u t t h r o u g h t h e n e w s p a p e r s u n d e r t h e auspices o f t h e P r o p o r t i o n a l
R e p r e s e n t a t i o n Society o f I r e l a n d i n 1911, i t was n o t u n t i l t h e e l e c t i o n i n I 9 1 9 i n
the t r o u b l e d b o r o u g h o f Sligo that I r i s h people got their first o p p o r t u n i t y o f
using
this
system.
The
success o f t h i s e x p e r i m e n t
was
followed
by
the
i n t r o d u c t i o n o f t h e s a m e system f o r a l l l o c a l e l e c t i o n s i n t h e c o u n t r y b y t h e
L o c a l G o v e r n m e n t ( I r e l a n d ) A c t , 1919, a n d f o r e l e c t i o n s t o t h e
proposed
S o u t h e r n a n d N o r t h e r n Houses o f C o m m o n s by the G o v e r n m e n t o f I r e l a n d
6. T h i s act also replaced the H a r e quota ( n u m b e r of valid votes divided by the n u m b e r of vacancies) by the
D r o o p quota ( n u m b e r o f valid votes divided by one m o r e than the n u m b e r o f vacancies) (Piesse, 1912, p. 6).
7. F o r instance, in the T a s m a n i a n H o u s e o f Assembly elections o f 1979 i n the constituency o f F r a n k l i n 137
votes were "lost" i n this m a n n e r out o f a total valid p o l l o f 48,766 ( T a s m a n i a , 1980b, p. 30).
A c t , 1920. T h e r e g u l a t i o n s t h e n a d o p t e d , t h o u g h d r o p p e d i n t h e 1920s f o r l o c a l
a n d p a r l i a m e n t a r y e l e c t i o n s i n N o r t h e r n I r e l a n d w h e n t h e p l u r a l i t y system was
r e - i n t r o d u c e d , w e r e b u i l t i n t o t h e e l e c t o r a l l a w o f t h e I r i s h Free State b y t h e
E l e c t o r a l A c t , 1923, a n d r e m a i n t h e basic r e g u l a t i o n s f o r I r i s h l o c a l a n d g e n e r a l
e l e c t i o n s . T h e y w e r e f u r t h e r e x t e n d e d t o g o v e r n p o p u l a r e l e c t i o n s t o t h e Senate
o n t h e o n l y o c c a s i o n o n w h i c h these t o o k p l a c e (1925).
T h e I r i s h r e g u l a t i o n s w e r e a d o p t e d i n t h e k n o w l e d g e o f t h e existence o f t h e
r a n d o m element; this h a d been p o i n t e d o u t forcefully b y one critic o f the STV
system,
w h o advocated
instead
a modification
o f the B e l g i a n list
system
8
( M e r e d i t h , 1913, p p . 8 7 - 9 0 ) . A c c o u n t has h a d t o b e t a k e n o f t h i s c r i t i c i s m i n t h e
case o f Senate e l e c t i o n s . T h e Senates o f S o u t h e r n I r e l a n d a n d N o r t h e r n I r e l a n d
proposed
b y t h e G o v e r n m e n t o f I r e l a n d A c t , 1920, w e r e t o h a v e
components,
elected
b u t t h e e l e c t o r a t e i n e a c h case w o u l d b e v e r y s m a l l . I n t h e
N o r t h e r n I r e l a n d Senate ( 1 9 2 1 - 1 9 7 2 ) , f o r i n s t a n c e , 24 m e m b e r s w e r e t o b e
elected f o r a n eight-year t e r m ( h a l f o f the m e m b e r s h i p r e t i r i n g a n d b e i n g
r e p l a c e d e v e r y f o u r years) b y 52 m e m b e r s o f t h e H o u s e o f C o m m o n s . A s
elections were to be b y the S T V f o r m o f p r o p o r t i o n a l representation, the q u o t a
w o u l d b e v e r y s m a l l (at m o s t , 5 votes) a n d t h e r a n d o m e l e m e n t , c o n s e q u e n t l y ,
w o u l d b e v e r y h i g h . A s i m i l a r p r o b l e m e x i s t e d i n t h e case o f t h e Senate o f t h e
I r i s h Free State (elected b y m e m b e r s o f t h e O i r e a c h t a s e x c e p t i n 1925) a n d o f t h e
p r e s e n t S e a n a d E i r e a n n (elected b y a v e r y s m a l l e l e c t o r a l c o l l e g e u p t o 1947 a n d
b y a l a r g e r o n e since t h e n ) . T h e q u o t a f o r e l e c t i o n i n S e a n a d E i r e a n n i n r e c e n t
e l e c t i o n s , f o r i n s t a n c e , has b e e n less t h a n 100 i n t h e case o f m o s t p a n e l s . I t was,
c o n s e q u e n t l y , f o u n d necessary t o a d o p t t h e G r e g o r y m o d i f i c a t i o n i n e l e c t i o n s
t o t h e Senates c r e a t e d b y t h e G o v e r n m e n t o f I r e l a n d A c t ( U n i t e d K i n g d o m ,
1921), a n d a s i m i l a r r e f o r m t o o k p l a c e i n t h e S o u t h ( I r e l a n d , 1927, p p . 117-119).
