In 1994 Anton Buhagiar wrote a report to Malta's Gonzi Commission in which he suggested a method for assuring a more proportionate distribution of parliamentary seats among the competing political parties. The present article is a follow-up to that report and demonstrates a way to assure a more equitable assignment, among the electoral districts, of the parliamentary seats that political parties have won.
THE PRIORITY QUEUE:
A FAIR METHOD FOR THE ASSIGNMENT
OF SEATS TO DISTRICTS.
by
Anton Buhagiar
Statistics Unit,
The University of Malta.
8th June 1995.
In the report submitted in November 1994 to the Commission on Electoral Reform, diverse electoral methods were suggested, which are gauranteed to secure the highly desirable feature of nationwide proportional representation. This means 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.
Of these methods, the easiest to use was the partywise distribution method. This method consists of first determining the total number of nationwide seats which should be assigned to a given party on a nationwide basis. This is achieved in the following way:
i) Count the first count votes for each party in each district;
ii) Add the votes obtained by a given party in each district, thus obtaining the nationwide total of first count votes for that party;
iii) Use the d'Hondt Divisor method on the nationwide first count total found in ii) to determine the total number of seats which a given party should be assigned on a nationwide basis.
The second step of the partywise distribution method is to assign the nationwide seats of a given party to the different districts. This necessitates further steps as follows:
iv) Sort the parties in descending order of nationwide first count vote (using the information in ii),
v) Calculate using i) the percentage of votes polled by a party in each district;
vi) Starting with the largest party, use the d'Hondt divisor on the district percentages for that party. The party's seats are then assigned to the districts with the highest quotients. The seats that have already been taken are then subtracted from the total of seats allowed for that district.
vii) Repeat the procedure in vi) with the next largest party as determined by the order in iv) above. Eventually, the seats of all the parties, from the largest down to the smallest, are assigned to the various districts.
When the number of seats of a given party have been determined for each district, the first count votes can then be inspected for the candidates' names, and the STV process can proceed exactly as in previous elections. In a given district, the predetermined number of candidates of a given party are elected. The number of seats 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.
Details of the partywise calculations on Maltese General Elections from 1962 to 1992, are given in the above mentioned report. For the convenience of the reader, we also give details of the partywise method for the election of 1992. Steps i) to vii) above are given in detail for this election in Appendix I of this report. No threshold is assumed in this case.
SEAT DISTRIBUTION BY DISTRICT IN THE PARTYWISE METHOD.
There are numerous advantages of the partywise distribution, and these were referred to in the previous report. However, the final distribution of the parties' seats by district is in some cases not wholly satisfactory. In the election of 1992, for instance, the partywise distribution assigns the only seat of the AD to the II District, rather than the XI District where they obtained most votes. (Please refer to Appendix I for details of this election). A similar instance occurs in the election of 1971, where the partywise method 'misplaces' an MLP seat from District IX to District I, and misplaces a PN seat the other way round.
It is therefore the aim of this study to find whether the partywise distribution can be modified to obtain an improved distribution of the contesting parties' seats in the districts. In particular, how can one amend steps iv) to vii) above to secure a fairer distribution of a party's seats in the different districts?
The proposed order for the party scans in the partywise distribution was that determined by the size of the nationwide first count vote, as mentioned in iv) above. The largest party has all its seats assigned first to the districts, then the next largest, and so on, until finally one assigns the seats of the smallest party. By the time one reaches the scan for the smallest party, most of the district seats will have been already filled, with the result, say, that such a party will be awarded its seat in a district where it does not the have highest number or the highest district percentage of votes.
The problem is that in the partywise distribution, where seats are distributed by party, all the seats of a given party will have a higher priority over the choice of district than any seat of a smaller party. It could therefore happen that a seat which was marginal for the larger party could be assigned to a district, which should have been assigned to a less marginal seat of a smaller party.
Conceivably one can alter the order, specified in iv) and vi) above, in which the parties are scanned for the partywise distribution of seats. If for example one were to start with the smallest party first, and end up with the largest, the partywise seat distribution in the districts might turn out to be unfair on some candidates of the larger parties. The problem is that whatever the order of the party scans, priority in the partywise distribution is determined by party size only, without any other consideration whatsoever.
THE PRIORITY QUEUE.
A possible remedy to this problem is to avoid using the concept of party priority implicit in the partywise distribution. A more sophisticated criterion to use is individual seat priority, or equivalently nationwide priority, whereby one has to decide which party gets the first seat, which party gets the second seat, and so on, up to the 65'th seat. This sequence of individual party seats determines the order in which each individual seat is assigned to the districts.
Once again the elegant method of d'Hondt can be easily utilised to determine which party has priority on each individual seat. As an illustration, we take the Maltese General Election of 1992, and assume that there is no threshold. In Table I, we give the calculation to determine the number of seats won by each party on a nationwide basis. The highest 65 quotients are chosen from the three columns, giving 34 seats to the PN, 30 seats to the MLP, and 1 seat to the AD.
To find the priority of the parties on these 65 seats, one again sorts these 65 numbers in descending order of magnitude. The largest quotient written in the columns of Table I is 127932, and corresponds to the first divisor of the PN. The PN has therefore priority over the first seat to be assigned to some district. The second largest quotient is 114861, which is the highest quotient for the MLP. The MLP therefore has priority over the second seat. The third largest quotient is 63966 in the PN column, which therefore has priority over the third seat. This can be repeated for each single seat.
The priority list for parties for each individual seat is given in Table II. As can be seen, the sequence is given by PN, MLP, PN, MLP, PN, ..... , PN. The AD, for example, has priority over the 58'th seat, whilst the PN has priority over the 65'th seat, which is the last one to be awarded.
The 65 party seats can therefore be considered as a queue of length 65. The party sequence in this queue determines the order in which each individual party seat is assigned to the districts. For this reason, this procedure can be termed the priority queue method. This is in clear contrast to the partywise distribution where all the seats of a larger party have a higher priority than any seat of a smaller party.
To see how seats are assigned to districts in the priority queue, the d'Hondt divisor is again used, this time on the percentage of votes each party polls in each district. Please refer to Table III.
For each separate party, a matrix is first set up having thirteen columns. In the first row there are the 13 district names, I, II, up to XIII, and in the second row there is the percentage of votes obtained by that party in each of the districts. Thus, in the matrix for the PN, it can be seen that this party got 54.80% of the first count votes in the first district, 31.93% of the first count votes in the second district, and so on. In the thirteenth district it obtained 58.94%. (In this case the percentages are multiplied by a factor of 100 for convenience). Since there is a total of five seats available in each district, these district percentages are divided by the d'Hondt divisors, 1, 2, 3, 4, 5 and the quotients are written in the appropriate column. The matrices for the other parties are constructed in an analogous manner.
Seats are then assigned to the districts according to the nationwide priority established in Table II. Here it was shown that the PN has priority over the first seat. The PN matrix in Table III is therefore scanned first for the largest quotient (7129) which turns out to be in the 10'th district. The PN is therefore awarded a seat in this district. The nationwide priority of the seat (1 in this case) is then written in boldface just beneath this quotient, which is also marked with an asterisk.
Similarly, from the priority list in Table II, it can be seen that the MLP has priority over the second seat. The MLP matrix in Table III is therefore scanned for the largest quotient. This turns out to be 6637 in the second district. The MLP is then awarded a seat in the second district. The priority of this seat (2 in this instance) is then written beneath this quotient, which is also marked with an asterisk.
Proceeding down the list, we assign the 3rd seat to the PN in the seventh district (with quotient 6162), and the fourth seat to the MLP in the third District (quotient 6105). At every step one chooses from the matrix of the relevant party, the highest quotient which has not yet been chosen. The priority is then written beneath it, and that quotient is then marked with an asterisk.
One must also be careful whilst following the priority list, that seats are not assigned to districts that already have their full complement of seats. Taking for instance the 58'th seat pertaining to the AD, it can be seen that the highest quotient for this party is 218 in the ninth district. However the seat cannot be assigned there because that district already has its full complement of five seats. The next available quotient is then taken, which is 210 in the eleventh district. This is in fact the district where AD obtained most votes.
Following this procedure, it is not difficult to assign every single seat in the priority queue individually to the districts. As can be deduced from Table III, the matrix for each party will then determine the number of seats awarded to that party in each district, along with the individual seat priorities.
Alternatively for convenience, each party's matrix of district quotients can be written as a list of quotient and district. This is then sorted for each party separately in descending order of quotient. (These lists are given next in Table III). One then follows the nationwide priority party sequence to choose the appropriate party list, and hence to assign the next available district to that party seat. The nationwide priority for each assigned seat is then written in the left hand column of the relevant list. Each of these lists can be considered as a queue, where districts are waiting to be assigned to the seats of a given party.
The final distribution of party seats in the districts as predicted by the priority queue method for the Maltese General Election of 1992 with no threshold assumed, is summarised in the last part of Table III. As pointed out before, this distribution is practically identical to the actual election result, except that the AD is awarded a seat in the eleventh district, where it polled the highest number of votes.
This assignment of the nationwide seats gained by a party to the various districts can also be appreciated by drawing up a detailed schedule of how the seats are allocated to the districts. This schedule is displayed in Table IV. Each district quotient shown in Table III is listed in a matrix, along with the corresponding information including party, district, and d'Hondt divisor. Each quotient and its relevant information occupies one row in this matrix. For the sake of clarity, these rows are then sorted in descending order of quotient magnitude, and are shown in this order in Table IV below. The order defined by the district quotients in this table can be referred to as districtwise priority, to distinguish it from the nationwide priority referred to earlier.
According to the nationwide priority list shown in Table II, one awards the first seat to the PN. Looking up the list in Table IV, the highest PN seat is the first seat of the tenth district, which is the first one to be awarded to the PN. The nationwide priority of this seat is then written in the left hand side under the PN column. Similarly the second nationwide seat is to be awarded to the MLP. In Table IV, the highest MLP seat is the first seat in the second district. The nationwide priority (namely 2) of this seat is then written in the left hand side under the MLP column. Continuing in this way, alternately scanning the nationwide and the districtwise priority lists (Tables II and IV respectively), one can determine how the party seats are assigned to the districts.
Thus for example, as can be easily seen from the comments in the right hand side of Table IV, the ninth district is awarded the seats with nationwide priority 11, 16, 36, 46, and 56. The numbers 11, 36, and 56 represent the seats of the PN, whereas the numbers 16 and 46 represent the priorities of the MLP seats. This ninth district gains its full complement of 5 seats when the PN is awarded the 56'th nationwide seat in this district.
Assuming one has already distributed the first 56 seats, the 57'th seat is then awarded to the MLP in District 4. On assigning the AD the 58th nationwide seat, one then searches for the highest quotient of the AD, which is 218 in District 9. This seat, however, cannot be awarded since District 9 was already filled with the 56'th seat. Therefore the next highest AD quotient is searched, which is 210 in the 11'th District. This seat is then awarded to the AD in the 11'th District, which now has its full complement of seats. Similarly, the 60'th seat is not awarded to the MLP in the 11'th District (with the highest available quotient of 1832), because that District is already full. The seat is then awarded to the District with the next highest MLP quotient (1819), namely the Seventh District. This District has now gained all its five seats, and henceforth cannot take any more seats.
Proceeding in this way, one finally arrives at the last seat, the 65th seat, which the PN gains in the Tenth District. The distribution of party seats over the districts can then be seen to be identical to that given in the last part of Table III.
SEAT DISTRIBUTION USING THE PRIORITY METHOD WITH THE D'HONDT SET OF DIVISORS FOR BOTH THE NATIONWIDE AND THE DISTRICT CALCULATIONS.
The predictions of the priority method for General Elections held in Malta in and after 1962, are shown in Table V. Here the d'Hondt set of divisors was used on both the nationwide first count votes and on the district percentages to obtain the nationwide priority and the seat distribution in the districts respectively.
For each election, the calculations are first done assuming that there is no threshold. A national threshold is then imposed to eliminate the smallest party with seats, and the distribution is recalculated using the priority method. This is repeated until only the two largest parties are left to compete for the available seats. In this and similar analysis, where a national threshold is imposed, parties which polled less than this threshold are not awarded any seats, but the district percentages of the other parties still in contention are not altered by the exclusion of the smaller parties.
The final distribution of party seats in the districts afforded by the priority queue seems to be fair in general, and agrees quite well with the actual election result. This is especially true in those elections, namely those of 1971 and 1976, where the nationwide number of party seats tallies exactly with the actual election result.
It can be seen from Table V, that for the elections of 1971 and that of 1976, the priority queue method predicts the exact election result. The partywise method by contrast fails to do so for the 1971 election. Relative to the actual election result, the partywise method displaced one MLP seat from the ninth to the first district, whereas one PN seat was displaced the other way. It should also be recalled that in this (1971) election, the number of seats available to each district was not constant, but was either five or six, depending on the district. In spite of this, the priority queue method predicts the election result exactly.
It was also shown above that in the election of 1992 with no threshold, the priority queue method awards a seat to the AD in the eleventh district, where it got most votes. By contrast, the partywise method awards this AD seat to the second district. The priority method yields a result which is fairer to the affected candidates of both parties concerned, the AD and the MLP in this case. It is also interesting to note that if a nationwide threshold of 5% is imposed in this election, the AD loses its seat in favour of the MLP, and the partywise and priority methods both agree exactly with the final election result.
Again, in the election of 1966 with no threshold, the priority queue method awards three seats to the CWP in the sixth, seventh and eighth districts, where this party is strongest. By contrast, the partywise distribution removes a CWP seat from the sixth district, and places it in the second district, where it polled only a relatively small number of votes. In general, the priority distribution seems to be fairer not only to the smaller parties, but also, indirectly, to the candidates of the larger parties affected by this change in district.
