The Buhagiar Report

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.





There were 5 appendices to the Buhagiar report, providing additional detail and illustrations of his proposals.

These appendices are omitted here.



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