These regulations, i n c o r p o r a t i n g the G r e g o r y m o d i f i c a t i o n , c o n t i n u e to a p p l y
i n e l e c t i o n s t o S e a n a d E i r e a n n . T h e y a r e also a d v o c a t e d b y t h e E l e c t o r a l
Reform
Society
o f the
United
Kingdom,
which
has
built
the
Gregory
m o d i f i c a t i o n i n t o its set o f m o d e l e l e c t i o n r u l e s ( N e w l a n d a n d B r i t t o n , 1976);
t h i s was a d o p t e d also i n t h e e l e c t o r a l l a w f o r t h e N o r t h e r n I r e l a n d A s s e m b l y
( U n i t e d K i n g d o m , 1973).
I t m a y b e a p p r o p r i a t e at t h i s stage t o s u m m a r i s e t h e m e a s u r e s t h a t h a v e b e e n
t a k e n t o r e d u c e t h e r a n d o m e l e m e n t i n S T V - b a s e d systems o f p r o p o r t i o n a l
9
representation .
O f t h e five m o s t i m p o r t a n t d i r e c t l y - e l e c t e d p a r l i a m e n t a r y
assemblies t h a t use t h i s system, t h e e l e c t o r a l r e g u l a t i o n s i n t h r e e ( D a i l E i r e a n n ,
the H o u s e o f Representatives
o f M a l t a a n d t h e A u s t r a l i a n Senate) r e t a i n t h e
o r i g i n a l H a r e - C l a r k rules f o r surplus d i s t r i b u t i o n a n d thus p e r m i t the i n t r u s i o n
8. T h e drafters o f the Electoral Act o f 1923 calculated the p r o b a b l e effects o f the r a n d o m element but decided
that they w o u l d not justify a d o p t i o n o f the G r e g o r y modification (information provided by Ernest Blythe to
Noel M u l c a h y in 1968).
9. F o r reviews o f the two most important systems outside I r e l a n d , see G r e g o r y (1971), Proctor (1980) a n d
O ' C o n n e l l (1983).
o f a r a n d o m e l e m e n t i n c e r t a i n c i r c u m s t a n c e s w h e r e s u r p l u s votes are b e i n g
d i s t r i b u t e d ( I r e l a n d , 1983, p p . 5 9 - 6 4 ; M a l t a , 1970, a r t . 1 1 ; A u s t r a l i a , 1980, a r t .