The priority method also gives a fair result for the election of 1966, assuming a national threshold of 6%. The CWP is eliminated with this threshold. (Please refer to Table V). The priority method predicts a marginal distribution of 26 seats for the PN, and 24 seats for the MLP, just like the partywise distribution. The seat assignment to the districts by the two methods, however, differs in the second and the seventh districts. The priority method predicts 1 seat for the PN and 4 seats to the MLP in the second district, and 3 seats to the PN and 2 seats to the MLP in the seventh district.
On the other hand, the partywise method predicts 2 seats for the PN and 3 seats for the MLP in the both the second and the seventh districts. This is not so fair on the PN candidates in the 7th district, since the PN got about 2000 more votes than the MLP in this district. An event such as this, where a party gets more votes than another in a district but gets less seats (or vice-versa) will henceforth be referred to as an inversion. It is clear that for a given nationwide distribution of seats, a districtwise distribution with a fewer number of inversions is fairer than a distribution with a larger number of inversions. The voting pattern in the districts will be respected more when there are fewer inversions, or better still, when there are none at all.
It is also interesting to note that in the eighth district both the priority and the partywise methods assign 3 seats to the MLP and 2 seats to the PN, even though the latter party polled 57 more votes than its rival in this district; (ie. both methods produce an inversion in the 8th district). However, such inversions have actually occurred also in past elections because a good number of votes can be wasted on unelected candidates. Besides such a paradoxical result can be interpreted as a 'seat swap', as in the districtwise a priori method, to restore an abnormal election result to nationwide proportionality.
More detailed comparisons of the priority and the partywise methods will be discussed in the following sections in this study.
THE EFFECT OF DIVISOR ON THE NATIONWIDE CALCULATION IN THE PARTYWISE AND PRIORITY METHODS.
The partywise and priority methods are two similar procedures based on the divisor method to translate a given number of party votes into parliamentary seats. So far only the d'Hondt set of divisors has been considered in our calculations, but there are other sets of divisors which are commonly used in such contexts. The most popular sets of divisors are the following:
a) the D'Hondt set of divisors: 1, 2, 3, 4, 5, ....;
b) the modified Sainte Lague : 1.4, 3, 5, 7, 9, ....;
c) the Sainte Lague : 1, 3, 5, 7, 9, ....;
d) equal proportions : (root 2)/3, root 2, root 6, root 12, ..;
e) the Danish system : 1, 4, 7, 10, 13, .... .
Different sets of divisors make it more or less difficult for the smaller parties to obtain representation in Parliament. The sets of divisors a) to e) listed above are given in the sequence of increasing ease with which a small party stands to gain seats. Thus for a given voting pattern, the d'Hondt set offers the greatest difficulty for a small party to gain seats. The Danish system conversely tends to give seats to smaller parties with very little votes! (In the case of the method of equal proportions, the first divisor is not usually defined, but for the purpose of this study, it was taken to be 0.4714, to retain the same ratio between the first and second seat as for the Sainte Lague system).
In the priority method, as for the partywise procedure, divisors are used on two separate occasions: firstly to determine the number of seats earned nationwide by a given party; and secondly to distribute each seat in the various districts. These two steps are mainly independent of each other, and, tentatively, one can use a different set of divisors for these two distinct purposes. At this point it is natural to ask the following question: how does the choice of divisor affect the performance and the fairness of the partywise and priority methods?
The numerous advantages of these methods were referred to in the previous report. One of the most notable was that, when the total number of seats available is odd, a party which polls more votes than all the others together on a nationwide basis will then get an absolute majority of seats. This very important majority rule only holds true provided one uses the d'Hondt divisor, rather than any of the other divisors. It is therefore clear that one cannot replace the d'Hondt divisor in the nationwide calculation without sacrificing this important majority rule.
This is readily illustrated using the Monte Carlo method. In Appendix II, examples are given of elections between three parties A, B, and C. In these elections, party A gets more nationwide votes than parties B and C together, yet A fails to gain an absolute majority of seats when divisors other than the d'Hondt are used. By contrast, the d'Hondt set of divisors unfailingly gaurantees a majority of seats for party A in such a situation. A majority of votes and/or seats for party A is distinguished by a + sign in Appendix II.
In view of the foregoing arguments therefore, it is not advisable to use the modified Sainte Lague, the Sainte Lague, the equal proportion, or the Danish sets of divisors for the initial calculation of the number of nationwide seats due to a given party. In fact, the main reason for these divisors is to enable the smaller parties to gain a seat, even when they have obtained a small fraction of the quota obtained by the larger parties. This is illustrated by some elections in Appendix II. For example, in election number v), the Danish system awards one seat to party C with only 342 votes, when the average quota for the larger parties is about one thousand. The reason is that these divisors tend to equalise the percentage of votes wasted for each party, rather than the absolute number of votes. Thus a party with ten times as many votes as a smaller party will have ten times as many votes wasted! These divisor systems therefore have an effect opposite to that of the threshold. Whereas a threshold tends to exclude the smaller parties from the electoral contest, these divisor systems are inclined to assign seats to parties with a very small nationwide vote. For this reason, it is not advisable to employ these divisors for the preliminary calculation of the number of seats to be awarded to a party on a nationwide basis.
THE SAINTE LAGUE PRIORITY METHOD.
Having calculated the number of nationwide seats for each party, both the partywise and priority methods proceed to assign the seats to the various districts. In both cases this is done using a suitable set of divisors on the district percentages for each party. So far we have only used the d'Hondt set of divisors for this purpose. However once the total number of seats due to each party has been determined, it is only reasonable to examine how the final seat distribution in the districts is affected when one employs an alternative set of divisors on the district percentages. In this instance, it is the relative strength of the parties in the districts which is affected rather than their overall nationwide strength.
As an example of this we give detailed calculations for the priority method for the election of 1962, assuming there is no threshold. The nationwide number of seats and their priority is first computed using the d'Hondt set of divisors. The seats are then assigned to the districts, employing the Sainte Lague system of divisors (1, 3, 5, 7 ...) on the district percentages of first count votes.
For convenience, this method will be referred to as the Sainte Lague priority method. The computational details of this method are shown in Appendix III for the election of 1962 without a threshold. It can be seen that the calculation is very similar to the method shown above in Tables I, II and III for 1992. We now give a formal description of this method.
The Sainte Lague priority method achieves nationwide proportional representation by a priori adjustments to the STV, and can be described as follows:
i) Count the first count votes for each party in each district;
ii) Add the votes obtained by a given party in each district, thus obtaining the nationwide total of first count votes for that party;
iii) Use the d'Hondt Divisor method on the nationwide first count total found in ii) to determine the total number of seats which a given party should be assigned on a nationwide basis (see Table I), and also to determine the priority of each individual seat. Set up the nationwide priority list (as in Table II).
iv) Calculate using i) the percentage of votes polled by a party in each district;
v) For each party, set up its matrix of district percentages and the corresponding quotients calculated with the Sainte Lague system of divisors as in Appendix III. (One can also set up for each party, the corresponding district queue for convenience. This is obtained by sorting a party's matrix in descending order of quotient and noting the corresponding district, as explained previously).
vi) Starting with the seat of highest priority, identify the party to which it belongs from iii) above, and then search in the matrix of quotients of that party (or the corresponding district queue) for the highest available quotient. The seat will then be assigned to the district associated with that quotient.
vii) Take the next seat on the nationwide priority list, and repeat the procedure just described in vi). In this step, care must be taken not to assign seats to districts which are already full. Repeat until all seats on the nationwide priority list have been assigned to the districts.
viii) The STV can then proceed as described above for the partywise method.
Priority methods with other options for district divisors can be easily described in a similar fashion.
THE EFFECT OF DIVISOR ON THE DISTRIBUTION OF SEATS IN THE DISTRICTS.
To examine the effect of divisor further, and for the sake of completeness, we also give calculations for all possible combinations of divisor systems for both partywise and priority methods. This is done for all elections in or after 1962, with or without a threshold. The d'Hondt, modified Sainte Lague, Sainte Lague, equal proportions, and Danish systems are first used, in that order, to obtain the nationwide number of seats for each party, (and the priorities of these seats also in the case of the priority method). For each of these methods, the distribution of the seats in the districts is then obtained by using each of these divisors, in turn, on the district percentages. For any particular election with a given threshold, therefore, there are a total of twenty five divisor combinations, (although many of these often turn out to give identical results). The sequence of divisors, d'Hondt through to Danish, represents a greater facility for smaller parties to gain seats in the nationwide calculation, and an increasing tendency to even out a party's seats in the districts in the subsequent computation.
The partywise calculations are shown in Appendix IV, whereas the results for the priority method are given in Appendix V. The distributions for these two methods are given for all different divisor combinations. In Appendix VI, we compare these two methods for different divisor options in the districts. (For the sake of simplicity, however, we comment only on the case when the d'Hondt set of divisors is used to obtain the nationwide distribution).
On inspection of the various distributions arising from these two methods, it appears that the priority method with d'Hondt divisors for the nationwide calculation, and Sainte Lague divisors for the districts gives a seat distribution which is generally fair to all the contesting parties whether large or small, and whether there is a threshold or not. With this choice of divisors, the partywise method sometimes gives identical results, but is generally speaking less accurate in the assignment of the smaller parties' seats in the districts. The advantages of the Sainte Lague priority method are listed below.
ADVANTAGES OF THE PRIORITY SAINTE-LAGUE METHOD.
In this method, the seats of the smaller parties are generally awarded in the districts where they are strongest. Indirectly, this is also fair on candidates, of whatever party, who would have lost their seat had the small party been awarded its seat in a district where its following is weak. The 'correct' assignment of a smaller party's seats to the right districts leads to a more equitable distribution for all the contesting parties and for their candidates.
There also seems to be a smaller number of inversions for this method than for the other methods. It is clear that an electoral system with constituencies should as far as possible respect the voting pattern in each constituency. A party which polled significantly more votes in a district than another party should gain more, rather than less, seats in that district than the other party. Given a marginal (nationwide) distribution of seats, therefore, one should strive to achieve that distribution in the districts with the smallest number of inversions. The number of inversions when one uses the Sainte Lague priority method is generally smaller than for the other methods.
Another feature of this method is that it does not concentrate the seats of a smaller party in just one district. It can well happen that a small party that is awarded two seats on a nationwide basis gets both those seats in one district, even though its vote was rather evenly spread out over more than one district. (This happens for instance in the election of 1962 under various thresholds, when the PCP and DNP parties are each awarded two seats in one district by the other methods.) Such a distribution is clearly unfair to the other parties in that district, and could easily lead to inversions in that same district, and possibly also in other districts. This priority method does not have this drawback and seems to distribute a small party's seats reasonably well in the districts.
In a similar fashion, the Sainte Lague priority method will make it slightly more difficult (though certainly not impossible) for a large party to get a fourth seat in a given district. In a district with two major contending parties, it is slightly more probable to get a 3 seats to 2 result than a 4 to 1 result. (Please refer to comments on 1992 election in Appendix VI). Whereas this might seem strange in the light of results of recent elections, this method spreads the parties' seats more evenly in the districts, thus leading to a less polarised distribution of party seats.
The two proportional elections of 1971 and 1976 are also predicted perfectly by this method. It is interesting to remember that in 1971, the number of seats available to the districts was not constant, but was five or six depending on the district.
The main characteristic of the Sainte Lague priority method is that it is fair, and is seen to be fair by all parties, whether large or small, and by their candidates. It leaves less to chance than the partywise method: each seat is individually assigned to a party and hence to a district. The smaller parties are awarded seats where they are stronger rather than in districts where the larger parties did not happen to gain seats! The method generally also respects the voters' wishes in the individual districts, in that it keeps the number of inversions to an absolute minimum. Besides, the parties' seats are distributed quite evenly in the districts, thus keeping regional polarisation in check.
CALCULATIONS.
Since hundreds of distributions had to be computed for this study, resort had to be made to the digital computer. The seat distribution predicted by the partywise and priority methods for the different divisor systems was calculated by two computer programs in the GWBASIC language. These were written expressly for this purpose by the present author. Some of the calculations were also performed manually to corroborate the distributions predicted by these programs.
REFERENCES.
Buhagiar Anton, November 1994. Can one achieve nationwide proportional representation in Malta without major changes to the present method of election? Report submitted to the Commission on Electoral Reform, The Palace, Valletta, Malta.
Carstairs Andrew McLaren, 1980. A Short History of Electoral Systems in Western Europe. Allen and Unwin, London.
Lane John C., 1993. Maltese Elections: District Data and Candidate Checklist; Preliminary Version. Amherst, New York.
Table I: Use of the d'Hondt divisor to calculate the number of seats
due to a party on the basis of its first count nationwide vote.
This is done for the election of 1992, and no threshold is assumed
for this particular example. To elect 65 seats, the largest 65 numbers
are chosen from the three columns. These are marked with an asterisk.
The smallest of these 65 numbers is essentially a quota for the
divisor method, and is denoted by *-. In this case, it is equal to
3763, corresponding to the 34'th seat of the PN. Numbers smaller than
this quota are unmarked corresponding to unelected candidates.
The number of candidates assigned will then be 34 seats for the PN,
30 seats for the MLP, and 1 seat for the AD. Sorting these 65 numbers
in descending order will then determine which party has priority over
a given seat. This is done in Table II.
