In June of 1994 the Maltese Government created a "Commission on the Electoral System" composed of one representative each from the three political parties, the PN, the MLP and the Alternattiva, under the chairmanship of the Speaker of the House. This Commission was appointed
"to draw up a report with proposals, suggestions and alternatives that could be implemented so that:--
(i) in respecting the principles which safeguard the citizens' democratic rights and the governability of the country, the electoral system will ensure that the number of seats of a political party Parliament is as much possible proportional to that party's first count vote; and
(ii) in improving the process and the electoral law, the related workings would be more transparent and at every stage enjoy the trust of all the citizens and of all the parties participating in the election; and possibly find means of how the final result of a general election could be announced earlier than it has been done so far."
When the Commission issued its report in November of 1994, it had agreed on recommendations to improve some procedural matters (such as speedier vote counting) but had not been able to achieve a consensus on questions relating to greater proportionality or the creation of a vote "threshold" for minor parties. The report of the Commission has never been officially published in the Government Gazette, although copies were made available to the Prime Minister, and (only on his insistence) to the Leader of the Opposition, as well as "limited photocopies" to the press. I have finally obtained one of those limited copies. It can be found elsewhere on this website.
One of the appendices to that Commission report was a paper by Professor Anton Buhagiar which the Commission had asked him to prepare. This contribution is reproduced below. It is a careful, comprehensive and lucid plan for a reform that would deal with the problem of disproportionality. It did not address, however, the question of "governability" and probably for that reason failed to receive the Commission's endorsement.
Anness F
CAN ONE ACHIEVE NATIONWIDE PROPORTIONAL REPRESENTATION IN MALTA
WITHOUT MAJOR CHANGES TO THE PRESENT METHOD OF ELECTION?
by
Anton Buhagiar
Statistics Unit,
The University of Malta.
Saturday, 1st October 1994.
It is a well known fact that in the General Elections held in Malta
in recent years, certain anomalous results can occur in the sense
that the party with more than 50% of the first count votes ends up
with less seats than another party which polled less than 50% of
the first count votes. Such an outcome happened for example in the
General Elections of 1981 and 1987. This anomaly can happen because
when the Single Transferable Vote (STV) is used to elect candidates
in the various constituencies, some votes are necessarily wasted,
and are not used to elect any candidate. If the total of the votes
wasted in the constituencies turn out to below mostly to one
political party, such a party will end up with less seats than it
should, thus leading to the above mentioned anomaly. In 1987,
Constitutional amendments were implemented to rectify such a
phenomenon. Essentially, if a party gets more than 50% of the first
count votes in an election, and fails to obtain a majority of seats
from the constituencies, a number of candidates are co-opted so
that the offended party will obtain a majority in the House of
Representatives.
One might be tempted to devise a completely new electoral system
to achieve a result which is fair to both the voters and to the
political parties concerned. However, the Single Transferable Vote
has been lauded by various authorities as being one of the fairest
methods of election. Besides, the STV is very close to the hearts
of the Maltese public - people are very eager to follow the
fortunes of their favourite candidate through the numerous counts
so typical of STV. The object of this study is therefore to start
off with the Maltese Electoral System as implemented prior to 1987,
and then to perform minor adjustments to this process in order to
secure the highly desirable feature of nationwide proportional
representation, i.e. that the total number of seats gained nationally by
a party should reflect the total number of votes earned by it in
the various constituencies, and this irrespective of the actual
configuration of the constituency boundaries.
Several questions come to mind when one attempts to secure
proportional representation on a national basis:
a) Is the nationwide total of first count votes cast for a given
political party a fair indicator for the number of seats to be
awarded nationwide to that party, or should one rather employ the
final court vote to compute the required number of representatives
for that party?
b) If the first count vote is chosen for the purpose mentioned in
paragraph (a) above, how does one proceed to compute the actual
number of seats to be assigned to a political party on a nationwide
basis?
c) How should the ideal number of seats assigned to a party
nationwide be implemented? Should the STV be allowed to proceed
exactly as at present, examine the final result, see whether it
tallies with the ideal nationwide distribution, and hence affect
changes, if any are required, to restore the STV to nationwide
proportionality? Should any deviations of the STV from a
proportional result be corrected a posteriori, i.e. after the
actual election has taken place?
d) When the total number of seats to be allotted to each party on
a nationwide basis has been determined, can one proceed to allocate
a priori the seats of a given party district by district? Can this
a priori distribution of party seats by district be made to guide
the actual evolution of a subsequently held STV? (Please note the
difference from paragraph c above). In particular, how can one
distribute a priori a party's seats amongst the various
constituencies, without changing the total number (65 at present)
of seats in the House and without altering the regional
representation of Parliament, i.e. that each constituency should
return 5 members to the House?
To examine these various questions, we consider the seven elections
held in Malta in the period 1962 to 1992. These were held in 1962,
1966, 1971, 1976, 1981, 1987, and 1992. A considerable range of
conditions prevailed in these elections: there was a varying number
of parties contesting, a variable number of minor parties, a
variable quantity of transferred votes, a varying number of
constituencies, and a varying total number of representatives.
These elections therefore provide a good testing ground for any
conjecture or theory one would like to make on Maltese elections.
DETERMINING THE NATIONWIDE NUMBER OF SEATS TO WHICH A PARTY IS
ENTITLED.
Throughout this study we use the well known d'Hondt divisor method to
convert a number of votes to a corresponding number of seats. The
virtue of divisor methods is that they tend to equalise as far as
possible the votes wasted for the various parties contesting a
given election. (For the benefit of the reader, an example of how
the divisor method works, is given in Appendix I at the end of this
study).
In this section, we use the divisor method to predict the number
of seats a party would win nationwide in the above mentioned
elections, both on the basis of its first count vote and also on
the basis of the final count vote. The results are then compared
to the actual outcome of that particular election.
Relevant information on these elections are given for convenience
in Table I. For each election between i962 and 1992, we give the
total first count vote for each party, the net number of votes
transferred to that party, as well as the final count vote which
is the sum of the first count vote plus the net votes transferred.
The number of representatives allotted nationwide to each party is
then calculated on the basis of (i) the first count and (ii) the
final count using the d'Hondt divisor method. The actual number
of seats (iii) earned by each party in that election is also given.
This information is also given in Table I.
For each election, we also give the discrepancy between the number
of seats as calculated in each of (i) and (ii) using the divisor
method, and the actual number of seats (iii) actually gained by a
given party in that election. These are given in parenthesis is near
columns (i) and (ii) in Table I.
On examining Table I, one can notice the following important facts:
a) The number of seats estimated by the d'Hondt divisor method on
the nationwide first count and on the final count (columns i and ii)
are identical in the elections of 1971, 1981 and 1987. These
were the elections where there were very few transfers. The
discrepancies between each of the divisor methods (i) and (ii) and
the actual election results (iii), shown in parenthesis in Table
I, are therefore identical for these three elections.
b) There is a small discrepancy between the first count estimate
of nationwide seats and the final count estimate in the elections
of 1962, 1966, 1976 and 1992.