135). I t s h o u l d , o f c o u r s e , b e n o t e d t h a t t h e e n o r m o u s A u s t r a l i a n e l e c t o r a t e
reduces the r a n d o m e l e m e n t t o insignificance -
i n N e w South. Wales, for
i n s t a n c e , t h e q u o t a is t y p i c a l l y i n t h e r e g i o n o f h a l f a m i l l i o n votes. I n t h e I w o
r e m a i n i n g cases ( t h e N o r t h e r n I r e l a n d A s s e m b l y a n d t h e T a s m a n i a n H o u s e o f
A s s e m b l y ) t h i s e l e m e n t is r e d u c e d t o i n s i g n i f i c a n c e b y t h e a d o p t i o n o f t h e
G r e g o r y p r o c e d u r e ( U n i t e d K i n g d o m , 1973, a r t . 5 6 ; T a s m a n i a , 1980a, s c h e d u l e
4 ) ; a n d t h i s is t h e case also i n i n d i r e c t e l e c t i o n s t o t h e I r i s h Senate ( I r e l a n d ,
1982, p p . 4 5 - 4 7 ) . I t s h o u l d b e m e n t i o n e d t h a t t h e a d d i t i o n a l r e f i n e m e n t : o f
t r e a t i n g each b a l l o t p a p e r as i f i t h a d t h e v a l u e 100 ( a d o p t e d f o r t h e Senates o f
N o r t h e r n I r e l a n d a n d o f S o u t h e r n I r e l a n d o n t h e S o u t h A f r i c a n m o d e l ) has
b e e n f u r t h e r d e v e l o p e d i n e l e c t i o n s t o t h e I r i s h Senate, w h e r e each p a p e r is
t r e a t e d as i f i t h a d t h e v a l u e 1000; i n N o r t h e r n I r e l a n d , values a r e
instead
c a l c u l a t e d t o t w o d e c i m a l places.
T h e essence o f t h e G r e g o r y p r o c e d u r e
is t h a t w h e n a s u r p l u s is b e i n g
d i s t r i b u t e d all o f t h e votes i n t h e p a r c e l last r e c e i v e d b y t h e c a n d i d a t e w h o has
b e e n e l e c t e d a r e passed o n , t h o u g h at a v a l u e r e d u c e d i n p r o p o r t i o n t o t h e r a t i o
b e t w e e n t h e s u r p l u s a n d t h e n u m b e r o f t r a n s f e r a b l e votes. I n o t h e r w o r d s , i n
t h e t e r m i n o l o g y u s e d a b o v e , each c o n t i n u i n g c a n d i d a t e receives a n u m b e r o f
b a l l o t p a p e r s e q u a l t o R^, so t h a t Sy = Ry, b u t each o f these p a p e r s has t h e v a l u e
Sj/Pj. W h i l e t h i s s i g n i f i c a n t l y increases t h e a m o u n t o f p a p e r - h a n d l i n g
and
c a l c u l a t i o n e n t a i l e d i n a n e l e c t i o n c o u n t , i t also i n t r o d u c e s a c o m p l i c a t i o n w h e n
votes o f e l i m i n a t e d c a n d i d a t e s a r e b e i n g d i s t r i b u t e d . I n a d d i t i o n t o his o w n f i r s t
p r e f e r e n c e votes, a c a n d i d a t e m a y h a v e r e c e i v e d t r a n s f e r r e d votes at a v a r i e t y o f
values. T h e rules p r o v i d e that the parcels o f a n e l i m i n a t e d candidate be re­
d i s t r i b u t e d i n stages i n t h e o r d e r i n w h i c h h e r e c e i v e d t h e m ; a n d a c a n d i d a t e
w h o reaches t h e q u o t a at t h e e n d o f o n e s u c h stage m a y b e d e c l a r e d e l e c t e d ,
b e f o r e t h e process o f v o t e t r a n s f e r has b e e n c o m p l e t e d .
VI CONCLUSION: R E M O V I N G T H E R A N D O M ELEMENT FROM IRISH
ELECTIONS
T h e c o m p l e x i t y a n d c u m b e r s o m e c o u n t i n g procedures that characterise I r i s h
e l e c t o r a l l a w a r e p a r t o f t h e p r i c e t h a t m u s t b e p a i d f o r a n e l e c t o r a l system chat
gives t h e v o t e r so g r e a t a d e g r e e o f f l e x i b i l i t y i n c h o o s i n g b e t w e e n
candidates
a n d p a r t i e s at l i t t l e r i s k o f v o t e wastage. T h e a d d i t i o n o f a n e x t r a cost, i n t h e
f o r m o f t h e p r e s e n c e o f a r a n d o m e l e m e n t i n c e r t a i n c i r c u m s t a n c e s , m i g h t seem
a s m a l l b u r d e n a n d o n e t h a t is w o r t h b e a r i n g w h e n t h e a d v a n t a g e s o f t h e I r i s h
e l e c t o r a l system a r e set a g a i n s t t h e d i s a d v a n t a g e s o f t h e p r e d o m i n a n t l i s t system
o f p r o p o r t i o n a l r e p r e s e n t a t i o n , o f w h i c h t h e m o s t o b v i o u s is t h e n a r r o w i n g o f
the voter's
options and
the advantage
given to party organisations.