TABLE I:
ELECTION OF 1992; NO THRESHOLD ASSUMED:
PARTY: MLP PN AD TOTAL
Nationwide 1st
count votes: 114861 127932 4186 246979
% votes : 46.51 51.80 1.69% 100%
DIVIDE BY: NO OF
DIVISOR SEATS
1 114861* 127932* 4186* AD 1
2 57431* 63966* 2093 2
3 38287* 42644* 1395 3
4 28715* 31983* 1047 4
5 22972* 25586* 837 5
6 19144* 21322* 698 6
7 16409* 18276* 598 7
8 14358* 15992* 523 8
9 12762* 14215* 465 9
10 11486* 12793* 419 10
11 10442* 11630* 381 11
12 9572* 10661* 349 12
13 8835* 9841* 322 13
14 8204* 9138* 299 14
15 7657* 8529* 279 15
16 7179* 7996* 262 16
17 6757* 7525* 246 17
18 6381* 7107* 233 18
19 6045* 6733* 220 19
20 5743* 6397* 209 20
21 5470* 6092* 199 21
22 5221* 5815* 190 22
23 4994* 5562* 182 23
24 4786* 5331* 174 24
25 4594* 5117* 167 25
26 4418* 4920* 161 26
27 4254* 4738* 155 27
28 4102* 4569* 150 28
29 3961* 4411* 144 29
30 3829* 4264* 140 MLP 30
31 3705 4127* 135 31
32 3589 3998* 131 32
33 3481 3877* 127 33
34 3378 3763* 123 PN 34
35 3282 3655 120 35
36 3191 3554 116 36
37 3104 3458 113 37
38 3023 3367 110 38
TABLE II. The nationwide priority list for parties for each individual seat.
The d'Hondt divisor illustrated in Table I can be used to determine the
priority in which the individual seats of the various parties are allocated
to the districts. The largest quotient written in the columns of
Table I is 127932, and corresponds to the first divisor of the PN.
The PN has therefore priority over the first seat to be assigned to
some district. The second largest quotient is 114861, which is the highest
quotient for the MLP. The third largest quotient is 63966 in the PN column,
which therefore has priority over the third seat. This can be repeated for
each single seat. The AD, for example, has priority over the 58'th seat,
whilst the PN has priority over the 65'th seat, which is the last one to
be awarded.
The 65 party seats can therefore be considered as a queue of length 65.
The party sequence in this queue determines the order in which each
individual party seat is assigned to the districts. This is in clear
contrast to the partywise distribution where all the seats of a larger
party have a higher priority than any seat of a smaller party.
d'Hondt Party Seat
quotients Priority Number.
from List.
Table I.
127932 PN 1
114861 MLP 2
63966 PN 3
57431 MLP 4
42644 PN 5
38287 MLP 6
31983 PN 7
28715 MLP 8
25586 PN 9
22972 MLP 10
21322 PN 11
19144 MLP 12
18276 PN 13
16409 MLP 14
15992 PN 15
14358 MLP 16
14215 PN 17
12793 PN 18
12762 MLP 19
11630 PN 20
11486 MLP 21
10661 PN 22
10442 MLP 23
9841 PN 24
9572 MLP 25
9138 PN 26
8835 MLP 27
8529 PN 28
8204 MLP 29
7996 PN 30
7657 MLP 31
7525 PN 32
7179 MLP 33
7107 PN 34
6757 MLP 35
6733 PN 36
6397 PN 37
6381 MLP 38
6092 PN 39
6045 MLP 40
5815 PN 41
5743 MLP 42
5562 PN 43
5470 MLP 44
5331 PN 45
5221 MLP 46
5117 PN 47
4994 MLP 48
4920 PN 49
4786 MLP 50
4738 PN 51
4594 MLP 52
4569 PN 53
4418 MLP 54
4411 PN 55
4264 PN 56
4254 MLP 57
4186 AD 58
4127 PN 59
4102 MLP 60
3998 PN 61
3961 MLP 62
3877 PN 63
3829 MLP 64
3763 PN 65
.......................
3705 MLP not elected
3655 PN not elected
3589 MLP ..
3554 PN ..
3481 MLP ..
3458 PN ..
Table III. The d'Hondt divisor method is used on the district percentages
of first count votes (as in the partywise distribution) to assign the
individual seats of the various parties to the different districts.
In the priority queue method, however, the order is not determined by
descending order of party size, as in the partywise method, but according
to the nationwide priority list described in Table II.
PN SEATS: DISTRICT PERCENTAGES
DISTRICT I II III IV V VI VII VIII IX X XI XII XIII
%*100 5480 3193 3718 4188 3848 4417 6162 6033 5712 7129 6127 5472 5894
1 5480 3193 3718 4188 3848 4417 6162 6033 5712 7129 6127 5472 5894
*13 *26 *22 *18 *20 *17 *3 *7 *11 *1 *5 *15 *9
2 2740 1597 1859 2094 1924 2209 3081 3017 2856 3565 3064 2736 2947
*37 *59 *45 *55 *43 *28 *32 *36 *24 *30 *39 *34
3 1827 1064 1239 1396 1283 1472 2054 2011 1904 2376 2042 1824 1965
*61 *47 *51 *56 *41 *49 *63 *53
4 1370 798 930 1047 962 1104 1541 1508 1428 1782 1532 1368 1474
*65
5 1096 639 744 838 770 883 1232 1207 1142 1426 1225 1094 1179
MLP SEATS: DISTRICT PERCENTAGES.
DISTRICT I II III IV V VI VII VIII IX X XI XII XIII
%*100 4390 6637 6105 5623 5988 5455 3637 3771 4071 2668 3663 4380 4042
1 4390 6637 6105 5623 5988 5455 3637 3771 4071 2668 3663 4380 4042 *12 *2 *4 *8 *6 *10 *25 *21 *16 *38 *23 *14 *19
2 2195 3319 3053 2812 2994 2728 1819 1886 2036 1334 1832 2190 2021
*42 *27 *29 *33 *31 *35 *60 *54 *46 *44 *50
3 1463 2212 2035 1874 1996 1818 1212 1257 1357 889 1221 1460 1347
*40 *48 *57 *52 *62
4 1098 1659 1526 1406 1497 1364 909 943 1018 667 916 1095 1011
*64
5 878 1327 1221 1125 1198 1091 727 754 814 534 733 876 808
AD SEATS: DISTRICT PERCENTAGES.
DISTRICT I II III IV V VI VII VIII IX X XI XII XIII
%*100 130 170 177 188 164 128 201 196 218 203 210 148 64
1 130 170 177 188 164 128 201 196 218 203 210 140 64
*58
2 65 85 89 94 82 64 101 98 109 102 105 74 32
3 43 57 59 63 55 43 67 65 73 68 70 49 21
4 33 43 44 47 41 32 50 49 55 51 53 37 16
5 26 34 35 38 33 26 40 39 44 41 42 30 13
Alternatively, each party's matrix of district quotients can be written
as a list of quotient and district. This is then sorted for each party
separately in descending order of quotient. One then follows the
nationwide priority party sequence to choose the appropriate party list,
and hence to assign the next available district to that party seat.
The nationwide priority for each assigned seat is then written in the
left hand column of the relevant list. Each of these lists can be
considered as a queue, where districts are waiting to be assigned to
the seats of a given party. These lists are given on the following page.
PN MLP AD
SEAT QUOTI- SEAT QUOTI- SEAT QUOTI-
PRIO DIS. ENT PRI DIS. ENT PRI DIS ENT
-------------- -------------- ------------
1 10 7129 2 2 6637 *58 9 218
3 7 6162 4 3 6105 58 11 210
5 11 6127 6 5 5988 10 203
7 8 6033 8 4 5623 7 201
9 13 5894 10 6 5455 8 196
11 9 5712 12 1 4389 4 188
13 1 5480 14 12 4380 3 177
15 12 5472 16 9 4070 2 170
17 6 4417 19 13 4042 5 164
18 4 4188 21 8 3771 12 148
20 5 3848 23 11 3662 1 130
22 3 3718 25 7 3637 6 128
24 10 3564 27 2 3319 9 109
26 2 3193 29 3 3052 11 105
28 7 3081 31 5 2994 10 102
30 11 3064 33 4 2812 7 101
32 8 3017 35 6 2727 8 98
34 13 2947 38 10 2668 4 94
36 9 2856 40 2 2212 3 88
37 1 2740 42 1 2195 2 85
39 12 2736 44 12 2190 5 82
41 10 2376 46 9 2035 12 74
43 6 2209 48 3 2035 9 73
45 4 2094 50 13 2021 11 70
47 7 2054 52 5 1996 10 68
49 11 2042 54 8 1886 7 67
51 8 2011 57 4 1874 8 65
53 13 1965 *60 11 1831 1 65
55 5 1924 60 7 1818 13 64
56 9 1904 62 6 1818 6 64
59 3 1859 64 2 1659 4 63
61 1 1827 3 1526 3 59
63 12 1824 5 1497 2 57
65 10 1782 1 1463 5 55
2 1596 12 1460 9 54
7 1540 4 1406 11 53
11 1532 6 1364 10 51
8 1508 9 1357 7 50
13 1473 13 1347 12 49
6 1472 10 1334 8 49
9 1428 2 1327 4 47
10 1426 8 1257 3 44
* signifies that the seat is not awarded since the relevant district
already has its full complement of seats.
PN MLP AD
SEAT QUOTI- SEAT QUOTI- SEAT QUOTI-
PRIO DIS. ENT PRI DIS. ENT PRI DIS ENT
-------------- -------------- --------------
4 1396 3 1221 9 44
1 1370 11 1221 1 43
12 1368 7 1212 6 43
5 1283 5 1198 2 43
3 1239 4 1125 11 42
7 1232 1 1097 5 41
11 1225 12 1095 10 41
8 1207 6 1091 7 40
13 1179 9 1018 8 39
9 1142 13 1010 4 38
6 1104 8 943 12 37
1 1096 11 916 3 35
12 1094 7 909 2 34
2 1064 10 889 5 33
4 1047 1 878 1 33
5 962 12 876 13 32
3 930 9 814 6 32
6 883 13 808 12 30
4 838 8 754 1 26
2 798 11 732 6 26
5 770 7 727 13 21
3 744 10 667 13 16
2 639 10 534 13 13
FINAL SEAT DISTRIBUTION BY DISTRICT (1992, NO THRESHOLD ASSUMED):
DISTRICT.
PARTY I II III IV V VI VII VIII IX X XI XII XIII TOTAL
PN: 3 1 2 2 2 2 3 3 3 4 3 3 3 34
MLP: 2 4 3 3 3 3 2 2 2 1 1 2 2 30
AD: 0 0 0 0 0 0 0 0 0 0 1 0 0 1
TOTAL: 5 5 5 5 5 5 5 5 5 5 5 5 5 65
As pointed out before, this distribution is practically identical to the
actual election result, except that the AD is awarded a seat in the
eleventh district, where it polled the highest number of votes.
By contrast, the partywise method assigns the AD seat to the second
district, where the AD did not get most votes. This improvement in the
allocation of party seats to districts by the priority queue method is
confirmed in many other elections.
TABLE IV: Detailed schedule for the assignment of party seats to the
districts. The d'Hondt quotients for the district percentages in
Table III are sorted in descending order of quotient, and written
in the following matrix along with the corresponding party and divisor.
The nationwide priority of each seat is given on the left. The final
seat distribution is identical to that given in Table III.
NATIONWIDE PARTY DISTRICT PARTY COMMENTS.
SEAT PRIORITY DISTRICT -WISE SEAT NO.
MLP PN AD PRIORITY IN DIST.
100*
DISTRICT%
1 PN 10 7129 1
2 MLP 2 6637 1
3 PN 7 6162 1
5 PN 11 6127 1
4 MLP 3 6105 1
7 PN 8 6033 1
6 MLP 5 5988 1
9 PN 13 5894 1
11 PN 9 5712 1 1st seat in District 9.
8 MLP 4 5623 1
13 PN 1 5480 1
15 PN 12 5472 1
10 MLP 6 5455 1
17 PN 6 4417 1
12 MLP 1 4390 1
14 MLP 12 4380 1
18 PN 4 4188 1
16 MLP 9 4071 1 2nd seat in District 9.
19 MLP 13 4042 1
20 PN 5 3848 1
21 MLP 8 3771 1
22 PN 3 3718 1
23 MLP 11 3663 1
25 MLP 7 3637 1
24 PN 10 3565 2
27 MLP 2 3319 2
26 PN 2 3193 1
28 PN 7 3081 2
30 PN 11 3064 2
29 MLP 3 3053 2
32 PN 8 3017 2
31 MLP 5 2994 2
34 PN 13 2947 2
36 PN 9 2856 2 3rd seat in District 9.
33 MLP 4 2812 2
37 PN 1 2740 2
39 PN 12 2736 2
35 MLP 6 2728 2
38 MLP 10 2668 1
41 PN 10 2376 3
40 MLP 2 2212 3
43 PN 6 2209 2
42 MLP 1 2195 2
44 MLP 12 2190 2
45 PN 4 2094 2
47 PN 7 2054 3
49 PN 11 2042 3
46 MLP 9 2036 2 4th seat in District 9.
48 MLP 3 2035 3
50 MLP 13 2021 2
51 PN 8 2011 3
52 MLP 5 1996 3
53 PN 13 1965 3 District 13 is now full.
55 PN 5 1924 2 District 5 is now full.
56 PN 9 1904 3 5th seat in District 9.
District 9 is now full.
54 MLP 8 1886 2 District 8 is now full.
57 MLP 4 1874 3 District 4 is now full.
59 PN 3 1859 2 District 3 is now full.
*60 MLP 11 1832 * District 11 already filled in step 58.
See below.
61 PN 1 1827 3 District 1 is now full.
63 PN 12 1824 3 District 12 is now full.
60 MLP 7 1819 2 District 7 is now full.
62 MLP 6 1818 3 District 6 is now full.
65 PN 10 1782 4 District 10 is now full.
64 MLP 2 1659 4 District 2 is now full.
PN 2 1597
PN 7 1541
PN 11 1532
MLP 3 1526
PN 8 1508
MLP 5 1497
PN 13 1474
.. . ..
.. . ..
PN 2 639
MLP 10 534
*58 AD 9 218 * District 9 already filled in step 56. See above.
58 AD 11 210 1 District 11 is now full.
AD 10 203
AD 7 201
.. . ..
.. . ..
An * in a given row signifies that the seat is not awarded in that district
because the district has already gained its full complement of five seats.