In 1976, the first count estimate agrees exactly with the outcome
of the election, and is actually better than the final count
estimate, which predicts one seat less for the MLP and one seat
more for the PN than what is actually observed in the election.
In the elections of 1962, 1966 and 1992, when there was a
considerable number of votes transferred between parties, the final
count estimate is slightly better than the first count
estimate.
In 1962, the first count estimate predicts three seats less for the
PN and one seat more for each of MLP, CWP and PCP - a malassignment
of 3 seats. The final count estimate is slightly nearer to the
actual election outcome since it predicts 1 seat less for each of
the PN and the DNP, and 1 seat more for each of the MLP and the
CWP, - a reshuffle of 2 seats.
Similarly, in the election of 1966, the first count estimate
predicts three seats less for the ?N an] three seats more for the
CWP - a malassignment of 3 seats. The final count estimate is
slightly nearer to the actual election outcome since it predicts
2 seats less for PN, and 2 seats more for CWP - a reshuffle of 2
seats.
c) In view of a) and b) above, the first count is practically as
near to the actual election result as is the final count, and this
seems to be true even when there is a considerable number of
transfers. Besides, the first count is a more immediate quantity
and is simpler to define, comprehend: and calculate than is a later
or final count. Many authors, while praising the STV for its
superior proportionality vis-vis other methods, have described
the higher counts of the STV system as rather unstable, and they
actually give examples where a small number of changed preferences
could profoundly affect which of the candidates are elected. The
first count should therefore be preferred in general to a later or
final count to maintain nationwide proportional representation.
5) The first count vote agrees exactly with the actual election
result in the elections of 1971 and 1976. In all the other
elections considered, a difference exists between the estimate of
seats based on the nationwide first count and the actual election
result. In the 1966 election say, the divisor estimate predicts 3
seats less for the PN and 3 seats more for the CWP than actually
obtained in the election. Similarly, in the elections of 1981 and
1987, the divisor method on the first count predicts 2 seats less
for the MLP, and 2 seats more for the PN. In 1992, the divisor
method predicts one seat less for the MLP, and one seat more for
AD. In all the elections held between 1962 and 1992, there never
was a disparity of more than 3 seats between the first count
divisor estimate and the actual election result.
TABLE I : Elections held in Malta between 1962 an] 1992. Comparison
of the number of seats obtained using the d'Hondt divisor method
on i) the national total of first count votes, and ii) the national
total of final count votes. These are compared to iii) the seats
actually obtained in the given election. The discrepancies in the
number of seats between method i), the first count estimate, and
method iii), the actual number of seats obtained in the election,
ie. (i)-(iii), are given in parenthesis next to the column
representing i). The difference between the final count estimate
ii) and the actual: number of seats iii) are also given in
parenthesis next to column (ii). It is important to note that in
all the elections between 1962 and 1992, the first count estimate is
nearly as accurate as the final count estimate in predicting the
final election result. Sometimes it is even better (as in 1976).
The maximum assignment error for the first count estimate is 3
seats (in 1962 and 1966), whilst the maximum error for the final
count estimate is 2 seats (also for the elections of 1962 and
1966). One can therefore conclude that the first count estimate
reliably predicts the actual number of seats obtained in an
election.
1962 ELECTION.
PARTY 1st Transfer Final D'Hondt d'Hondt Actual
count to party count 1st final Election;
count count STV in 10
SEATS SEATS constit.
PN 63262 7442 70704 22 (-3) 24 (-1) 25
MLP 50974 24 50998 17 (+1) 17 (+1) 16
CWP 14285 -25 14260 5 (+1) 5 (+1) 4
DNP 13968 -3030 10938 4 3 (-1) 4
PCP 7290 -3719 3571 2 (+1) 1 1
DCP 699 -577 122 0 0 0
IND 128 -115 13 0 0 0
TOTAL 150606 0 150606 50 50 50
1966 ELECTION.
PARTY 1st Transfer Final D'Hondt d'Hondt Actual
count to party count 1st final Election;
count count STV in 10
SEATS SEATS constit.
PN 68656 6013 74669 25 (-3) 26 (-2) 28
MLP 61774 340 62114 22 22 22
CWP 8594 -3055 5539 3 (+3) 2 (+2) 0
PCP 2086 -1494 592 0 0 0
DNP 1845 -1543 302 0 0 0
IND 392 -261 131 0 0 0
TOTAL 143347 0 143347 50 50 50
1971 ELECTION.
PARTY 1st Transfer Final D'Hondt d'Hondt Actual
count to party count 1st final Election;
count count STV in 10
SEATS SEATS constit.
MLP 85448 297 85745 28 28 28
PN 80753 1321 82074 27 27 27
PCP 1756 -1530 226 0 0 0
OTHERS 102 -88 14 0 0 0
TOTAL 168059 0 168059 55 55 55
1976 ELECTION.
PARTY 1st Transfer Final D'Hondt d'Hondt Actual
count to party count 1st final Election;
count count STV in 13
SEATS SEATS constit.
MLP 105854 -113 105741 34 33 (-1) 34
PN 99551 141 99692 31 32 (+1) 31
OTHERS 35 -28 7 0 0 0
TOTAL 205440 0 205440 65 65 65
1981 ELECTION.
PARTY 1st Transfer Final D'Hondt d'Hondt Actual
count to party count 1st final Election;
count count STV in 13
SEATS SEATS constit.
MLP 109990 1 109991 32 (-2) 32 (-2) 34
PN 114134 16 114150 33 (+2) 33 (+2) 31
OTHERS 29 -17 12 0 0 0
TOTAL 224153 0 224153 65 65 65
1987 ELECTION.
PARTY 1st Transfer Final D'Hondt d'Hondt Actual
count to party count 1st final Election;
count count STV in 13
SEATS SEATS constit.
MLP 114936 259 115195 32 (-2) 32 (-2) 34
PN 119721 43 119764 33 (+2) 33 (+2) 31
OTHERS 511 -302 209 0 0 0
TOTAL 235168 0 235168 65 65 65
1992 ELECTION.
PARTY 1st Transfer Final D'Hondt d'Hondt Actual
count to party count 1st final Election;
count count STV in 13
SEATS SEATS constit.
PN 127932 1802 129734 32 (-2) 32 (-2) 34
MLP 114861 1535 116396 33 (+2) 33 (+2) 31
AD 4186 -3337 849 0 0 0
TOTAL 246979 0 246979 65 65 65
End of Table I
IMPORTANT FEATURES OF THE NATIONWIDE DISTRIBUTION OF SEATS.