The
p l u r a l i t y - b a s e d e l e c t o r a l systems o f t h e m a j o r E n g l i s h - s p e a k i n g c o u n t r i e s , i n
a d d i t i o n t o e n h a n c i n g the r o l e o f the p o l i t i c a l parties a n d r e s t r i c t i n g the voter's
c h o i c e t o a s i n g l e d i m e n s i o n ( i . e . , t o v o t e f o r t h e p a r t y or t o v o t e f o r t h e p e r s o n ) ,
p r o v i d e an a d d e d measure o f c r u d i t y a n d capriciousness,
system
seem
almost
flawless.
I t has
been
shown
m a k i n g the S T V
above
that
in
certain
c i r c u m s t a n c e s t h a t o c c u r q u i t e f r e q u e n t l y i n I r i s h e l e c t i o n s ( a n d w h e r e t h e r e are
n o c o u n t i n g e r r o r s ) t h e p r o b a b i l i t y o f a m a t h e m a t i c a l l y exact r e p r o d u c t i o n o f
t h e r e s u l t o n a c o m p l e t e r e c o u n t is v e r y l o w , b u t t h e p r o b a b i l i t y o f t h e same
g e n e r a l o u t c o m e ( i n t e r m s o f p e r s o n s elected) is v e r y h i g h . E v e n t h i s c h a n c e
element can be r e m o v e d w i t h a little t r o u b l e .
T h e m o r e c o m p l i c a t e d t h e system t h e less i n t u i t i v e l y o b v i o u s its fairness t o
t h e e l e c t o r a t e a n d t h e m o r e d i f f i c u l t i t is f o r t h e r e t u r n i n g o f f i c e r t o a d m i n i s t e r .
P r o c e d u r a l a n d c o u n t i n g e r r o r s a n d t h e r a n d o m c o m p o n e n t i n t h e system a r e
t o l e r a t e d , p r e s u m a b l y , i n p a r t a t least because t h e c a n d i d a t e s i n v o l v e d , t h e i r
agents a n d t h e e l e c t o r a t e find t h e finer p o i n t s o f t h e e l e c t i o n r u l e s b e w i l d e r i n g .
F u r t h e r m o r e , t h e r u l e s seek t o m i n i m i s e t h e r i s k o f a d i f f e r e n t r e s u l t i n t h e e v e n t
o f a r e c o u n t b y p r o v i d i n g f o r t h e p e r f o r a t i o n o r m a r k i n g o f p a p e r s selected f o r
t r a n s f e r ; t h e s a m e p a p e r s s h o u l d t h u s b e selected i n a n y r e c o u n t , d i s g u i s i n g t h e
random
element.
Adoption
o f the
Gregory
modification,
which
would
u n d o u b t e d l y p r o d u c e a fairer result, w o u l d be u n l i k e l y to lead t o f u r t h e r p u b l i c
e n l i g h t e n m e n t o r t o lessen s i g n i f i c a n t l y t h e p o s s i b i l i t y o f e r r o r . T h e c o m p u t e r
w o u l d seem t o o f f e r a s o l u t i o n t o s o m e o f these d i f f i c u l t i e s , a n d c o u l d also
resolve some o t h e r anomalies o f STV-based p r o p o r t i o n a l representation.
T h e existence o f a r a n d o m e l e m e n t i n t h e I r i s h e l e c t o r a l system is t h e
consequence o f a short cut i n t e n d e d to simplify c o u n t i n g procedures.