TABLE V: Distribution of seats using the priority queue method for
Elections on and after 1962. The d'Hondt divisor is used throughout,
both nationwide and in the districts.
ELECTION OF 1962.
No Threshold.
District 1 2 3 4 5 6 7 8 9 10 TOTAL
PN 2 2 2 2 3 3 1 2 3 2 22
MLP 2 3 2 3 2 1 1 2 1 0 17
CWP 0 0 1 0 0 1 0 1 1 1 5
DNP 1 0 0 0 0 0 1 0 0 2 4
PCP 0 0 0 0 0 0 2 0 0 0 2
TOTAL: 5 5 5 5 5 5 5 5 5 5 50
5% Threshold. PCP eliminated.
District 1 2 3 4 5 6 7 8 9 10 TOTAL
PN 2 1 2 2 3 3 2 2 3 2 22
MLP 2 3 2 3 2 1 2 2 1 0 18
CWP 0 1 1 0 0 1 0 1 0 1 5
DNP 1 0 0 0 0 0 1 0 1 2 5
TOTAL: 5 5 5 5 5 5 5 5 5 5 50
9.3% Threshold. DNP eliminated.
District 1 2 3 4 5 6 7 8 9 10 TOTAL
PN 3 1 2 2 3 3 2 2 3 4 25
MLP 2 3 2 3 2 1 3 2 2 0 20
CWP 0 1 1 0 0 1 0 1 0 1 5
10% Threshold. CWP eliminated.
District 1 2 3 4 5 6 7 8 9 10 TOTAL
PN 3 1 2 2 3 4 2 3 3 5 28
MLP 2 4 3 3 2 1 3 2 2 0 22
TOTAL: 5 5 5 5 5 5 5 5 5 5 50
ELECTION OF 1966.
No Threshold.
District 1 2 3 4 5 6 7 8 9 10 TOTAL
PN 3 1 2 2 3 3 2 2 3 4 25
MLP 2 4 3 3 2 1 2 2 2 1 22
CWP 0 0 0 0 0 1 1 1 0 0 3
TOTAL: 5 5 5 5 5 5 5 5 5 5 50
6% Threshold. CWP eliminated.
District 1 2 3 4 5 6 7 8 9 10 TOTAL
PN 3 1 2 2 3 3 3 2 3 4 26
MLP 2 4 3 3 2 2 2 3 2 1 24
TOTAL: 5 5 5 5 5 5 5 5 5 5 50
ELECTION OF 1971.
No Threshold.
District 1 2 3 4 5 6 7 8 9 10 TOTAL
MLP 2 4 4 3 3 2 2 3 3 2 28
PN 3 2 2 2 2 3 4 3 3 3 27
TOTAL: 5 6 6 5 5 5 6 6 6 5 55
ELECTION OF 1976.
No Threshold.
District 1 2 3 4 5 6 7 8 9 10 11 12 13 TOTAL
MLP 3 4 3 3 3 3 3 2 2 2 2 2 2 34
PN 2 1 2 2 2 2 2 3 3 3 3 3 3 31
TOTAL: 5 5 5 5 5 5 5 5 5 5 5 5 5 65
ELECTION OF 1981.
No Threshold.
District 1 2 3 4 5 6 7 8 9 10 11 12 13 TOTAL
PN 3 1 2 2 2 3 2 3 3 3 3 3 3 33
MLP 2 4 3 3 3 2 3 2 2 2 2 2 2 32
TOTAL: 5 5 5 5 5 5 5 5 5 5 5 5 5 65
ELECTION OF 1987.
No Threshold.
District 1 2 3 4 5 6 7 8 9 10 11 12 13 TOTAL
PN 3 1 2 2 2 2 3 3 3 3 3 3 3 33
MLP 2 4 3 3 3 3 2 2 2 2 2 2 2 32
TOTAL: 5 5 5 5 5 5 5 5 5 5 5 5 5 65
ELECTION OF 1992.
No Threshold.
District 1 2 3 4 5 6 7 8 9 10 11 12 13 TOTAL
PN 3 1 2 2 2 2 3 3 3 4 3 3 3 34
MLP 2 4 3 3 3 3 2 2 2 1 1 2 2 30
AD 0 0 0 0 0 0 0 0 0 0 1 0 0 1
TOTAL: 5 5 5 5 5 5 5 5 5 5 5 5 5 65
5% Threshold. AD eliminated.
District 1 2 3 4 5 6 7 8 9 10 11 12 13 TOTAL
PN 3 1 2 2 2 2 3 3 3 4 3 3 3 34
MLP 2 4 3 3 3 3 2 2 2 1 2 2 2 31
TOTAL: 5 5 5 5 5 5 5 5 5 5 5 5 5 65
APPENDIX I.
ELECTION OF 1992. SEAT DISTRIBUTION BY THE PARTYWISE METHOD.
First count votes for parties in each district, district percentages,
and partywise calculations for the 1992 election. No threshold is assumed.
Number of parties is 3. Number of seats is 65.
Number of districts is 13. Number of seats/ district is 5.
FIRST COUNT VOTES PARTIES.
DISTRICTS MLP PN AD
I 8153 10179 242
II 12680 6100 325
III 11936 7270 346
IV 10061 7494 337
V 11852 7616 325
VI 10241 8293 241
VII 6960 11792 385
VIII 7030 11247 365
IX 7808 10956 418
X 5025 13426 383
XI 7337 12275 421
XII 8249 10305 278
XIII 7529 10979 120
TOTAL: 114861 127932 4186
NATIONWIDE SEATS: 30 34 1
% vote of each party by district:
I 43.895 54.802 1.303
II 66.370 31.929 1.701
III 61.047 37.183 1.770
IV 56.232 41.885 1.884
V 59.880 38.478 1.642
VI 54.546 44.170 1.284
VII 36.369 61.619 2.012
VIII 37.711 60.332 1.958
IX 40.705 57.116 2.179
X 26.680 71.286 2.034
XI 36.625 61.274 2.102
XII 43.803 54.721 1.476
XIII 40.418 58.938 0.644
Parties in descending order of first count vote: PN, MLP, AD.
Direct assignment of seats to districts (1992):
PN scan:
--------
Dist. I II III IV V VI VII VIII IX X XI XII XIII TOTAL
Seats still available:
5 5 5 5 5 5 5 5 5 5 5 5 5 65
%*102: 548 319 372 419 385 442 616 603 571 713 613 547 589
1 548* 319* 372* 419* 385* 442* 616* 603* 571* 713* 613* 547* 589*
2 274* 160 186* 210* 193* 221* 308* 302* 286* 357* 307* 274* 295*
3 183* 106 124 140 128 147 205* 201* 190* 238* 204* 182* 196*
4 137 80 93 105 96 111 154 151 143 178* 153 137 147
5 110 64 74 84 77 88 123 121 114 143 123 109 118
Choose largest 34 numbers. Smallest is 178 in District X, Seat 4.
PN: 3 1 2 2 2 2 3 3 3 4 3 3 3 34
Seats still available:
2 4 3 3 3 3 2 2 2 1 2 2 2 31
MLP scan:
---------
Dist. I II III IV V VI VII VIII IX X XI XII XIII TOTAL
Seats still available:
2 4 3 3 3 3 2 2 2 1 2 2 2 31
%*10 439 664 610 562 599 545 364 377 407 267 366 438 404
1 439* 664* 610* 562* 599* 545* 364* 377* 407* 267* 366* 438* 404*
2 220* 332* 305* 281* 300* 273* 182* 189* 204* 183* 219* 202*
3 221* 203* 187* 200* 182*
4 166
Choose largest 30. Smallest is 182 in District VI, Seat 3.
MLP: 2 3 3 3 3 3 2 2 2 1 2 2 2 30
Seats still available:
0 1 0 0 0 0 0 0 0 0 0 0 0 1
AD scan:
--------
Dist. I II III IV V VI VII VIII IX X XI XII XIII TOTAL
Seats still available:
0 1 0 0 0 0 0 0 0 0 0 0 0 1
%*100 130 170 177 188 164 128 201 196 218 203 210 148 64
1 170
Choose largest 1 number. Smallest is 170 in District II, Seat 1.
AD: 0 1 0 0 0 0 0 0 0 0 0 0 0 1
Seats still available:
0 0 0 0 0 0 0 0 0 0 0 0 0 0
ALL SEATS ARE NOW ASSIGNED.
FINAL SEAT DISTRIBUTION BY DISTRICT (1992):
DISTRICT
PARTY I II III IV V VI VII VIII IX X XI XII XIII TOTAL
PN: 3 1 2 2 2 2 3 3 3 4 3 3 3 34
MLP: 2 3+ 3 3 3 3 2 2 2 1 2 2 2 30
AD: 0 1- 0 0 0 0 0 0 0 0 0 0 0 1
TOTAL 5 5 5 5 5 5 5 5 5 5 5 5 5 65
In the actual election, the MLP got one seat more, and the AD one seat less in the II district.
APPENDIX II.
EFFECT OF DIVISOR ON MAJORITY RULE.
Comparison of different divisors on fictitious elections between three
parties, A, B and C, where A has the largest following, B is slightly
smaller than A, and C is a small party. In each case Party A gains more
votes than parties B and C put together, ie. A has an absolute majority of
votes. A total of 65 seats is then distributed amongst the three parties.
The quota per seat is about 1000 votes for the larger parties A and B.
Different divisor methods are then used to calculate the number of
nationwide seats to each party, The elections and the divisor systems
with a majority of votes and seats respectively are marked with a +.
Of all the divisor methods, it is only the d'Hondt set of divisors which
is mathematically gauranteed to give an absolute majority of seats to
party A. The Danish system in particular is extremely generous to small
parties. As can be deduced from election v), it awards one seat to
party C with only 342 votes, when the quota for the larger parties is
about 1000. This is because divisors other than the d'Hondt do not
equalise the number of wasted votes to each party; rather they equalise
the proportion of votes wasted by each party.
PARTY A B C
i) Votes 33010 : 32000 : 712 +
SEATS:
d'Hondt 33 32 0 +
Modified St. Lague 32 32 1
St. Lague 32 32 1
Equal Proportions 32 32 1
Danish 32 32 1
ii) 34020 : 32000 : 1572 +
SEATS:
d'Hondt 33 31 1 +
Modified St. Lague 32 31 2
St. Lague 32 31 2
Equal Proportions 32 31 2
Danish 32 31 2
iii) 35210 : 32000 : 2710 +
SEATS:
d'Hondt 33 30 2 +
Modified St. Lague 32 30 3
St. Lague 32 30 3
Equal Proportions 32 30 3
Danish 32 30 3
iv) 36450 : 32000 : 3927 +
SEATS:
d'Hondt 33 29 3 +
Modified St. Lague 32 29 4
St. Lague 32 29 4
Equal Proportions 32 29 4
Danish 32 29 4
PARTY A B C
v) Votes 33018 : 32000 : 342 +
SEATS:
d'Hondt 33 32 0 +
Modified St. Lague 33 32 0 +
St. Lague 33 32 0 +
Equal Proportions 33 32 0 +
Danish 32 32 1
vi) 33000 : 31000 : 1361 +
SEATS:
d'Hondt 33 31 1 +
Modified St. Lague 33 31 1 +
St. Lague 33 31 1 +
Equal Proportions 33 31 1 +
Danish 32 31 2
vii) 34150 : 31000 : 2470 +
SEATS:
d'Hondt 33 30 2 +
Modified St. Lague 33 30 2 +
St. Lague 33 30 2 +
Equal Proportions 33 30 2 +
Danish 32 30 3
viii) 34230 : 30000 : 3530 +
SEATS:
d'Hondt 33 29 3 +
Modified St. Lague 33 29 3 +
St. Lague 33 29 3 +
Equal Proportions 33 29 3 +
Danish 32 29 4
APPENDIX III. The Sainte Lague priority method for the election of 1962.
No threshold is assumed. The d'Hondt divisor is first used to determine
the number of seats for each party, and their priority. The seats are
then distributed in the districts, using the Sainte Lague system of divisors.
The D'Hondt set of divisors is used on the nationwide total of first count
votes obtained by each party. In this election, the PN polled 63262 votes,
the MLP 50974, the CWP 14285, the DNP 13968, the PCP 7290. The nationwide
totals for each party are divided by the divisors 1, 2, 3, 4, etc, and
sorted in descending order of this quotient. The sequence of this sorted
list determines the number of seats due to each party, and also the
nationwide priority of each seat.
NATIONWIDE PARTY D'HONDT
PRIORITY QUOTIENT
1 PN 63262
2 MLP 50974
3 PN 31631
4 MLP 25487
5 PN 21087
6 MLP 16991
7 PN 15816
8 CWP 14285
9 DNP 13968
10 MLP 12744
11 PN 12652
12 PN 10544
13 MLP 10195
14 PN 9037
15 MLP 8496
16 PN 7908
17 PCP 7290
18 MLP 7282
19 CWP 7143
20 PN 7029
21 DNP 6984
22 MLP 6372
23 PN 6326
24 PN 5751
25 MLP 5664
26 PN 5272
27 MLP 5097
28 PN 4866
29 CWP 4762
30 DNP 4656
31 MLP 4634
32 PN 4519
33 MLP 4248
34 PN 4217
35 PN 3954
36 MLP 3921
37 PN 3721
38 PCP 3645
39 MLP 3641
40 CWP 3571
41 PN 3515
42 DNP 3492
43 MLP 3398
44 PN 3330
45 MLP 3186
46 PN 3163
47 PN 3012
48 MLP 2998
49 PN 2876
50 CWP 2857
---------------------------------
not elected ... MLP 2832
not elected ... DNP 2794
.. PN 2751
.. MLP 2683
.. PN 2636
.. MLP 2549
PN 2530
PN 2433
PCP 2430
MLP 2427
CWP 2381
PN 2343
DNP 2328
MLP 2317
PN 2259
MLP 2216
PN 2181
MLP 2124
PN 2109
CWP 2041
PN 2041
MLP 2039
DNP 1995
PN 1977
MLP 1961
PN 1917
MLP 1888
The Sainte Lague Priority Method;
Sainte Lague's set of divisors is used on the districtwise proportions to
determine the order in which districts are assigned to the seats of a
given party. The nationwide priority of each seat is written under the
relevant quotient. The distribution of the contesting parties' seats in
the districts arising from using this set of divisors is usually fairer
to the parties and the individual candidates than when the d'Hondt's
divisors are used in this step.