The divisor method for nationwide proportional representation has
some important properties:
i) If the number of available seats is odd, and two parties are
contesting the election, the party with the larger number of votes
will always get a larger number of seats, however minimal the
difference. This is important in that a situation like the
elections of 1981 or 1987 cannot arise where the party with the
larger number of votes obtains a smaller number of seats.
ii) The result in i) can in fact be generalised. If there is any
number of parties contesting the election, if the number of
available seats is odd], and one party gets more votes than all the
others put together, then that party will obtain more than 50% of
the available seats. This is a very important majority rule satisfied
by this procedure.
iii) The effect of a threshold, if any, is to ignore the relevant
parties for the assignment of seats. Therefore, a party which has
a majority of votes without the threshold will potentially have an
even greater majority in the presence of a threshold when some
parties are excluded. The results in i) and ii) therefore hold a
fortiori.
iv) If the total number of available seats is even, rather than
odd, an election result can be imagined where a party gets a
majority of votes but gets an equal number of seats as the total
number of seats gained by the other parties. For example, suppose
in a three party election,
..
Party A polled 32200 votes,
Party B polled 32000 votes,
Party C polled 100 votes.
If the total number of seats available is 64, then 32 seats will
be allotted by the divisor method to each of A and B, and none to
party C. This will result in a hung Parliament, even though A has
an absolute majority of votes. For this reason it is better to have
the total number of available seats to be odd, as it has in fact
been for all elections in Malta since 1971, 55 at first and finally
65.
v) It is also easy to imagine an election contested say by three
parties where party A gets more votes than party B, but less votes
than the total of votes polled by parties B and C together. In this
case it could happen that party A gets more seats than the total
number of seats gained by B and C. This could happen when, say,
party C just fails to win a single seat. An example can be
furnished by a result such as:
Party A polled 32001 votes,
Party B polled 32000 votes,
Party C polled 100 votes.
In this case, if 65 seats are to be distributed, A wins 33 seats,
B wins 32 seats, and C fails to win a seat. So A wins more seats
than B and C together although it polled less votes than B and C
together. This the familiar problem of the divided vote.
vi) It is sometimes possible that the divisor method necessarily
requires more seats than the total number of seats stipulated
before the election. Take for instance the following example for
a three party election with the following result:
Party A polled 33000 votes,
Party B polled 32000 votes,
Party C polled 1000 votes.
Assuming the total number of seats to be fixed beforehand to 65,
the divisor method distributes the first 63 seats, 32 to A and 31
to B without any problem. When one tries to assign the 64'th seat
by the divisor method, the next vote to seat ratio will be exactly
equal to 1000 for all three parties. So then 3 further seats will
have to be assigned, one each to A, B, and C. A will get 33, B 32
and C will get 1 seat. The total number of seats will then add up
to 66 not 65! Fortunately the probability of such an event
happening is very remote: the votes polled by the parties will have
to be exactly in a very unlikely ratio! However should this
actually happen, one might decide by law which party is to forfeit
the seat.
The above properties are very important. In particular, the
fairness of the nationwide distribution of seats towards the
contesting parties can be deduced from the important result ii)
mentioned in this section, as well as its corollaries i) and iii).
The features mentioned in this section can be vividly illustrated
using the Monte Carlo method. An election, assumed for simplicity
to be between three parties, is simulated by the computer, which
assigns a random number of votes to each of the parties. The
divisor estimate for seats won nationwide by each party is then
calculated for that election. When this simulation is carried out
many times, one can simulate the various combinations occurring in
items I) to v) in this section. These results are indeed borne out
by these simulations. Whenever party A has more votes than B and
C together, it had the absolute majority of seats.
The phenomenon mentioned in vi) above is extremely rare and
millions of such elections will have to be simulated to actually
arrive at such an unusual voting pattern.
THE EFFECT OF A THRESHOLD.
In several electoral systems, parties have to gain at least a
certain percentage (usually 5%) of the national first count votes
to secure representation in Parliament. It is important therefore
to gauge the effect of a hypothetical threshold on the nationwide
distribution of seats. This is done in Appendix II.
Disclaimer: The purpose of this section is not to encourage the
adoption or non-adoption of a threshold in Maltese elections, but to
objectively determine the effect of a threshold on the calculations
performed in this study.
A POSTERIORI RESTORATION OF AN STV TO NATIONWIDE PROPORTIONALITY.
Since it was found in Table I above that the result of the election
as concluded at present is not more than 3 seats different from the
first count divisor estimate, and since this estimate is morally
preferable to the actual: outcome of such an election in case they
are different, one should treat this outcome as provisional, and
then try to adjust it to tally exactly with the nationwide first
count estimate of seats. (A similar method was advocated by Mr M.
C. Spiteri in a letter to The Sunday Times of 24th June 1984.)
If we take as an example the election of 1987, it is found that the
first count estimate predicts 2 seats less for the MLP and 2 seats
more for the PN than the number of seats actually obtained in the
election. In this case it is clear that changing 2 seats from MLP
to PN will restore the result to naticnwide proportionality. This
can be done by first identifying two constituencies where the PN
has a relatively high percentage of votes and a relatively small
percentage of seats (or vice versa for MLP). The difference of these
two percentages in a given district can be termed the under
representation of the PN in that district..
The details of such a transfer is illustrated in Table II. The
first part of this table shows how to calculate the under
representation of the PN in every district. In a similar way, one
can calculate the under representation for each party in each
district. Such an array of numbers can be termed the under
representation matrix and is displayed in the second part of Table II.
Districts I and II are those where the PN is under represented
most, to the tune of 8.74% and 11.71% respectively. In each of
these constituencies, therefore, the last MLP candidate who was
elected is unseated, and the seat is offered to the as-yet
unelected NP candidate who has most votes. It is therefore clear
that in such a system, any candidate who is 'elected' is deemed to
have done so only provisionally, subject to subsequent seat
changes. A candidate can have his 'election' confirmed or repealed
by subsequent adjustments to the STV.
In this way, not only is nationwide proportional representation
achieved, but also the number of seats in Parliament is held
constant at a value of 65 MP's. Each district still returns 5
members, so that regional representation is equitably maintained.
Further, the fact that a change of seats occurs where the offended
party is most under represented encourages the drawing of
constituency boundaries which are more likely to give proportional
results.
The method is also readily applicable to more complex situations
where many seat swaps are necessary to achieve nationwide
proportional representation. The seat swaps can generally be easily
resolved using the under representation matrix. For more on this
topic, see Appendices III and IV at the end of this study.
The swaps in seats necessary to restore a given election to
nationwide proportional representation is given in Table III
for the elections of 1962, 1966, 1981 , 1987, and 1992. The elections
of 1971 and 1976 do not need any such adjustment.