For
s i m i l a r r e a s o n s o t h e r a r b i t r a r y d e c i s i o n s have b e e n m a d e . T h e m o s t s i g n i f i c a n t
o f these is t h e r u l e , c o m m o n t o a l l S T V - t y p e systems, t h a t i n d i s t r i b u t i n g
surpluses o n l y t h e votes i n t h e p a r c e l last r e c e i v e d b y t h e e l e c t e d c a n d i d a t e s b e
c o n s i d e r e d . I t has b e e n a r g u e d t h a t t h i s f a c t o r r e n d e r s t h e S T V system less t h a n
s a t i s f a c t o r y b y the s t a n d a r d s o f s o c i a l c h o i c e t h e o r y , i n t h a t i t fails t o m i n i m i s e
t h e t e m p t a t i o n t o t a c t i c a l v o t i n g a n d t o m a x i m i s e e q u a l i t y o f votes ( M e e k , 1969).
I t is, h o w e v e r , p o s s i b l e i n t h e o r y t o o v e r c o m e these d i f f i c u l t i e s : i n t r o d u c t i o n o f
a s c a l i n g f a c t o r f o r each c a n d i d a t e o n each c o u n t (0 f o r e l i m i n a t e d c a n d i d a t e s , 1
for c o n t i n u i n g , non-elected candidates a n d a value r a n g i n g between 0 a n d 1 f o r
elected c a n d i d a t e s ) w o u l d p e r m i t a c c o u n t t o b e t a k e n o f f u r t h e r preferences i n
all o f t h e p a p e r s o f a l l elected c a n d i d a t e s , a n d w o u l d a l l o w t r a n s f e r r e d votes t o
be a t t r i b u t e d also t o c a n d i d a t e s w h o h a d a l r e a d y e x c e e d e d t h e q u o t a ( M e e k ,
1969; M e e k , 1970). T h e v e r y c o m p l i c a t e d c a l c u l a t i o n s i n v o l v e d w o u l d
present
n o p r o b l e m i n a c o m p u t e r - b a s e d system, w h i c h c o u l d s i m u l t a n e o u s l y e l i m i n a t e
t h i s a r b i t r a r y e l e m e n t a n d t h e r a n d o m e l e m e n t ( W o o d a l l , 1982).
E v e n m o r e r a d i c a l l y , use o f t h e c o m p u t e r w o u l d p e r m i t g r e a t e r f l e x i b i l i t y i n
the a d o p t i o n o f r u l e s f o r t h e c o u n t i n g o f votes. I t has b e e n p o i n t e d o u t t h a t t h e
H a r e system m a y r e s u l t i n t h e e l i m i n a t i o n o f t h e C o n d o r c e t w i n n e r (i.e., t h a t
c a n d i d a t e w h o , i n a succession o f t w o - c a n d i d a t e contests, w o u l d b e p r e f e r r e d t o
every o t h e r c a n d i d a t e ) ( N u r m i , 1983), b u t a c o m p u t e r - b a s e d c o u n t i n g system
c o u l d b e f u n d a m e n t a l l y d i f f e r e n t w h i l e r e t a i n i n g t h e same v o t i n g
procedure
and r e m a i n i n g compatible w i t h existing constitutional provisions.