PARTY DISTRICT.
DIVISOR
PN 1 2 3 4 5 6 7 8 9 10
%*100 4518 2672 3494 4272 4977 4913 3626 3739 4910 5188
1 4518 2672 3494 4272 4977 4913 3626 3739 4910 5188
*11 *23 *20 *12 *3 *5 *16 *14 *7 *1
3 1506 891 1165 1424 1659 1638 1209 1246 1637 1729
*34 *44 *35 *26 *28 *41 *37 *32 *24
5 904 534 699 854 995 983 725 748 982 1038
*47 *49 *46
7 645 382 499 610 711 702 518 534 701 741
9 502 297 388 475 553 546 403 415 546 576
MLP 1 2 3 4 5 6 7 8 9 10
%*100 3308 5620 4635 4747 3430 2402 2648 3541 2597 626
1 3308 5620 4635 4747 3430 2402 2648 3541 2597 626
*15 *2 *6 *4 *13 *25 *18 *10 *22
3 1103 1873 1545 1582 1143 801 883 1180 866 209
*45 *27 *33 *31 *39 *36
5 662 1124 927 949 686 480 530 708 519 125
*43 *48
7 473 803 662 678 490 343 378 506 371 89
9 368 624 515 527 381 267 294 393 289 70
CWP 1 2 3 4 5 6 7 8 9 10
585 1025 1213 467 755 1097 878 1240 910 1407
1 585 1025 1213 467 755 1097 878 1240 910 1407
*50 *29 *40 *19 *8
3 195 342 404 156 252 366 293 413 303 469
5 117 205 243 93 151 219 176 248 182 281
7 84 146 173 67 108 157 125 177 130 201
9 65 114 135 52 84 122 98 138 101 156
DNP 1 2 3 4 5 6 7 8 9 10
1028 574 467 347 553 986 1347 936 902 2162
1 1028 574 467 347 553 986 1347 936 902 2162
*30 *42 *21 *9
3 343 191 156 116 184 329 449 312 301 721
5 206 115 93 69 111 197 269 187 180 432
7 147 82 67 50 79 141 192 134 129 309
9 114 64 52 39 61 110 150 104 100 240
PCP 1 2 3 4 5 6 7 8 9 10
475 109 192 168 285 431 1413 466 654 522
1 475 109 192 168 285 431 1413 466 654 522
*17 *38
3 158 36 64 56 95 144 471 155 218 174
5 95 22 38 34 57 86 283 93 131 104
7 68 16 27 24 41 62 202 67 93 75
9 53 12 21 19 32 48 157 52 73 58
Alternatively, each party's district quotients can be sorted in descending
order for each party, and listed as district queues.
Alternatively, each party's matrix of district quotients can be written as
a list of quotient and district. This is then sorted for each party
separately in descending order of quotient. One then follows the nationwide
priority party sequence to choose the appropriate party list, and hence to
assign the next available district to that party seat. The nationwide
priority for each assigned seat is then written in the left hand column
of the relevant list. Each of these lists can be considered as a queue,
where districts are waiting to be assigned to the seats of a given party.
PN MLP CWP DNP PCP
SEAT QUOTI- SEAT QUOTI- SEAT QUOTI- SEAT QUOTI- SEAT QUOTI-
PRIO DIS. ENT PRI DIS. ENT PRI DIS ENT PR DIS ENT PR DIS ENT
-------------- -------------- ------------ ------------ ----------
1 10 5188 2 2 5620 8 10 1407 9 10 2162 17 7 1413
3 5 4977 4 4 4747 19 8 1240 21 7 1347 38 9 654
5 6 4913 6 3 4635 29 3 1213 30 1 1028 10 522
7 9 4910 10 8 3541 40 6 1097 42 6 986 1 475
11 1 4518 13 5 3430 50 2 1025 8 936 7 471
12 4 4272 15 1 3308 9 910 9 902 8 466
14 8 3739 18 7 2648 7 878 10 721 6 431
16 7 3626 22 9 2597 5 755 2 574 5 285
20 3 3494 25 6 2402 1 585 5 553 7 283
23 2 2672 27 2 1873 10 469 3 467 9 218
24 10 1729 31 4 1582 4 467 7 449 7 202
26 5 1659 33 3 1545 8 413 10 432 3 192
28 6 1638 36 8 1180 3 404 4 347 10 174
32 9 1637 39 5 1143 6 366 1 343 4 168
34 1 1506 43 2 1124 2 342 6 329 1 158
35 4 1424 45 1 1103 9 303 8 312 7 157
37 8 1246 48 4 949 7 293 10 309 8 155
41 7 1209 3 927 10 281 9 301 6 144
44 3 1165 7 883 5 252 7 269 9 131
46 10 1038 9 866 8 248 10 240 2 109
47 5 995 2 803 3 243 1 206 10 104
49* 6 983 6 801 6 219 6 197 1 95
49 9 982 8 708 2 205 7 192 5 95
1 904 5 686 10 201 2 191 9 93
2 891 4 678 1 195 8 187 8 93
4 854 3 662 9 182 5 184 6 86
8 748 1 662 8 177 9 180 10 75
10 741 10 626 7 176 3 156 9 73
* signifies that the seat with priority 49 is not awarded to the PN in
district 6, since this is already full (with seats 5, 25, 28, 40 and 42).
Instead, the PN is awarded the seat in the next district available on its
list, namely the ninth district.
PN MLP CWP DNP PCP
QUOTIENT QUOTIENT QUOTIENT QUOTIENT QUOTIENT
DISTRICT DISTRICT DISTRICT DISTRICT DISTRICT
------------ ----------- ---------- ----------- -----------
7 725 2 624 3 173 7 150 1 68
5 711 7 530 6 157 1 147 8 67
6 702 4 527 10 156 6 141 3 64
9 701 9 519 4 156 8 134 6 62
3 699 3 515 5 151 9 129 10 58
1 645 8 506 2 146 4 116 5 57
4 610 5 490 8 138 2 115 4 56
10 576 6 480 3 135 1 114 1 53
5 553 1 473 9 130 5 111 8 52
6 546 8 393 7 125 6 110 6 48
9 546 5 381 6 122 8 104 5 41
2 534 7 378 1 117 9 100 3 38
8 534 9 371 2 114 3 93 2 36
7 518 1 368 5 108 2 82 4 34
1 502 6 343 9 101 5 79 5 32
3 499 7 294 7 98 4 69 3 27
4 475 9 289 4 93 3 67 4 24
8 415 6 267 5 84 2 64 2 22
7 403 10 209 1 84 5 61 3 21
3 388 10 125 4 67 3 52 4 19
2 382 10 90 1 65 4 50 2 16
2 297 10 70 4 52 4 39 2 12
Final seat distribution for the Sainte Lague priority method:
DISTRICTS: 1 2 3 4 5 6 7 8 9 10 TOTAL
PN 2 1 2 2 3 2 2 2 3 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 1 1 0 0 1 4
PCP 0 0 0 0 0 0 1 0 1 0 2
DIST. TOTALS: 5 5 5 5 5 5 5 5 5 5 50
APPENDIX IV.
PARTYWISE CALCULATIONS WITH DIFFERENT DIVISORS
FOR THE ELECTIONS 1962-1992.
ELECTION OF 1962. PARTYWISE CALCULATIONS.
No threshold assumed.
Number of parties is 7
Total number of seats is 50
Total number of districts is 10
Number of seats available in each district is 5.
VOTES OF EACH PARTY BY DISTRICT:
DISTRICT MLP PN PCP CWP DNP DCP IND
1 5532 7556 795 979 1720 143 0
2 9170 4359 178 1672 937 0 0
3 6512 4908 269 1704 656 0 0
4 6919 6226 245 681 505 0 0
5 4860 7051 404 1069 784 0 0
6 3457 7072 621 1579 1419 247 0
7 4493 6152 2397 1489 2285 152 0
8 5292 5588 697 1853 1399 116 0
9 3896 7368 981 1366 1353 41 0
10 843 6982 703 1893 2910 0 128
TOTAL: 50974 63262 7290 14285 13968 699 128
Nationwide Divisor: D'HONDT:
PARTY: PN MLP CWP DNP PCP DCP IND
SEATS: 22 17 5 4 2 0 0
District divisors: D'HONDT to DANISH; all same:
DISTRICTS: 1 2 3 4 5 6 7 8 9 10 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
TOTALS: 5 5 5 5 5 5 5 5 5 5 50
Nationwide Divisor: SAINTE LAGUE MODIFIED, SAINTE LAGUE, EQUAL PROPORTIONS:
PARTY: PN MLP CWP DNP PCP DCP IND
SEATS: 21 17 5 5 2 0 0
District divisors: D'HONDT to DANISH; all same:
DISTRICTS 1 2 3 4 5 6 7 8 9 10 TOTAL
PN 2 1 2 2 3 2 2 2 2 3 21
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 1 1 0 1 1 5
PCP 0 0 0 0 0 0 1 0 1 0 2
TOTALS 5 5 5 5 5 5 5 5 5 5 50
Nationwide Divisor: DANISH:
PARTY: PN MLP CWP DNP PCP DCP IND
SEATS: 20 17 5 5 3 0 0
District divisors: D'HONDT to DANISH; all same:
DISTRICTS 1 2 3 4 5 6 7 8 9 10 TOTAL
PN 2 1 2 2 2 2 2 2 2 3 20
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 1 1 0 1 1 5
PCP 0 0 0 0 1 0 1 0 1 0 3
TOTALS: 5 5 5 5 5 5 5 5 5 5 50
ELECTION OF 1962. THRESHOLD 5%.
PCP eliminated.
Nationwide Divisors: D'HONDT to DANISH; ALL SAME:
PARTY: PN MLP CWP DNP PCP DCP IND
SEATS: 22 18 5 5 0 0 0
District divisors: D'HONDT to DANISH; all same:
DISTRICTS: 1 2 3 4 5 6 7 8 9 10 TOTAL
PN 2 1 2 2 3 3 2 2 2 3 22
MLP 2 3 3 3 2 1 1 2 1 0 18
CWP 0 1 0 0 0 1 0 1 1 1 5
DNP 1 0 0 0 0 0 2 0 1 1 5
DIST. TOTALS: 5 5 5 5 5 5 5 5 5 5 50
ELECTION OF 1962. THRESHOLD = 9.3 % of national vote.
DNP eliminated.
NATIONWIDE DIVISORS: D'HONDT only:
PARTY: PN MLP CWP DNP PCP DCP IND
SEATS: 25 20 5 0 0 0 0
DISTRICTS: 1 2 3 4 5 6 7 8 9 10 TOTAL
District divisors: D'HONDT only:
PN 3 1 2 3 3 3 2 2 3 3 25
MLP 2 4 3 2 2 1 2 2 2 0 20
CWP 0 0 0 0 0 1 1 1 0 2 5
District divisors: SAINTE LAGUE MODIFIED to DANISH; all same:
PN 3 2 2 2 3 3 2 2 3 3 25
MLP 2 3 3 3 2 1 2 2 2 0 20
CWP 0 0 0 0 0 1 1 1 0 2 5
NATIONWIDE DIVISORS: SAINTE LAGUE MODIFIED to DANISH; all same:
PARTY: PN MLP CWP DNP PCP DCP IND
SEATS: 24 20 6
DISTRICTS: 1 2 3 4 5 6 7 8 9 10 TOTAL
District divisors: D'HONDT:
PN 3 1 2 2 3 3 2 2 3 3 24
MLP 2 4 3 3 2 1 2 2 1 0 20
CWP 0 0 0 0 0 1 1 1 1 2 6
District divisors: SAINTE LAGUE MODIFIED, SAINTE LAGUE:
PN 3 1 2 2 3 3 2 2 3 3 24
MLP 2 3 3 3 2 1 2 2 2 0 20
CWP 0 1 0 0 0 1 1 1 0 2 6
District divisors: EQUAL PROPORTIONS, DANISH:
PN 2 2 2 2 3 3 2 2 3 3 24
MLP 2 3 3 3 2 1 2 2 2 0 20
CWP 1 0 0 0 0 1 1 1 0 2 6
TOTAL: 5 5 5 5 5 5 5 5 5 5 50
Election of 1962; THRESHOLD = 10 % of national vote.
CWP eliminated.
NATIONWIDE DIVISORS: D'HONDT to DANISH; ALL SAME:
PARTY: PN MLP CWP DNP PCP DCP IND
SEATS: 28 22 0
District divisors: D'HONDT to DANISH; ALL SAME:
DISTRICTS: 1 2 3 4 5 6 7 8 9 10 TOTAL
PN 3 2 2 3 3 3 2 3 3 4 28
MLP 2 3 3 2 2 2 3 2 2 1 22
TOTAL 5 5 5 5 5 5 5 5 5 5 50
ELECTION OF 1966. PARTYWISE CALCULATIONS.
No threshold.
Number of parties is 6.
Total number of seats is 50.
Total number of districts is 10.
Number of seats available in each district is 5.
VOTES OF EACH PARTY BY DISTRICT.