TABLE II: The 1987 election. Change of seats to achieve nationwide proportional
representation. Identification of districts where change of seats ought to
happen. The PN should get 2 seals more according to nationwide proportional
representation. So two districts are identified where the PN has a surplus of
votes as shown below. For each district, one calculates the % first count votes
cast to the PN in that district, as well as the percentage of seats obtained by
the PN. The discrepancy between these two percentages is a measure of the lack
of representation of the PN in that particular constituency. It is given in the
last column in this table. In the 1987 election, the maximum discrepancy occurred
in Districts I and II as can be seen below. The MLP candidate who was elected
last in each of these districts forfeits his seat to the PN candidate whob is
next in line to be elected.
District PN party Total % Vote Seats % Seats Under
first first in acquired acquired Representation
count count District in in in
votes votes District District District (%)
I 8396 17226 48.74% 2 40% 8.74%
II 580 18317 31.71 1 20 11.71
III 6486 17917 36.20 2 40 -3.80
IV 7412 17656 41.98 2 40 1.98
V 8284 18437 44.93 2 40 4.93
VI 8746 18853 46.39 2 40 6.39
VII 8366 17562 47.64 2 40 7.64
VIII 11227 18317 61.29 3 60 1.29
IX 11884 18917 62.82 3 60 2.82
X 11259 17472 64.44 3 60 4.44
XI 11438 18651 61.33 3 60 1.33
XII 10986 18439 59.58 3 60 -0.42
XIII 9429 17404 54.18 3 60 -5.82
UNDER REPRESENTATION MATRIX (1987)
District MLP PN OTHERS
I & -8.91% * 8.74% 0.17% ... Maximum under representation
II &-11.83 *11.71 0.13 ... of PN in the 13 districts.
III 3.72 -3.80 0.08
IV -2.10 1.98 0.12 NB: * = Seat gain;
V -5.01 4.93 0.08 & = Seat loss;
VI -6.53 6.39 0.14 positive % = under rep;
VII -7.88 7.64 0.24 negative % = over rep.
VIII -1.70 1.29 0.40
IX -3.20 2.82 0.38
X -4.89 4.44 0.45
XI -1.63 1.33 0.31
XII 0.09 -0.42 0.33
XIII 5.82 -5.82 0.00
TABLE III: Swaps of seats to restore the elections of 1962, 1966, 1981, 1987 and
1992 to nationwide proportional representation. The District listed is that where
the under representation of the offended party is maximum. The corresponding
under representation is shown in the fourth column as a percentage.
Year Seat Swap District Under Party seat is Party seat is
Representation taken from given to
1962 PN to MLP IV 7.47% PN MLP
PN to PCP IX 6.54 PN PCP
PN to CWP X 14.06 PN CWP
1966 PN to CWP VI 7.54 PN CWP
PN to CWP VII 9.53 PN CWP
PN to CWP VIII 7.72 PN CWP
1981 MLP to PN I 8.56 MLP PN
MLP to PN II 10.49 MLP PN
1987 MLP to PN I 8.74 MLP PN
MLP to PN II 11.71 MLP PN
1992 MLP to AD IX 2.18 MLP AD
METHOD A: AN STV ADJUSTED A POSTERIORI.
This method is proposed to achieve nationwide proportional
representation by a posterior) adjustments to the STV, and can be
described as follows:
i) Perform a Maltese Election exactly as at present, i.e. using STV
with a Droop Quota in 13 constituencies; 65 members are
provisionally elected, 5 from every constituency. These are at
first elected on a provisional basis.
ii) Perform a nationwide count of first votes for each party
contesting the election in a) . Hence assign the 65 seats available
to the various parties using the divisor method of d'Hondt.
iii) If the provisional distribution of seats among the parties (in
i) is exactly the same as the nationwide first count estimate (in
ii), there is no need to dc perform seat swaps between the parties,
and the result of the election in i) becomes permanent.
iv) On the other hand, if the two distributions differ, one has to
decide which parties ought to gain or lose seats, how many seats
to change, and in what constituency to perform each swap . The
district for a swap will be that where the offended party is most
under represented (see Tables II and III for details). In this
case, one superimposes on the provisional result in i) the
appropriate changes of seats between parties, thus obtaining the
final result which automatically incorporates nationwide
proportional representation.
PREDETERMINING THE NUMBER OF PARTY SEATS IN EACH DISTRICT.
In the previous sections, we used the d'Hondt divisor on the
nationwide first count vote to determine the total number of seats
to be assigned national to each party. Potentially, this was the
most important step, because it guarantees proportional
representation on a nationwide basis. We then proceeded with the
STV election, and resolved any deviations from this ideal by
performing relevant seat swaps a posteriori.
As an alternative method to the above, one could try to
predetermine the distribution of a stipulated number of seats a
party should get in each district, and hence allow a subsequently
held STV to be guided by such a distribution. The next step is
therefore to distribute the predetermined number of party seats
amongst the various districts in an equitable way, and such
that every district returns a pre-established number of members - this
was fixed to 5 since 1976.
A possible solution to this is to fall back to the divisor method
at the district level. The 5 seats in a given district are assigned
by the divisor method to the contesting parties, on the basis of
their votes. This is repeated for every particular district. One
can then easily compute the total number of seats attained by a
given party over all the districts. This procedure of assigning
seats to parties by district can be termed the districtwise divisor
method. This is to distinguish it from the other method of
assignment, the nationwide divisor method (explained previously) based
on the nationwide total of each party's votes.
There are some important questions to ask at this point:
i) How does the districtwise estimate of a given party's seats
compare with the seats actually gained in the election in
each district separately, and over all districts?
ii) How does the total number of seats of a given party calculated
by the districtwise divisor method compare with the number
of seats assigned to that party by the nationwide divisor method?
To clarify these points, we take the example of the General
Election of 1987, and compare these quantities for this particular
election. This is done in Table IV. In this table, we compare the
nationwide divisor estimate of seats, with the districtwise divisor
estimate, an] with the total seats each party gained in that
election. One can note that in this elect ion, the number of seats
computed by the divisor method for each party in each district
coincides exactly with the corresponding number of seats actually
gained in the election. This is therefore also true of the totals
of seats over all the districts. In both cases, 34 seats are
assigned to the MLP, and 31 to the PN. These estimates, however,
vary from the nationwide estimate of seats which predicts 33 seats
for the PN, and 32 seats for the MLP. In both cases, there is a
discrepancy of 2 seats: the nationwide divisor method predicts 2
seats more for the PN, and 2 seats less for the MLP than the actual
election or the districtwise estimate. Using the method of under
representation as above, one can then adjust the districtwise
allocation of seats to agree exactly with the distribution afforded
by the nationwide divisor method, since this is the ideal solution
which guarantees proportional representation on the national scale.
The nationwide and districtwise estimates of seats for the
elections between 1962 and 1992 are shown in columns i) and ii)
respectively in Table V. We also display the actual election result
in column iii) in this table. The discrepancies between the various
quantities are given in brackets and are measured from the
nationwide estimate, which is the most desirable distribution of
seats.
It can be noted that in all elections between T966 and 1992, the
districtwise estimate of seats is exactly equal to the result of
the actual: election, whereas it is in general different from the
nationwide divisor estimate. There is a maximum error of 3 seats
between the nationwide and districtwise quantities for these
elections.