I t is, h o w e v e r , i r o n i c t h a t c o m p u t e r s h a v e b e e n u s e d so f a r o n l y i n instances
w h e r e , as i n t h e U n i t e d States a n d G e r m a n y , t h e e l e c t o r a l system is v e r y s i m p l e
a n d o n l y e l e m e n t a r y processes o f c o u n t i n g a r e r e q u i r e d . T h e d i f f i c u l t y o f
d e v i s i n g a satisfactory i n p u t m e c h a n i s m f o r a c o m p u t e r - b a s e d v o t i n g system
with
the
S T V has
discouraged
certain
British
electoral
reformers
from
a d v o c a t i n g t o o strongly the i n t r o d u c t i o n o f m e c h a n i c a l v o t i n g procedures i n
the U n i t e d K i n g d o m ( o p p o n e n t s o f r e f o r m c o u l d , f o r instance, s u p p o r t
the
i n t r o d u c t i o n o f t h e c o m p u t e r b u t a r g u e t h a t t h i s r u l e s o u t use o f t h e r e l a t i v e l y
c o m p l i c a t e d p r e f e r e n t i a l v o t i n g system). I n a d d i t i o n , p r o v i s i o n o f e q u i p m e n t
f o r m e c h a n i c a l o r e l e c t r o n i c r e c o r d i n g o f votes i n p o l l i n g b o o t h s o r o f f a c i l i t i e s
f o r c o n v e r t i n g t r a d i t i o n a l b a l l o t p a p e r s i n t o m a c h i n e - r e a d a b l e f o r m at s o m e
central l o c a t i o n m i g h t be p r o h i b i t i v e l y expensive, a n d the latter, w h i c h w o u l d
involve the p u n c h i n g u p o r k e y i n g i n o f each b a l l o t paper, m i g h t m a k e the
c o u n t e v e n s l o w e r t h a n i t is at p r e s e n t ( S i m p s o n , 1981).
T h e c o m p u t e r has, nevertheless,
b e e n used i n C a m b r i d g e , Mass., i n S T V
e l e c t i o n s , a n d a d e m o n s t r a t i o n o f its usefulness was m a d e b y P r o f e s s o r P. M .
Q u i n t a n d u r i n g t h e 1968 r e f e r e n d u m c a m p a i g n o n t h e p r o p o s e d a b o l i t i o n o f
proportional
representation.
I n order
to counter
the allegation that
the
r a n d o m e l e m e n t was a necessary f e a t u r e o f t h e S T V system, h e h e l d a m o c k
e l e c t i o n i n C o r k i n w h i c h t h e c o u n t was c a r r i e d o u t b y c o m p u t e r ; n o t a l o n e d i d
his p r o g r a m m e e l i m i n a t e the r a n d o m element, b u t the error-free c o u n t lasted
1 0
o n l y h a l f a n h o u r . A l t h o u g h Professor Q u i n l a n ' s p r e d i c t i o n that I r i s h e l e c t i o n
results w o u l d b e p r o d u c e d b y c o m p u t e r s w i t h i n five years has n o t b e e n b o r n e
o u t , i t is p o s s i b l e t h a t t e c h n o l o g i c a l d e v e l o p m e n t s m a y e v e n t u a l l y m a k e t h e
p r o s p e c t o f r e c o n c i l i n g t h e S T V system w i t h t h e c o m p u t e r m o r e r e a l i s t i c ( f o r
i n s t a n c e , use o f s o p h i s t i c a t e d o p t i c a l r e a d e r s m i g h t c u t d o w n t h e n e e d f o r a
large v o l u m e o f expensive hardware).
T h e i n t r o d u c t i o n o f t h e p a r a p h e r n a l i a o f t h e c o m p u t e r age t o I r i s h p o l l i n g
b o o t h s m i g h t seem U t o p i a n ; the electorate w o u l d have to be assured that the
secrecy o f t h e act o f v o t i n g w o u l d b e m a i n t a i n e d a n d t h a t t h e p o s s i b i l i t y o f
f r a u d w o u l d b e e l i m i n a t e d . T h e s e p r o b l e m s h a v e b e e n o v e r c o m e w h e r e , as i n
t h e U n i t e d States, v o t i n g m a c h i n e s a r e c o m m o n l y u s e d . A t t h e p r e s e n t stage o f
t e c h n o l o g i c a l a n d social d e v e l o p m e n t a m o r e serious p r o b l e m r e m a i n s :
competence
the
( o b j e c t i v e a n d subjective) o f t h e v o t e r t o use a n e l e c t r o n i c o r
mechanical i n s t r u m e n t , however simple, to o r d e r candidates ( t h o u g h l e a r n i n g
t o use s u c h i n s t r u m e n t s is less d e m a n d i n g t h a n l e a r n i n g t o r e a d ) . Y e t t h e shift t o
s u c h a system, w h i c h p u t s a p r e m i u m o n l y o n a w i l l i n g n e s s a n d a b i l i t y t o a d a p t
t o t e c h n o l o g i c a l c h a n g e , is s u r e l y less r e v o l u t i o n a r y t h a n t h e s h i f t f r o m o r a l
10. Irish Times, 5-7 O c t o b e r 1968.
v o t i n g t o v o t i n g b y b a l l o t p a p e r (1872), w h i c h p u t a p r e m i u m o n l i t e r a c y .