2DISTRICT MLP PN PCP CWP DNP IND
1 6151 7623 191 747 351 0
2 9517 4771 0 598 0 20
3 7756 5356 0 954 99 0
4 7812 5761 0 347 0 29
5 6176 7231 0 495 0 0
6 4561 7725 180 1033 199 0
7 5622 7737 915 1554 476 0
8 6402 6459 163 1134 523 9
9 5010 7805 257 853 197 67
10 2767 8188 380 879 0 267
TOTAL: 61774 68656 2086 8594 1845 392
NATIONWIDE DIVISORS: D'HONDT only:
PARTY: PN MLP CWP DNP PCP IND
SEATS: 25 22 3 0 0 0
DISTRICTS: 1 2 3 4 5 6 7 8 9 10 TOTAL
Districtwise divisor: D'HONDT only:
PN 3 1 2 2 3 3 2 2 3 4 25
MLP 2 3 3 3 2 2 2 2 2 1 22
CWP 0 1 0 0 0 0 1 1 0 0 3
Districtwise divisors: SAINTE LAGUE MODIFIED to DANISH; all same:
PN 3 2 2 2 3 3 2 2 3 3 25
MLP 2 3 3 3 2 2 2 2 2 1 22
CWP 0 0 0 0 0 0 1 1 0 1 3
TOTAL: 5 5 5 5 5 5 5 5 5 5 50
NATIONWIDE DIVISORS: SAINTE LAGUE MODIFIED only:
PARTY: PN MLP CWP DNP PCP IND
SEATS: 24 22 3 1 0 0
DISTRICTS: 1 2 3 4 5 6 7 8 9 10 TOTAL
Districtwise divisor: D'HONDT only:
PN 3 1 2 2 3 3 2 2 3 3 24
MLP 2 3 3 3 2 2 2 2 2 1 22
CWP 0 0 0 0 0 0 1 1 0 1 3
PCP 0 1 0 0 0 0 0 0 0 0 1
Districtwise divisors: SAINTE LAGUE MODIFIED to DANISH; all same:
PN 2 2 2 2 3 3 2 2 3 3 24
MLP 2 3 3 3 2 2 2 2 2 1 22
CWP 0 0 0 0 0 0 1 1 0 1 3
PCP 1 0 0 0 0 0 0 0 0 0 1
NATIONWIDE DIVISORS: SAINTE LAGUE to DANISH; all same:
PARTY: PN MLP CWP DNP PCP IND
SEATS: 24 21 3 1 1 0
DISTRICTS: 1 2 3 4 5 6 7 8 9 10 TOTAL
Districtwise divisor: D'HONDT only:
PN 3 1 2 2 3 3 2 2 3 3 24
MLP 2 3 3 3 2 1 2 2 2 1 21
CWP 0 0 0 0 0 1 1 1 0 0 3
PCP 0 0 0 0 0 0 0 0 0 1 1
DNP 0 1 0 0 0 0 0 0 0 0 1
Districtwise divisors: SAINTE LAGUE MODIFIED to DANISH; all same:
PN 2 2 2 2 3 3 2 2 3 3 24
MLP 2 3 2 3 2 2 2 2 2 1 21
CWP 0 0 0 0 0 0 1 1 0 1 3
PCP 1 0 0 0 0 0 0 0 0 0 1
DNP 0 0 1 0 0 0 0 0 0 0 1
TOTAL: 5 5 5 5 5 5 5 5 5 5 50
ELECTION OF 1966; 6% THRESHOLD.
CWP eliminated.
NATIONWIDE DIVISORS: D'HONDT to DANISH; ALL SAME:
PARTY: PN MLP CWP DNP PCP IND
SEATS: 26 24 0
DISTRICTS: 1 2 3 4 5 6 7 8 9 10 TOTAL
Districtwise divisor: D'HONDT only:
PN 3 2 2 2 3 3 2 2 3 4 26
MLP 2 3 3 3 2 2 3 3 2 1 24
Districtwise divisors: SAINTE LAGUE MODIFIED to DANISH; all same:
PN 3 2 2 2 3 3 3 2 3 3 26
MLP 2 3 3 3 2 2 2 3 2 2 24
TOTAL: 5 5 5 5 5 5 5 5 5 5 50
ELECTION OF 1971. PARTYWISE CALCULATION.
No threshold.
Number of parties is 4.
Total number of seats is 55.
Total number of districts is 10.
Seats available in each district:
District: 1 2 3 4 5 6 7 8 9 10 TOTAL
Number of seats: 5 6 6 5 5 5 6 6 6 5 55.
VOTES OF EACH PARTY BY DISTRICT:
DISTRICT MLP PN PCP OTH
1 7728 8266 204 0
2 11827 5293 43 8
3 11354 6888 55 22
4 10288 6324 36 0
5 8151 8130 23 0
6 6664 9332 349 0
7 7617 11032 682 26
8 8480 8631 171 0
9 7232 9392 165 27
10 6107 7465 28 19
TOTAL: 85448 80753 1756 102
NATIONWIDE DIVISORS: D'HONDT and SAINTE LAGUE MODIFIED:
PARTY: MLP PN PCP OTH
SEATS: 28 27
DISTRICTS: 1 2 3 4 5 6 7 8 9 10 TOTAL
Districtwise divisor: D'HONDT only:
MLP 3 4 4 3 3 2 2 3 2 2 28
PN 2 2 2 2 2 3 4 3 4 3 27
Districtwise divisors: SAINTE LAGUE MODIFIED to DANISH; all same:
MLP 3 4 3 3 3 2 2 3 2 3 28
PN 2 2 3 2 2 3 4 3 4 2 27
TOTAL 5 6 6 5 5 5 6 6 6 5 55
NATIONWIDE DIVISORS: SAINTE LAGUE to DANISH; all same:
PARTY: MLP PN PCP OTH
SEATS: 28 26 1
DISTRICTS: 1 2 3 4 5 6 7 8 9 10 TOTAL
Districtwise divisor: D'HONDT only:
PN 3 4 4 3 3 2 2 3 2 2 28
MLP 2 2 2 2 2 3 4 3 3 3 26
PCP 0 0 0 0 0 0 0 0 1 0 1
Districtwise divisors: SAINTE LAGUE MODIFIED to DANISH; all same:
PN 3 4 3 3 3 2 2 3 2 3 28
MLP 2 2 2 2 2 3 4 3 4 2 26
PCP 0 0 1 0 0 0 0 0 0 0 1
TOTAL: 5 6 6 5 5 5 6 6 6 5 55
ELECTION OF 1976. PARTYWISE CALCULATION.
No threshold.
Number of parties is 3.
Total number of seats is 65.
Total number of districts is 13.
Seats available in each district is 5.
VOTES OF EACH PARTY BY DISTRICT:
DISTRICT MLP PN OTH
1 7537 7408 0
2 11282 4346 0
3 10400 5497 0
4 9639 6051 0
5 9193 6420 0
6 9300 7455 0
7 8446 7492 11
8 6442 8969 0
9 7554 8898 0
10 5647 9875 24
11 7388 8564 0
12 6134 9501 0
13 6892 9075 0
TOTAL 105854 99551 35
NATIONWIDE DIVISORS: D'HONDT only:
PARTY: MLP PN OTH
SEATS: 34 31
DISTRICTS: 1 2 3 4 5 6 7 8 9 10 11 12 13 TOTAL
Districtwise divisor: D'HONDT to DANISH; all same:
MLP 3 4 3 3 3 3 3 2 2 2 2 2 2 34
PN 2 1 2 2 2 2 2 3 3 3 3 3 3 31
NATIONWIDE DIVISORS: SAINTE LAGUE MODIFIED to DANISH; all same
PARTY: MLP PN OTH
SEATS: 33 32
DISTRICTS: 1 2 3 4 5 6 7 8 9 10 11 12 13 TOTAL
Districtwise divisor: D'HONDT to DANISH; all same:
PN 2 4 3 3 3 3 3 2 2 2 2 2 2 33
MLP 3 1 2 2 2 2 2 3 3 3 3 3 3 32
ELECTION OF 1981. PARTYWISE CALCULATION.
No threshold.
Number of parties is 3.
Total number of seats is 65.
Total number of districts is 13.
Number of seats available in each district is 5.
VOTES OF EACH PARTY BY DISTRICT:
DISTRICT MLP PN OTH
1 8240 7786 9
2 11871 5207 0
3 10355 6375 0
4 9972 6848 0
5 9949 7569 0
6 9316 8333 0
7 9267 8210 13
8 6923 10945 0
9 6673 10856 0
10 6282 10793 0
11 7604 10048 0
12 6550 10999 0
13 6988 10165 7
TOTAL: 109990 114134 29
NATIONWIDE DIVISORS: D'HONDT to DANISH; ALL SAME:
PARTY: PN MLP OTH
SEATS: 33 32
Districtwise divisor: D'HONDT only:
DISTRICTS: 1 2 3 4 5 6 7 8 9 10 11 12 13 TOTAL
PN 3 1 2 2 2 2 2 3 3 4 3 3 3 33
MLP 2 4 3 3 3 3 3 2 2 1 2 2 2 32
Districtwise divisor: SAINTE LAGUE MODIFIED to DANISH; all same:
DISTRICTS: 1 2 3 4 5 6 7 8 9 10 11 12 13 TOTAL
PN 3 2 2 2 2 2 2 3 3 3 3 3 3 33
MLP 2 3 3 3 3 3 3 2 2 2 2 2 2 32
DIST. TOTALS: 5 5 5 5 5 5 5 5 5 5 5 5 5 65
ELECTION OF 1987. PARTYWISE CALCULATION.
No threshold.
Number of parties is 3.
Total number of seats is 65.
Total number of districts is 13.
Number of seats available in each district is 5.
VOTES OF EACH PARTY BY DISTRICT:
DISTRICT MLP PN AD
1 8800 8396 30
2 12486 5808 23
3 11417 6486 14
4 10223 7412 21
5 10139 8284 14
6 10080 8746 27
7 9154 8366 42
8 7016 11227 74
9 6962 11884 71
10 6135 11259 78
11 7156 11438 57
12 7393 10986 60
13 7975 9429 0
TOTAL: 114936 119721 511
NATIONWIDE DIVISORS: D'HONDT to DANISH; ALL SAME:
PARTY: PN MLP AD
SEATS: 33 32
Districtwise divisor: D'HONDT only:
DISTRICTS: 1 2 3 4 5 6 7 8 9 10 11 12 13 TOTAL
PN 3 1 2 2 2 2 2 3 3 4 3 3 3 33
MLP 2 4 3 3 3 3 3 2 2 1 2 2 2 32
Districtwise divisor: SAINTE LAGUE MODIFIED to DANISH; all same:
DISTRICTS: 1 2 3 4 5 6 7 8 9 10 11 12 13 TOTAL
PN 3 2 2 2 2 2 2 3 3 3 3 3 3 33
MLP 2 3 3 3 3 3 3 2 2 2 2 2 2 32
DIST. TOTALS: 5 5 5 5 5 5 5 5 5 5 5 5 5 65
ELECTION OF 1992. PARTYWISE CALCULATION.
No threshold.
Number of parties is 3.
Total number of seats is 65.
Total number of districts is 13.
Number of seats in each district is 5.
VOTES OF EACH PARTY BY DISTRICT:
DISTRICT MLP PN AD
1 8153 10179 242
2 12680 6100 325
3 11936 7270 346
4 10061 7494 337
5 11852 7616 325
6 10241 8293 241
7 6960 11792 385
8 7030 11247 365
9 7808 10956 418
10 5025 13426 383
11 7337 12275 421
12 8249 10305 278
13 7529 10979 120
TOTAL: 114861 127932 4186
NATIONWIDE DIVISORS: D'HONDT to DANISH; ALL SAME:
PARTY: PN MLP AD
SEATS: 34 30 1
Districtwise divisor: D'HONDT only:
DISTRICTS: 1 2 3 4 5 6 7 8 9 10 11 12 13 TOTAL
PN 3 1 2 2 2 2 3 3 3 4 3 3 3 34
MLP 2 3 3 3 3 3 2 2 2 1 2 2 2 30
AD 0 1 0 0 0 0 0 0 0 0 0 0 0 1
Districtwise divisor: SAINTE LAGUE MODIFIED to DANISH; all same:
DISTRICTS: 1 2 3 4 5 6 7 8 9 10 11 12 13 TOTAL
PN 3 2 2 2 2 2 3 3 3 3 3 3 3 34
MLP 2 3 3 3 3 3 2 2 2 1 2 2 2 30
AD 0 0 0 0 0 0 0 0 0 1 0 0 0 1
DIST. TOTALS: 5 5 5 5 5 5 5 5 5 5 5 5 5 65
ELECTION OF 1992. THRESHOLD OF 5%.
AD eliminated.
NATIONWIDE DIVISORS: D'HONDT to DANISH; ALL SAME:
PARTY: PN MLP AD
SEATS: 34 31 0
Districtwise divisor: D'HONDT only:
DISTRICTS: 1 2 3 4 5 6 7 8 9 10 11 12 13 TOTAL
PN 3 1 2 2 2 2 3 3 3 4 3 3 3 34
MLP 2 4 3 3 3 3 2 2 2 1 2 2 2 31
DIST. TOTALS: 5 5 5 5 5 5 5 5 5 5 5 5 5 65
Districtwise divisor: SAINTE LAGUE MODIFIED to DANISH; all same:
DISTRICTS: 1 2 3 4 5 6 7 8 9 10 11 12 13 TOTAL
PN 3 2 2 2 2 2 3 3 3 3 3 3 3 34
MLP 2 3 3 3 3 3 2 2 2 2 2 2 2 31
DIST. TOTALS: 5 5 5 5 5 5 5 5 5 5 5 5 5 65
Fictitious election. No threshold.
Number of parties is 6.
Total number of seats is 50.
Total number of districts is 10.
Seats available in each district is 5.