For the election of 1962, however there is a substantial difference
between the nationwide estimate and the districtwise estimate, and
between these quantities and the actual election result. This is
due to the CWP which had a consistent following in most of the
constituencies, but did not have enough first count votes to win seats
in the individual districts by the divisor method. The total
nationwide of the CWP vote will eventually entitle it to a
substantial number of seats . (The fact the CWP actually obtained
several seats in the actual election is due to the fact that there
were many vote transfers to it in the early counts of the actual
election) . In all, there is a discrepancy of 7 seats between the
districtwise and nationwide estimates for the election of 1962, and
most of this difference (4 seats) is due to the CWP!
Such a phenomenon occurred also in 1992. In this election, the AD
had a small but consistent following in every district, but it did
not have enough votes. to elect a candidate in any of the
constituencies. When AD's total nationwide vote is calculated,
however, they will be entitled to one seat in Parliament.
The discrepancies between districtwise and nationwide estimates,
can be resolved using the principle of under representation as was
done for the previously described posterior method.
TABLE IV: THE ELECTION OF 1987. Comparison of the nationwide
divisor estimate of seats, with the districtwise divisor estimate,
and with the total seats each party gained in that election. One
can note that the number of seats computed by the divisor method
for each party in each district coincides exactly with the
corresponding number of seats actually gained in the election. This
is therefore also true of the totals of seats over all the
districts. In both cases, 34 seats are assigned to the MLP, 31 to
the PN, and none to the other parties. These estimates, however,
vary from the nationwide estimate of seats which predicts 33 seats
for the PN, and 32 seats for the MLP. In both cases, there is a
discrepancy of 2 seats: The nationwide divisor method predicts 2
seats more for the PN, and 2 seats less for the MLP than the actual
election or the districtwise estimate.
ELECTION Districtwise assignment of Actual Election
1987 seats by divisor method.
DISTRICT ..... PARTIES .... ..... PARTIES ....
MLP PN OTHERS MLP PN OTHERS
I 3 2 0 3 2 0
II 4 1 0 4 1 0
III 3 2 0 3 2 0
IV 3 2 0 3 2 0
V 3 2 0 3 2 0
VI 3 2 0 3 2 0
VII 3 2 0 3 2 0
VIII 2 3 0 2 3 0
IX 2 3 0 2 3 0
X 2 3 0 2 3 0
XI 2 3 0 2 3 0
XII 2 3 0 2 3 0
XIII 2 3 0 2 3 0
TOTAL SEATS: 34 31 0 34 31 0
(This is the total of seals assigned to (Actual seats attained
each party by the divisor method by parties in election).
in each individual district).
NATIONWIDE EST.: 32 33 0 32 33 0
(This is estimated by the d'Hondt divisor method on the nationwide totals of party
votes. [It is written on the right hand side also for convenience.)
DISCREPANCY: -2 20 -2 2 0
(This is the difference between the (This is the difference between
nationwide and the districtwise the nationwide estimate and
estimates). the actual election).
TABLE V : Elections held in Malta between 1962 and 1992. Comparison
of the number of seats obtained using the d'Hondt divisor method
on i) the national total of first count votes, and ii) on the first
count votes obtained by the parties in the districts separately.
Column iii) gives the seats actually obtained in the given
election. The discrepancies in the number of seats between method
i), the first count nationwide estimate, and method ii), the first
count districtwise estimate of seats, i.e. (i)-(ii), are given in
parenthesis next to the column representing ii). The difference
between the nationwide divisor estimate i) and the actual number
of seats gained in the election iii) are also given in parenthesis
next to column (iii). Please note that in this table discrepancies
are measured from the nationwide estimate, which henceforth will
be our norm. In the elections held on or after 1966, the
districtwise estimate of seats is identical to the outcome of the
election. For these elections also, the maximum discrepancy between
nationwide and districtwise estimates is one of 3 seats (in 1966).
In 1962, there is a considerable discrepancy of seven seats between
the two estimates, mainly due to the small but consistent following
of the CWP.
1962 ELECTION.
(i) (ii) (iii)
PARTY 1st Transfers Final D'Hondt d'Hondt Actual
count to party count 1st count 1st count Election;
Nationwide District- STV in 10
SEATS wise SEATS constit.
PN 63262 7442 70704 22 26 (-4) 25 (-3)
MLP 50974 24 50998 17 20 (-3) 16 (+1)
CWP 14285 -25 14260 5 1 (+4) 4 (+1)
DNP 13968 3030 10938 4 2 (+2) 4
PCP 7290 -3719 3571 2 1 (+1) 1 (+1)
pop 699 -577 122
IND 128 -115 13
TOTAL 150606 0 150606 50 50 50
1966 ELECTION.
(i) (ii) (iii)
PARTY 1st Transfers Final D'Hondt d'Hondt Actual
count to party count 1st count 1st count Election;
Nationwide District- STV in 10
SEATS wise SEATS constit.
PN 68656 6013 74669 25 28 (-3) 28 (-3)
MLP 61774 340 62114 22 22 22
CWP 8594 -3055 5539 3 0 (+3) 0 (+3)
PCP 2086 -1494 592
DNP 1845 -1543 302
IND 392 -261 131
TOTAL 143347 0 143347 50 50 50
1971 ELECTION.
(i) (ii) (iii)
PARTY 1st Transfers Final D'Hondt d'Hondt Actual
count to party count 1st count 1st count Election;
Nationwide District- STV in 10
SEATS wise SEATS constit.
MLP 85448 297 85745 28 28 28
PN 80753 1321 82074 27 27 27
PCP 1756 -1530 226
OTHERS 102 -88 14
TOTAL 168059 0 168059 55 55 55
1976 ELECTION.
(i) (ii) (iii)
PARTY 1st Transfers Final D'Hondt d'Hondt Actual
count to party count 1st count 1st count Election;
Nationwide District- STV in 13
SEATS wise SEATS constit.
MLP 105854 -113 10574 34 34 34
PN 99551 141 99692 31 31 31
Others 35 -28 7
TOTAL 205440 0 205440 65 65 65
1981 ELECTION.
(i) (ii) (iii)
PARTY 1st Transfers Final D'Hondt d'Hondt Actual
count to party count 1st count 1st count Election;
Nationwide District- STV in 13
SEATS wise SEATS constit.
MLP 109990 1 109991 32 34 (-2 34 (-2)
PN 114134 16 114150 33 31 (+2) 31 (+2)
Others 29 -17 12
TOTAL 224153 0 224153 65 65 65
1987 ELECTION.
(i) (ii) (iii)
PARTY 1st Transfers Final D'Hondt d'Hondt Actual
count to party count 1st count 1st count Election;
Nationwide District- STV in 13
SEATS wise SEATS constit.