Would
to
assist
c o m p u t e r p h o b e s i n p r e s s i n g b u t t o n s t h a n f o r h i m t o assist i l l i t e r a t e s i n
i t be
any
more
objectionable
for
a
r e t u r n i n g officer
filling
o u t b a l l o t papers? I f n o t , i f prejudice against the c o m p u t e r c o u l d be o v e r c o m e
a n d i f candidates a n d observers were p r e p a r e d t o f o r g o the d o u b t f u l pleasures
a n d excitement o f a l o n g d r a w n - o u t count, then t h e c o m p u t e r m i g h t present
t h e a n s w e r t o t h e m a i n t e c h n i c a l f l a w i n t h e I r i s h e l e c t o r a l system a n d m i g h t
p a v e t h e w a y f o r a r a d i c a l r e - c o n s i d e r a t i o n o f t h e r u l e s f o r c o u n t i n g votes.
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A U S T R A L I A 1980. Commonwealth Electoral Act 1918, Incorporating all Amendments by
Legislation made to 30 June 1980, Canberra: C o m m o n w e a l t h G o v e r n m e n t Printer.
F L A N D I N , P I E R R E - E T I E N N E 1914. La Question de la Representation proportionnelle en
Angleterre et dans les Colonies Anglaises: le Vote Transferable, Paris: L i b r a i r i e Dalloz.
G A L L A G H E R , M I C H A E L 1984. " T h e Political Consequences o f the Electoral System
i n the Republic o f I r e l a n d " , Paper presented to the ECPR w o r k s h o p o n C o m p a r i n g
Electoral Systems, Salzburg, 13-18 A p r i l 1984.
G R E G O R Y , M A U R I C E 1971. " T h e M e t h o d o f V o t i n g i n M a l t a " , The Parliamentarian,
V o l , 52, N o . 4, p p . 275-277.
H A R E , T H O M A S 1859. A Treatise on the Election of Representatives, Parliamentary and
Municipal, L o n d o n : L o n g m a n , B r o w n , Green, Longmans a n d Roberts.
H U M P H R E Y S , J O H N 1911. Proportional Representation, L o n d o n : M e t h u e n .
I R E L A N D 1927. Department of Local Government and Public Health: First Report 1922-1925,
D u b l i n : Stationery Office.
I R E L A N D 1982. Seanad General Election, August 1981, and Bye-Elections to 1977-81 Seanad,
D u b l i n : Stationery Office.
I R E L A N D 1983. Election Results and Transfer of Votes in General Election (November, 1982J for
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D u b l i n : Stationery Office.
L A K E M A N , E N I D 1974. How Democracies Vote: A Study of Electoral Systems 4th ed.,
L o n d o n : Faber and Faber.
M A L T A 1970. The Polling Regulations, 1939 [as amended u p to 31 January 1970], Valetta:
Department o f Information.
M E E K , B . L . , 1969. " U n e Nouvelle A p p r o c h e d u Scrutin Transferable", Mathematiques et
Sciences Humaines, V o l . 7, N o . 25, p p . 13-23.
M E E K , B . L . , 1970. " U n e Nouvelle A p p r o c h e d u Scrutin Transferable ( f i n ) " ,
Mathematiques et Sciences Humaines, V o l . 9, N o . 29, p p . 33-39.
M E R E D I T H , J.C., 1913. Proportional Representation in Ireland, D u b l i n : E d w a r d
Ponsonby.
N E W L A N D ' , R O B E R T A . , and F R A N K S. B R I T T O N 1976. How to Conduct an Election by
the Single Transferable Vote, L o n d o n : Electoral R e f o r m Society.
N U R M I , H A N N U 1983. " V o t i n g Procedures: a Summary Analysis", British Journal of
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