VOTES OF EACH PARTY BY DISTRICT:
DISTRICT A B C D E F
1 3200 2100 100 921 930 925
2 2200 3100 110 980 990 985
3 4100 1200 989 930 910 950
4 2100 3221 980 970 982 994
5 1100 4050 970 981 902 911
6 1120 1050 3050 910 940 980
7 2500 3010 950 960 970 975
8 3020 2400 960 943 921 910
9 2500 3500 950 960 965 948
10 2500 980 3022 981 982 978
TOTAL: 24340 24611 12081 9536 9492 9556
NATIONWIDE DIVISORS: D'HONDT to DANISH; ALL SAME:
PARTIES: B A C F D E
SEATS: 14 14 7 5 5 5
continued ...
Fictitious election continued ...
DISTRICTS: 1 2 3 4 5 6 7 8 9 10 TOTAL
Districtwise divisor: D'HONDT only:
B 1 2 1 2 3 0 2 1 2 0 14
A 2 1 3 1 0 1 2 2 1 1 14
C 0 0 1 0 1 3 0 0 0 2 7
F 1 1 0 1 0 1 1 0 0 0 5
D 1 1 0 1 1 0 0 0 0 1 5
E 0 0 0 0 0 0 0 2 2 1 5
Districtwise divisor: SAINTE LAGUE MODIFIED only:
B 1 2 1 2 2 1 2 1 2 0 14
A 2 1 3 1 0 1 2 2 1 1 14
C 0 0 1 0 1 3 0 0 0 2 7
F 1 1 0 1 0 0 1 0 0 1 5
D 1 1 0 1 1 0 0 0 0 1 5
E 0 0 0 0 1 0 0 2 2 0 5
Districtwise divisor: SAINTE LAGUE only:
B 1 2 1 2 2 1 2 1 2 0 14
A 2 1 3 1 1 1 1 2 1 1 14
C 0 0 1 1 1 2 0 0 0 2 7
F 1 1 0 1 0 1 1 0 0 0 5
D 1 1 0 0 1 0 0 1 0 1 5
E 0 0 0 0 0 0 1 1 2 1 5
Districtwise divisor: EQUAL PROPORTIONS only:
B 1 2 1 2 2 1 2 1 2 0 14
A 2 1 2 1 1 1 2 2 1 1 14
C 0 0 1 1 1 2 0 0 0 2 7
F 1 1 1 1 0 1 0 0 0 0 5
D 1 1 0 0 1 0 0 1 0 1 5
E 0 0 0 0 0 0 1 1 2 1 5
Districtwise divisor: DANISH only:
B 1 2 1 2 2 1 1 1 2 1 14
A 2 1 2 1 1 1 2 2 1 1 14
C 0 0 1 1 1 1 1 1 0 1 7
F 1 1 1 1 0 1 0 0 0 0 5
D 1 1 0 0 1 1 0 0 0 1 5
E 0 0 0 0 0 0 1 1 2 1 5
DIST. TOTALS: 5 5 5 5 5 5 5 5 5 5 50
Fictitious election continued.
National threshold of 12%.
Parties D, E, F eliminated.
NATIONWIDE DIVISORS: D'HONDT to DANISH; ALL SAME:
PARTIES: B A C F D E
SEATS: 20 20 10
Districtwise divisor: D'HONDT only:
DISTRICTS: 1 2 3 4 5 6 7 8 9 10 TOTAL
B 2 3 1 3 3 1 2 2 3 0 20
A 3 2 3 2 1 1 2 2 2 2 20
C 0 0 1 0 1 3 1 1 0 3 10
DIST. TOTALS: 5 5 5 5 5 5 5 5 5 5 50
Districtwise divisors: SAINTE LAGUE MODIFIED to DANISH; all same:
B 2 3 1 2 3 1 2 2 3 1 20
A 3 2 3 2 1 1 2 2 2 2 20
C 0 0 1 1 1 3 1 1 0 2 10
DIST. TOTALS: 5 5 5 5 5 5 5 5 5 5 50
APPENDIX V.
PRIORITY CALCULATIONS WITH DIFFERENT DIVISORS
FOR THE ELECTIONS 1962-1992.
ELECTION OF 1962. PRIORITY CALCULATION.
No threshold assumed.
Number of parties is 7
Total number of seats is 50
Total number of districts is 10
Number of seats available in each district is 5.
VOTES OF EACH PARTY BY DISTRICT:
DISTRICT MLP PN PCP CWP DNP DCP IND
1 5532 7556 795 979 1720 143 0
2 9170 4359 178 1672 937 0 0
3 6512 4908 269 1704 656 0 0
4 6919 6226 245 681 505 0 0
5 4860 7051 404 1069 784 0 0
6 3457 7072 621 1579 1419 247 0
7 4493 6152 2397 1489 2285 152 0
8 5292 5588 697 1853 1399 116 0
9 3896 7368 981 1366 1353 41 0
10 843 6982 703 1893 2910 0 128
TOTAL: 50974 63262 7290 14285 13968 699 128
NATIONWIDE Divisor: D'HONDT only:
PARTY: PN MLP CWP DNP PCP DCP IND
SEATS: 22 17 5 4 2 0 0
DISTRICTS: 1 2 3 4 5 6 7 8 9 10 TOTAL
District divisors: D'HONDT to SAINTE LAGUE MODIFIED; all same:
PN 2 2 2 2 3 3 1 2 3 2 22
MLP 2 3 2 3 2 1 1 2 1 0 17
CWP 0 0 1 0 0 1 0 1 1 1 5
DNP 1 0 0 0 0 0 1 0 0 2 4
PCP 0 0 0 0 0 0 2 0 0 0 2
District divisors: SAINTE LAGUE to DANISH; all same:
PN 2 1 2 2 3 2 2 2 3 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 1 1 0 0 1 4
PCP 0 0 0 0 0 0 1 0 1 0 2
DIST. TOTALS: 5 5 5 5 5 5 5 5 5 5 50
NATIONWIDE DIVISOR: SAINTE LAGUE MODIFIED to EQUAL PROPORTION; all same:
PARTY: PN MLP CWP DNP PCP DCP IND
SEATS: 21 17 5 5 2 0 0
DISTRICTS: 1 2 3 4 5 6 7 8 9 10 TOTAL
District divisors: D'HONDT to SAINTE LAGUE MODIFIED; all same:
PN 2 1 2 2 3 3 1 2 3 2 21
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 2 5
PCP 0 0 0 0 0 0 2 0 0 0 2
District divisors: SAINTE LAGUE to DANISH; all same:
PN 2 1 2 2 3 2 2 2 2 3 21
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 1 1 0 1 1 5
PCP 0 0 0 0 0 0 1 0 1 0 2
DIST. TOTALS: 5 5 5 5 5 5 5 5 5 5 50
NATIONWIDE DIVISOR: DANISH only:
PARTY: PN MLP CWP DNP PCP DCP IND
SEATS: 20 17 5 5 3
District divisors: D'HONDT to SAINTE LAGUE MODIFIED; all same:
DISTRICTS: 1 2 3 4 5 6 7 8 9 10 TOTAL
PN 2 1 2 2 3 3 1 2 2 2 20
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 2 5
PCP 0 0 0 0 0 0 2 0 1 0 3
District divisors: SAINTE LAGUE to DANISH; all same:
PN 2 1 2 2 2 2 2 2 2 3 20
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 1 1 0 1 1 5
PCP 0 0 0 0 1 0 1 0 1 0 3
DIST. TOTALS: 5 5 5 5 5 5 5 5 5 5 50
ELECTION OF 1962. Threshold 5%.
PCP eliminated.
NATIONWIDE Divisor: D'HONDT:
PARTY: PN MLP CWP DNP PCP DCP IND
SEATS: 22 18 5 5
DISTRICTS: 1 2 3 4 5 6 7 8 9 10 TOTAL
District divisors: D'HONDT to SAINTE LAGUE MODIFIED; all same:
PN 2 1 2 2 3 3 2 2 3 2 22
MLP 2 3 2 3 2 1 2 2 1 0 18
CWP 0 1 1 0 0 1 0 1 0 1 5
DNP 1 0 0 0 0 0 1 0 1 2 5
District divisors: SAINTE LAGUE to DANISH; all same:
PN 2 1 2 2 3 2 2 2 3 3 22
MLP 2 3 2 3 2 1 2 2 1 0 18
CWP 0 1 1 0 0 1 0 1 0 1 5
DNP 1 0 0 0 0 1 1 0 1 1 5
DIST. TOTALS: 5 5 5 5 5 5 5 5 5 5 50
NATIONWIDE Divisor: SAINTE LAGUE MODIFIED to DANISH; all same:
PARTY: PN MLP CWP DNP PCP DCP IND
SEATS: 22 18 5 5
District divisors: D'HONDT:
PN 2 1 2 2 3 2 2 2 4 2 22
MLP 2 3 2 3 2 1 2 2 1 0 18
CWP 0 1 1 0 0 1 0 1 0 1 5
DNP 1 0 0 0 0 1 1 0 0 2 5
District divisor: SAINTE LAGUE MODIFIED:
PN 2 1 2 2 3 2 3 2 3 2 22
MLP 2 3 2 3 2 1 1 2 2 0 18
CWP 0 1 1 0 0 1 0 1 0 1 5
DNP 1 0 0 0 0 1 1 0 0 2 5
District divisor: SAINTE LAGUE to DANISH; all same:
PN 2 1 2 2 3 2 2 2 3 3 22
MLP 2 3 2 3 2 1 2 2 1 0 18
CWP 0 1 1 0 0 1 0 1 0 1 5
DNP 1 0 0 0 0 1 1 0 1 1 5
DIST. TOTALS: 5 5 5 5 5 5 5 5 5 5 50
ELECTION OF 1962. National threshold of 9.3%.
DNP eliminated.
NATIONWIDE Divisor: D'HONDT:
PARTY: PN MLP CWP DNP PCP DCP IND
SEATS: 25 20 5
DISTRICTS: 1 2 3 4 5 6 7 8 9 10 TOTAL
District divisors: D'HONDT to SAINTE LAGUE MODIFIED; all same:
PN 3 1 2 2 3 3 2 2 3 4 25
MLP 2 3 2 3 2 1 3 2 2 0 20
CWP 0 1 1 0 0 1 0 1 0 1 5
District divisors: SAINTE LAGUE to DANISH; all same:
PN 3 1 2 2 3 3 3 2 3 3 25
MLP 2 3 2 3 2 1 2 2 2 1 20
CWP 0 1 1 0 0 1 0 1 0 1 5
DIST. TOTALS: 5 5 5 5 5 5 5 5 5 5 50
NATIONWIDE Divisor: SAINTE LAGUE MODIFIED to EQUAL PROPORTIONS; all same:
PARTY: PN MLP CWP DNP PCP DCP IND
SEATS: 24 20 6
DISTRICTS: 1 2 3 4 5 6 7 8 9 10 TOTAL
District divisors: D'HONDT to SAINTE LAGUE MODIFIED; all same:
PN 3 1 2 2 3 3 2 2 3 3 24
MLP 2 3 2 3 2 1 3 2 2 0 20
CWP 0 1 1 0 0 1 0 1 0 2 6
District divisors: SAINTE LAGUE to DANISH; all same:
PN 3 1 2 2 3 3 2 2 3 3 24
MLP 2 3 2 3 2 1 2 2 2 1 20
CWP 0 1 1 0 0 1 1 1 0 1 6
DIST. TOTALS: 5 5 5 5 5 5 5 5 5 5 50
NATIONWIDE Divisor: DANISH only:
PARTY: PN MLP CWP DNP PCP DCP IND
SEATS: 24 20 6
District divisors: D'HONDT to DANISH; all same:
DISTRICTS: 1 2 3 4 5 6 7 8 9 10 TOTAL
PN 3 1 2 2 3 3 2 2 3 3 24
MLP 2 3 2 3 2 1 2 2 2 1 20
CWP 0 1 1 0 0 1 1 1 0 1 6
DIST. TOTALS: 5 5 5 5 5 5 5 5 5 5 50
ELECTION OF 1962. National threshold of 10%.
CWP eliminated.
NATIONWIDE Divisor: D'HONDT to DANISH; ALL SAME:
PARTY: PN MLP CWP DNP PCP DCP IND
SEATS: 28 22 0
DISTRICTS: 1 2 3 4 5 6 7 8 9 10 TOTAL
District divisors: D'HONDT only:
PN 3 1 2 2 3 4 2 3 3 5 28
MLP 2 4 3 3 2 1 3 2 2 0 22
District divisors: SAINTE LAGUE MODIFIED only:
PN 3 2 2 2 3 3 2 3 3 5 28
MLP 2 3 3 3 2 2 3 2 2 0 22
District divisors: SAINTE LAGUE to DANISH:
PN 3 2 2 2 3 3 3 3 3 4 28
MLP 2 3 3 3 2 2 2 2 2 1 22
DIST. TOTALS: 5 5 5 5 5 5 5 5 5 5 50
ELECTION OF 1966. PRIORITY CALCULATION.
No Threshold.
Number of parties is 6
Total number of seats is 50
Total number of districts is 10
Number of seats available in each district is 5.