MLP 114936 259 115195 32 34 (-2) 34 (-2)
PN 119721 43 119764 33 31 (+2) 31 (+2)
Others 511 -302 209
TOTAL 235168 0 235168 65 65 65
1992 ELECTION.
(i) (ii) (iii)
PARTY 1st Transfers Final D'Hondt d'Hondt Actual
count to party count 1st count 1st count Election;
Nationwide District- STV in 13
SEATS wise SEATS constit.
PN 127932 1802 129734 34 34 34
MLP 114861 1535 116396 30 31 (-1) 31 (-1)
AD 4186 -3337 849 1 0 (+1) 0 (+1)
TOTAL 246979 0 246979 65 65 65
End of Table V.
METHOD B: THE DISTRICTWISE A PRIORI METHOD.
This method is proposed to achieve nationwide proportional
representation by a priori adjustments to the STV, and can be
described as follows:
i) Perform the first count of a General Election as carried out
presently in Malta, but without referring to candidates' names.
This first step will determine the first count vote for every party
in each district.
ii) Find the grand total of votes each party polls over the
different districts. This will give the nationwide first count
vote.
iii) Calculate the nationwide estimate of seats won by a party
using the d'Hondt divisor method. This gives the definitive number
of candidates that will be elected from a given party.
iv) Calculate the number of first count votes each party
polls in each district, and by simple addition, deduce the districtwise
estimate of seats. (This estimate very often turns out to be
identical to the actual outcome of the STV as carried out at
present).
v) If the nationwide and districtwise estimates are equal, the
latter estimate will give the correct distribution of party seats
in each district, which on adding over all districts will
automatically give the desired nationwide proportionality.
vi) If the districtwise estimate of seats differs from the
nationwide estimate, the appropriate number of seats are swapped
between parties in the individual districts as explained above.
After the swaps, nationwide proportionality will have been
achieved, and the districtwise estimate so modified will give the
number of candidates to be elected from each district for each
party.
vii) The first count votes are now inspected for the candidates'
names, and the STV election can proceed exactly as in previous
elections. In a given district, the predetermined number of
candidates of a given party, as explained in v) or vi) above, are
elected. The number of candidates a party can win in a district has
to be equal to this preassigned number, and cannot exceed it.
Counting of votes for a party or transfer of votes to that party's
candidates can then be stopped in that district, once the
predetermined number of candidates for that party is elected.
A DIRECT METHOD FOR ASSIGNING SEATS TO DISTRICTS.
In the previous sections, an attempt was made to find the
definitive distribution of the nationwide seats of a party by
finding the divisor distribution for each district, and hence
affecting a number of pertinent seat swaps to achieve nationwide
proportionality. Whereas it is generally easy to perform these
swaps, hypothetical elections can be conjured up, in which it can
prove to be difficult to determine which swaps are required. In
this section an easier and more direct distribution of the
nationwide seats amongst the districts is described. This procedure
is done for the election of 1962 in Table VI. In Appendix V the
analysis is done for all General Elections on and after 1966, and
also for a hypothetical election in which it proved to be difficult
to implement the seat swaps described previously.
We now discuss the output for the election of 1962 in Table VI. The
first count votes of each party in each district is first given,
followed by the national total of first count votes. The number of
nationwide seats for each party is then calculated using the
d'Hondt divisor method, and written in the next line.
For each party, the percentage vote it obtained in each district
is calculated and written down in a matrix as shown below. The sum
of each row adds up to 100%. This matrix gives the relative
strength of each party 1n a given district. It gives the number of
votes a party would have obtained if there were 100 valid votes
cast in that district.
The parties are then sorted in descending order of first count
votes obtained on the national level, and district seats will be
assigned to the parties in this order. Referring to the election
of 1962, the PN is the largest party, and so we start by assigning
its nationwide complement (22) of seats amongst the districts. The
22 seats are assigned amongst the 10 districts by the d'Hondt
divisor method on the basis of the relative strength of the party
in the districts. (Whereas before, seats were assigned to the
various parties in a given district, the divisor method can be
analogously used to assign seats to districts for a given party.
It is as if the districts are competing between themselves to gain
these 22 seats.)
The percentages of the PN in the 10 districts (given in the second
column in the last matrix mentioned) are multiplied by a suitable
factor, say 100, for convenience and are written in a row under
the heading of the corresponding district. Since 5 seats are at
first available to each district, these quantities are divided by
divisors I, 2, 3, 4, 5 and the quotients are written in the
appropriate column. One then proceeds to choose, as in the divisor
method, the largest 22 numbers from these 50 numbers. The number
of numbers chosen in each column gives the number of PN candidates
assigned to that district. In the first district for instance, the
PN was assigned 2 seats leaving 3 seats still available in that
district for the other parties. Similarly in the second district
4 seats are left for the other parties since the PN managed to get
only 1 seat in this district. In the tenth district, the PN obtains
3 seats, leaving the remaining 2 seats for the other parties.
The second assignment is then performed for the second largest
party, the MLP. Its vote percentages in the districts are
multiplied by a suitable factor, say 100, for convenience, and are
written in a row under the corresponding district heading. They are
then divided by the divisors 1, 2, ... up to the number of seats
still available in that district. In the first district only the
first 3 quotients are written in the relevant column, since only
3 seats are left for that district. Similarly, in the second
district, only 4 quotients are calculated since that is the number
of seats still available for that district. This is done also for
the other districts. The largest 17 numbers are then chosen from
the ten columns for the assignment of the 17 seats of the MLP in
the ten districts. Thus for example, the MLP gets 2 and 3 seats
respectively in the first two districts, leaving 1 seat still
available for the other parties in each of these districts.
It is clear that this procedure can be repeated until the seats of
every party are all assigned to the various districts. The final
seat distribution by party and by district obtained in this manner
can be termed the partywise distribution of seats. This is to
distinguish it from the districtwise distribution explained
previously.
The partywise distribution of seats is given at the end of the
analysis of each election. This distribution is compared to the
result of the actual election. A + near a number signifies that
that party got an extra seat in that district in the actual
election. Conversely, a - sign indicates that the party got a seat
less in that district in the election. Thus for example, in 1962,
in the II district, the PN got one seat more, and the CWP one seat
less in the actual election than what is shown in the actual table.
The plusses and minuses for the other districts, can be similarly
interpreted.
The partywise distribution of seats automatically satisfies the
constraint of nationwide proportional representation. It is
independent of the configuration of the district boundaries, and
hence does not necessitate any seat swaps. This is in direct
contrast with the districtwise distribution which usually needs a
number of seat swaps to be restored to proportionality.
TABLE VI. Direct assignment of the nationwide seats of a party to
the various districts for the election of 1962. This depends solely
on the percentage vote of the party in a given district, and does
not depend on seat swaps. It is therefore easier to implement. The
divisor method is used to distribute a party's seats between the
districts on the basis of its relative (percentage) strength in the
districts. It is as if the districts are competing with each other
to obtain the party's seats. This distribution is termed the
partywise distribution, to distinguish it from the previously
described districtwise distribution. See also Appendix V at the end
of this study, for elections after 1962.
ELECTION OF 1962.
Number of parties is 7. Number of seats is 50. Number of districts is 10. Number of seats/ district is 5.
DISTRICTS PARTIES.
MLP PN PCP CWP DNP DCP IND
I 5532 7556 795 979 1720 143 0
II 9170 4359 178 1672 937 0 0
III 6512 4908 269 1704 656 0 0
IV 6919 6226 245 681 505 0 0
V 4860 7051 404 1069 784 0 0
VI 3457 7072 621 1579 1419 247 0
VII 4493 6152 2397 1489 2285 152 0
VIII 5292 5588 697 1853 1399 116 0
IX 3896 7368 981 1366 1353 41 0
X 843 6982 703 1893 2910 0 128
TOTAL VOTE:
50974 63262 7290 14285 13968 699 128
NATIONWIDE SEATS:
17 22 2 5 4 0 0
% vote of each party by district:
I 33.076 45.178 4.753 5.854 10.284 0.855 0.000
II 56.203 26.716 1.091 10.248 5.743 0.000 0.000
III 46.352 34.935 1.915 12.129 4.669 0.000 0.000
IV 47.468 42.714 1.681 4.672 3.465 0.000 0.000
V 34.303 49.767 2.851 7.545 5.534 0.000 0.000
VI 24.015 49.128 4.314 10.969 9.858 1.716 0.000
VII 26.479 36.256 14.127 8.775 13.467 0.896 0.000
VIII 35.410 37.390 4.664 12.399 9.361 0.776 0.000
IX 25.965 49.104 6.538 9.104 9.017 0.273 0.000
X 6.263 51.876 5.223 14.065 21.621 0.000 0.951
Parties in descending order of size: PN, MLP, COOP, DNP, PCP.
Direct assignment of seats (1962):
PN scan
-------
District I II III IV V VI VII VII IX X TOTAL
Seats available:
5 5 5 5 5 5 5 5 5 5 65
%*100: 4518 2672 3494 4271 4977 4913 3626 3739 4910 5188
1 4518 * 2672 * 3494 * 4271 * 4977 * 4913 * 3626 * 3739 * 4910 * 5188 *
2 2259 * 1336 1747 * 2136 * 2489 * 2457 * 1813 * 1870 * 2455 * 2594 *
3 1506 891 1165 1424 1659 * 1638 1209 1246 1637 1729 *
4 1130 668 874 1068 1244 1228 907 935 1228 1297
5 904 534 699 854 995 983 725 748 982 1038
Choose largest 22 Smallest 1683 in District VI Seat 3.
PN 2 1 2 2 3 3 2 2 2 3 22
Seats still available:
3 4 3 3 2 2 3 3 3 2 28
MLP scan
--------
District I II III IV V VI VII VII IX X TOTAL
Seats available:
3 4 3 3 2 2 3 3 3 2 28
%*100: 3308 5620 4635 4747 3430 2402 2648 3541 2597 626
1 3308 * 5620 * 4635 * 4747 * 3430 * 2402 * 2648 * 3541 * 2897 * 626
2 1654 * 2810 * 2318 * 2374 * 1715 * 1201 1324 1771 * 1299 313
3 1103 1873 * 1545 1582 * 883 1180 866
4 1405
Choose largest 17 Smallest 1582 in District IV Seat 3.
MLP 2 3 2 3 2 1 1 2 1 0
Seats still available:
1 1 1 0 0 1 2 1 2 2
CWP scan
--------
District I II III IV V VI VII VII IX X TOTAL
Seats available:
1 1 1 0 0 1 2 1 2 2 11
%*100: 585 1025 1213 467 754 1097 878 1240 910 1407
1 585 1025 * 1213 * 467 754 1097 * 878 1250 * 910 1407 *
2 585 439 455 704
Choose largest 5 Smallest 1025 in District II Seat 1
CWP 0 1 1 0 0 1 0 1 0 1 5
Seats still available:
1 0 0 0 0 0 2 0 2 1 6
DNP scan
--------
District I II III IV V VI VII VII IX X TOTAL
Seats available:
1 0 0 0 0 0 2 0 2 1 6
%*100: 1028 574 467 347 553 986 1347 936 902 2162
1 1028 * 574 467 347 553 986 1347 * 936 902 * 2162 *
2 674 451
Choose largest 4 Smallest is 902 in District IX Seat 1
DNP 1 0 0 0 0 0 1 0 1 1 4
Seats still available:
0 0 0 0 0 0 1 0 1 0 2
PCP scan
--------
District I II III IV V VI VII VII IX X TOTAL
Seats available:
0 0 0 0 0 0 1 0 1 1 2
%*100: 479 109 192 168 285 439 1425 470 656 527
1 1425 * 656 *
Choose largest 2 Smallest is 656 in District IX Seat 1
PCP 0 0 0 0 0 0 1 0 1 0 2
Seats still available:
0 0 0 0 0 0 1 0 1 0 2
ALL SEATS ARE NOW ASSIGNED.
FINAL SEAT ASSIGNMENT IN DISTRICTS (1962):
District I II III IV V VI VII VIII IX X TOTAL
PN 2 1+ 2 2+ 3 3 2 2 2+ 3 22
MLP: 2 3 2 3- 2 1 1 2 1 0 17
CWP: 0 1- 1 0 0 1 0+ 1 0+ 1- 5
DNP: 1 0 0 0 0 0 1 0 1- 1+ 4
PCP: 0 0 0 0 0 0 1 0 1- 0 2
TOTAL: 5 5 5 5 5 5 5 5 5 5 50
Each + indicates that in that district a party gained one more seat in the actual
election. Thus for example, the PN got an extra seat in the II, IV and IX district in
the actual election. Plus and minus signs should balance in each district.
See also Appendix V at the end of this study for elections on and after 1996 and
for a hypothetical election where seat swaps were difficult to implement.
End of Table VI.
METHOD C: THE PARTYWISE A PRIORI METHOD.
This method is proposed to achieve nationwide proportional
representation by a priori adjustments to the STV, and can be
described as follows:
i) Perform the first count of a General Election as carried out
presently in Malta, but without referring to candidates' names.
This first step will determine the first count vote for every party
in each district.
ii) Find the grand total of votes each party polls over the
different districts. This will give the nationwide first count vote.
iii) calculate the nationwide estimate of seats won by a party
using the d'Hondt divisor method. This gives the definitive number
of candidates that will be elected from a given party. List the
parties in descending order of their nationwide first count vote.
iv) Starting with the largest party, calculate the percentage of
first count votes a given party polls in each District. These
percentages give the relative strength of the party in the various
districts. The nationwide seats of the party are then distributed
amongst the districts. The number of seats still available to the
remaining parties in each district is then calculated.
v) This process is repeated for the smaller parties until all the
remaining seats have been assigned.
vi) The distribution of seats as described in iv) an] v) is the
partywise distribution of seats, and is identical to the nationwide
distribution of seats.
vii) The first count votes are now inspected for the candidates'
names, and the STV election can process exactly as in previous
elections. In a given district, the predetermined number of
candidates of a given party, as explained in iv), v) or vi) above,
are elected. The number of candidates a party can win in a district
has to be equal to this preassigned number, and cannot exceed it.
Counting of votes for a party or transfer of votes to that party's
candidates can then be stopped in that district, once the
predetermined number of candidates for that party is elected.
COMMON ADVANTAGES OF METHODS A, B AND C
The proposed systems A, B, and C afford numerous advantages:
i) Nationwide proportionality is necessarily guaranteed;
ii) The total number of seats in Parliament is fixed at 65;
iii) Regional representation is preserved, since 5 members are
returned from every district;
iv) The voter will be required to vote in exactly the same way
as he did before. The proportional adjustments to the election are
transparent to him;
v) Since the number of seats is fixed and parties gain seats at
the expense of other parties, the system is more difficult to be
exploited by a number of parties working in collusion to manipulate
the number of seats in their favour:
vi) The system is fair to all parties whether large or small; in
particular a party which obtains many votes nationwide but still
fails to win a seat can obtain representation in Parliament by this
method;
vii) In methods A and B, swaps of seats between parties are done
in a logical way; ie. seats will change where the offended party
is most under represented - this will in fact actually encourage
the drawing of fair constituency boundaries.
COMPARISON OF METHODS A, B WITH C.
viii) In method A, the STV is carried out exactly as usual, and
this will certainly please diehard advocates of STV. However, the
result of the STV has to be necessarily treated as provisional, and
potentially subject to subsequent seat swaps. Also candidates who
are 'unseated' could feel a little cheated of success if their seat
happens to be repealed by a subsequent swap.
ix) In methods A and B, the notion a: under representation is an
attractive mechanism to redress an inherent injustice in the STV,
that is the possible lack of nationwide proportionality in the
partial result. However, it can turn cut to be quite difficult to
determine which swaps are necessary to achieve proportionality in
the final result.
x) The method C does not suffer from the disadvantages listed in
viii and ix, because it does not necessitate any seat swaps to
achieve a proportional result. Besides, since the number of seats
for each party in each district is determined a priori, candidates
in an election will not feel so aggrieved if they do not succeed
in being elected. By method C (and B also), the candidates are
simply not elected, rather than first 'elected' and then 'unseated'
as in Method A.
xi) Because of the reasons given in viii, ix, and x, Method C seems to
be superior to the other two methods. It arrives at the final
distribution of seats in an elegant manner, without necessitating
any seat swaps. The reason for this is that unlike A and B, the
method C is independent of the district boundaries.
THE STV IN METHOD C.
The STV is an important feature of all the three methods proposed
in this study. In all of these, the important features of STV are
retained as far as possible. It is clear that an STV conducted
exactly as it was prior to 1987 could easily lead to a non
proportional result, which is not at all desirable by any
standards. These three methods all retain the STV process with a
minimum of amendments, and this only to attain an outcome which is
deemed fair both by the parties and the electorate.
The ethos of the STV process is maintained throughout. Votes are
still inherited from candidate to candidate, from party to party.
It is only when the STV deviates from proportionality, that such
amendments come into play, and this only to achieve a highly
desirable end. In Method C (and B also), counting of votes and
transfers to a party stop when it has gained its complement of
seats in the district. Although this seems unnatural in an STV, it
is not at all different from the normal STV. Here counting stops
when all the five candidates of the district are elected,
irrespective of the nationwide result.
Fervent supporters of the STV method of election, who are also keen
on the democratic principle of nationwide proportionality, should
consider methods A, B and C to be logical extensions to the STV
process, which ultimately serve to make the system even fairer than
it was before. All parties, whether large or small, are treated by
these methods in as fair a manner as one is liable to get in any
electoral system. In particular, small parties which do not get a
whole quota in the individual constituencies, stand to gain several
seats in parliament on the basis of their nationwide first count
vote. The individual parties, whatever their size, should not be
apprehensive of methods such as are described in this study.
The personal preference of this author is for Method C, the a priori
partywise distribution. This seems to be the most streamlined
process, without- either the need of any seat swaps, or the need of
'unseating' a provisionally elected candidate. Unlike Methods A
and of B also, Method C is independent of the constituency boundaries.
CALCULATIONS.
The first count votes, transfers, the candidate data and the other
raw data used above for the General Elections between 1962 and 1992
were obtained from the book by John C. Lane quoted below. For each
election, the first count votes were added together over the
districts to find the quota: vote for each party. The divisor method
of d'Hondt was used to estimate the number of seats won nationwide
by each party. The predetermined number of seats is then chosen
with the highest vote to seat ratio. The same procedure is also
carried out for the final count vote. These calculations were
performed using Lotus 123 Version 2.01.
Various other divisors are mentioned in the literature, so we
repeated the analysis with the St. Lague system of divisors. The
d'Hondt estimate for the number of seats was found to be always
nearer the actual election result than the predictions of the St.
Lague system. For clarity and simplicity, we therefore decided to
discuss only the d'Hondt estimates in the text.
The calculation of the number of seats using the d'Hondt estimate
was also corroborated: by entering the nationwide vote counts into
a GWBASIC program called Divisor.bas. This automatically calculates
the number of seats won by a party in a given election.
The simulation of elections between three parties was done using
a GWBASIC program called Simulate.bas. Paragraphs i) to v) of the
previous section were illustrated by this simulation.
A floppy disc containing these items of software is included for
the perusal of the reader.
ACKNOWLEDGMENTS
I would like to thank Mr Joe Grima, Dr Lawrence Gonzi, Dr Austin
Gatt, Dr Paul Lia and Dr Wenzu Mintoff for their kind assistance
and helpful comments white this study was being completed.
REFERENCES.
Bogdanor Vernon, 1984. What Is Proportional Representation? Martin
Robertson, Oxford.
Carstairs Andrew McLaren, 1980. A Short History of Electoral Systems in
Western Europe. Allen and Unwin, London.
Dingli Adrian, 1988. A Comparative Study Of Electoral Systems.
Dissertation in part fulfilment for the degree of Doctor of Laws,
University of Malta.
Dummett Michael, 1984. Voting Procedures. Clarendon Press, Oxford.
Harrop Martin and Miller William L., 1987. Elections and Voters.
Macmillan Education, London.
Lane John C., 1993. Maltese Elections: District Data and Candidate Checklist;
Preliminary Version. Amherst. New York.
Spiteri M. C., 1984. Cutting the Gordian Knot. Letter to The Sunday Times
of the 24th June 1984, Malta. Also quoted in Dingli Adrian above.
These appendices are omitted here.