VOTES OF EACH PARTY BY DISTRICT:
DISTRICT MLP PN PCP CWP DNP IND
1 6151 7623 191 747 351 0
2 9517 4771 0 598 0 20
3 7756 5356 0 954 99 0
4 7812 5761 0 347 0 29
5 6176 7231 0 495 0 0
6 4561 7725 180 1033 199 0
7 5622 7737 915 1554 476 0
8 6402 6459 163 1134 523 9
9 5010 7805 257 853 197 67
10 2767 8188 380 879 0 267
2TOTAL: 61774 68656 2086 8594 1845 392
NATIONWIDE Divisor: D'HONDT only:
PARTY: PN MLP CWP PCP DNP
SEATS: 25 22 3
DISTRICTS: 1 2 3 4 5 6 7 8 9 10 TOTAL
District divisors: D'HONDT only:
PN 3 1 2 2 3 3 2 2 3 4 25
MLP 2 4 3 3 2 1 2 2 2 1 22
CWP 0 0 0 0 0 1 1 1 0 0 3
District divisors: SAINTE LAGUE MODIFIED to DANISH; all same:
PN 3 2 2 2 3 3 2 2 3 3 25
MLP 2 3 3 3 2 2 2 2 2 1 22
CWP 0 0 0 0 0 0 1 1 0 1 3
DIST. TOTALS: 5 5 5 5 5 5 5 5 5 5 50
NATIONWIDE Divisor: SAINTE LAGUE MODIFIED only:
PARTY: PN MLP CWP PCP DNP
SEATS: 24 22 3 1
DISTRICTS: 1 2 3 4 5 6 7 8 9 10 TOTAL
District divisors: D'HONDT only:
PN 3 1 2 2 3 3 2 2 3 3 24
MLP 2 4 3 3 2 1 2 2 2 1 22
CWP 0 0 0 0 0 1 1 1 0 0 3
PCP 0 0 0 0 0 0 0 0 0 1 1
District divisors: SAINTE LAGUE MODIFIED to DANISH; all same:
PN 2 2 2 2 3 3 2 2 3 3 24
MLP 3 3 3 3 2 1 2 2 2 1 22
CWP 0 0 0 0 0 1 1 1 0 0 3
PCP 0 0 0 0 0 0 0 0 0 1 1
DIST. TOTALS: 5 5 5 5 5 5 5 5 5 5 50
NATIONWIDE Divisors: SAINTE LAGUE to EQUAL PROPORTIONS:
PARTY: PN MLP CWP PCP DNP
SEATS: 24 21 3 1 1
DISTRICTS: 1 2 3 4 5 6 7 8 9 10 TOTAL
District divisors: D'HONDT only:
PN 2 1 2 2 3 3 2 2 3 4 24
MLP 2 4 3 3 2 1 1 2 2 1 21
CWP 0 0 0 0 0 1 1 1 0 0 3
PCP 0 0 0 0 0 0 1 0 0 0 1
DNP 1 0 0 0 0 0 0 0 0 0 1
District divisors: SAINTE LAGUE MODIFIED to DANISH.
PN 2 2 2 2 2 3 2 2 3 4 24
MLP 2 3 3 3 3 1 1 2 2 1 21
CWP 0 0 0 0 0 1 1 1 0 0 3
PCP 0 0 0 0 0 0 1 0 0 0 1
DNP 1 0 0 0 0 0 0 0 0 0 1
DIST. TOTALS: 5 5 5 5 5 5 5 5 5 5 50
NATIONWIDE Divisors: DANISH only:
PARTY: PN MLP CWP PCP DNP
SEATS: 24 21 3 1 1
DISTRICTS: 1 2 3 4 5 6 7 8 9 10 TOTAL
District divisors: D'HONDT only:
PN 3 1 2 2 3 3 2 1 3 4 24
MLP 2 4 3 3 2 1 1 2 2 1 21
CWP 0 0 0 0 0 1 1 1 0 0 3
PCP 0 0 0 0 0 0 1 0 0 0 1
DNP 0 0 0 0 0 0 0 1 0 0 1
District divisors: SAINTE LAGUE MODIFIED to DANISH; all same:
PN 2 2 2 2 3 3 2 1 3 4 24
MLP 3 3 3 3 2 1 1 2 2 1 21
CWP 0 0 0 0 0 1 1 1 0 0 3
PCP 0 0 0 0 0 0 1 0 0 0 1
DNP 0 0 0 0 0 0 0 1 0 0 1
DIST. TOTALS: 5 5 5 5 5 5 5 5 5 5 50
ELECTION OF 1966. National threshold of 6%.
CWP eliminated.
NATIONWIDE Divisors: D'HONDT to DANISH; ALL SAME:
PARTY: PN MLP CWP PCP DNP
SEATS: 26 24
DISTRICTS: 1 2 3 4 5 6 7 8 9 10 TOTAL
District divisors: D'HONDT only:
PN 3 1 2 2 3 3 3 2 3 4 26
MLP 2 4 3 3 2 2 2 3 2 1 24
District divisors: SAINTE LAGUE MODIFIED to DANISH; all same:
PN 3 2 2 2 3 3 3 2 3 3 26
MLP 2 3 3 3 2 2 2 3 2 2 24
DIST. TOTALS: 5 5 5 5 5 5 5 5 5 5 50
ELECTION OF 1971. PRIORITY CALCULATION.
No threshold.
Number of parties is 4
Total number of seats is 55
Total number of districts is 10
Seats available in each district:
District: 1 2 3 4 5 6 7 8 9 10
Number: 5 6 6 5 5 5 6 6 6 5.
VOTES OF EACH PARTY BY DISTRICT:
DISTRICT MLP PN PCP OTH
1 7728 8266 204 0
2 11827 5293 43 8
3 11354 6888 55 22
4 10288 6324 36 0
5 8151 8130 23 0
6 6664 9332 349 0
7 7617 11032 682 26
8 8480 8631 171 0
9 7232 9392 165 27
10 6107 7465 28 19
TOTAL: 85448 80753 1756 102
NATIONWIDE Divisors: D'HONDT to SAINTE LAGUE MODIFIED; all same:
PARTY: MLP PN PCP OTH
SEATS: 28 27
DISTRICTS: 1 2 3 4 5 6 7 8 9 10 TOTAL
District divisors: D'HONDT to DANISH; all same:
MLP 2 4 4 3 3 2 2 3 3 2 28
PN 3 2 2 2 2 3 4 3 3 3 27
NATIONWIDE Divisors: SAINTE LAGUE to DANISH; all same:
PARTY: MLP PN PCP OTH
SEATS: 28 26 1
District divisors: D'HONDT to DANISH; all same:
MLP 2 4 4 3 3 2 2 3 3 2 28
PN 3 2 2 2 2 3 3 3 3 3 26
PCP 0 0 0 0 0 0 1 0 0 0 1
DIST. TOTALS: 5 6 6 5 5 5 6 6 6 5 55
ELECTION OF 1976. PRIORITY CALCULATION.
No threshold.
Number of parties is 3
Total number of seats is 65
Total number of districts is 13
Number of seats available in each district is 5.
VOTES OF EACH PARTY BY DISTRICT:
DISTRICT MLP PN OTH
1 7537 7408 0
2 11282 4346 0
3 10400 5497 0
4 9639 6051 0
5 9193 6420 0
6 9300 7455 0
7 8446 7492 11
8 6442 8969 0
9 7554 8898 0
10 5647 9875 24
11 7388 8564 0
12 6134 9501 0
13 6892 9075 0
TOTAL: 105854 99551 35
NATIONWIDE Divisors: D'HONDT only:
PARTY: MLP PN OTH
SEATS: 34 31
DISTRICTS: 1 2 3 4 5 6 7 8 9 10 11 12 13 TOTAL
District divisors: D'HONDT to DANISH; all same:
MLP 3 4 3 3 3 3 3 2 2 2 2 2 2 34
PN 2 1 2 2 2 2 2 3 3 3 3 3 3 31
NATIONWIDE Divisors: SAINTE LAGUE MODIFIED to DANISH; all same:
PARTY: MLP PN OTH
SEATS: 33 32
District divisors: D'HONDT to DANISH; all same:
MLP 2 4 3 3 3 3 3 2 2 2 2 2 2 33
PN 3 1 2 2 2 2 2 3 3 3 3 3 3 32
DIST. TOTALS: 5 5 5 5 5 5 5 5 5 5 5 5 5 65
ELECTION OF 1981. PRIORITY CALCULATION.
No threshold.
Number of parties is 3.
Total number of seats is 65.
Total number of districts is 13.
Number of seats available in each district is 5.
VOTES OF EACH PARTY BY DISTRICT:
DISTRICT MLP PN OTH
1 8240 7786 9
2 11871 5207 0
3 10355 6375 0
4 9972 6848 0
5 9949 7569 0
6 9316 8333 0
7 9267 8210 13
8 6923 10945 0
9 6673 10856 0
10 6282 10793 0
11 7604 10048 0
12 6550 10999 0
13 6988 10165 7
TOTAL: 109990 114134 29
NATIONWIDE Divisors: D'HONDT to DANISH; ALL SAME:
PARTY: PN MLP OTH
SEATS: 33 32
DISTRICTS: 1 2 3 4 5 6 7 8 9 10 11 12 13 TOTAL
District divisors: D'HONDT only:
PN 3 1 2 2 2 3 2 3 3 3 3 3 3 33
MLP 2 4 3 3 3 2 3 2 2 2 2 2 2 32
District Divisors: SAINTE LAGUE MODIFIED to DANISH; all same:
PN 3 2 2 2 2 2 2 3 3 3 3 3 3 33
MLP 2 3 3 3 3 3 3 2 2 2 2 2 2 32
DIST. TOTALS: 5 5 5 5 5 5 5 5 5 5 5 5 5 65
ELECTION OF 1987. PRIORITY CALCULATION.
No threshold.
Number of parties is 3.
Total number of seats is 65.
Total number of districts is 13.
Number of seats available in each district is 5.
VOTES OF EACH PARTY BY DISTRICT:
DISTRICT MLP PN AD
1 8800 8396 30
2 12486 5808 23
3 11417 6486 14
4 10223 7412 21
5 10139 8284 14
6 10080 8746 27
7 9154 8366 42
8 7016 11227 74
9 6962 11884 71
10 6135 11259 78
11 7156 11438 57
12 7393 10986 60
13 7975 9429 0
TOTAL: 114936 119721 511
NATIONWIDE Divisors: D'HONDT to DANISH; ALL SAME:
PARTY: PN MLP AD
SEATS: 33 32
DISTRICTS: 1 2 3 4 5 6 7 8 9 10 11 12 13 TOTAL
District divisors: D'HONDT only:
PN 3 1 2 2 2 2 3 3 3 3 3 3 3 33
MLP 2 4 3 3 3 3 2 2 2 2 2 2 2 32
District Divisors: SAINTE LAGUE MODIFIED to DANISH; all same:
PN 3 2 2 2 2 2 2 3 3 3 3 3 3 33
MLP 2 3 3 3 3 3 3 2 2 2 2 2 2 32
DIST. TOTALS: 5 5 5 5 5 5 5 5 5 5 5 5 5 65
ELECTION OF 1992. PRIORITY CALCULATION.
No threshold.
Number of parties is 3.
Total number of seats is 65.
Total number of districts is 13.
Number of seats available in each district is 5.
VOTES OF EACH PARTY BY DISTRICT:
DISTRICT MLP PN AD
1 8153 10179 242
2 12680 6100 325
3 11936 7270 346
4 10061 7494 337
5 11852 7616 325
6 10241 8293 241
7 6960 11792 385
8 7030 11247 365
9 7808 10956 418
10 5025 13426 383
11 7337 12275 421
12 8249 10305 278
13 7529 10979 120
TOTAL: 114861 127932 4186
NATIONWIDE Divisors: D'HONDT only:
PARTY: PN MLP AD
SEATS: 34 30 1
DISTRICTS: 1 2 3 4 5 6 7 8 9 10 11 12 13 TOTAL
District divisors: D'HONDT only:
PN 3 1 2 2 2 2 3 3 3 4 3 3 3 34
MLP 2 4 3 3 3 3 2 2 2 1 1 2 2 30
AD 0 0 0 0 0 0 0 0 0 0 1 0 0 1
District divisors: SAINTE LAGUE MODIFIED to DANISH:
PN 3 2 2 2 2 2 3 3 2 4 3 3 3 34
MLP 2 3 3 3 3 3 2 2 2 1 2 2 2 30
AD 0 0 0 0 0 0 0 0 1 0 0 0 0 1
DIST. TOTALS: 5 5 5 5 5 5 5 5 5 5 5 5 5 65
This last array is also the distribution obtained by all the remaining
divisor combinations, namely, Sainte Lague modified to Danish nationwide,
combined with any divisor for the districts.
ELECTION OF 1992. National threshold of 5%.
AD eliminated.
NATIONWIDE Divisors: D'HONDT to DANISH; ALL SAME:
PARTY: PN MLP AD
SEATS: 34 31
DISTRICTS: 1 2 3 4 5 6 7 8 9 10 11 12 13 TOTAL
District divisors: D'HONDT only:
PN 3 1 2 2 2 2 3 3 3 4 3 3 3 34
MLP 2 4 3 3 3 3 2 2 2 1 2 2 2 31
District divisors: SAINTE LAGUE MODIFIED to DANISH:
PN 3 2 2 2 2 2 3 3 3 3 3 3 3 34
MLP 2 3 3 3 3 3 2 2 2 2 2 2 2 31
DIST. TOTALS: 5 5 5 5 5 5 5 5 5 5 5 5 5 65
FICTITIOUS ELECTION. PRIORITY CALCULATION.
No threshold.
Number of parties is 6.
Total number of seats is 50.
Total number of districts is 10.
Number of seats available in each district is 5.
VOTES OF EACH PARTY BY DISTRICT:
DISTRICT A B C D E F
1 3200 2100 100 921 930 925
2 2200 3100 110 980 990 985
3 4100 1200 989 930 910 950
4 2100 3221 980 970 982 994
5 1100 4050 970 981 902 911
6 1120 1050 3050 910 940 980
7 2500 3010 950 960 970 975
8 3020 2400 960 943 921 910
9 2500 3500 950 960 965 948
10 2500 980 3022 981 982 978
TOTAL: 24340 24611 12081 9536 9492 9556
ALL NATIONWIDE DIVISORS give:
PARTIES: B A C F D E
SEATS: 14 14 7 5 5 5.
NATIONWIDE DIVISOR: D'HONDT only:
Districtwise Divisor D'HONDT:
B 1 1 0 2 3 0 2 2 3 0 14
A 1 1 3 1 0 0 2 3 2 1 14
C 0 0 1 0 1 2 1 0 0 2 7
F 1 1 1 1 0 1 0 0 0 0 5
D 1 1 0 0 1 1 0 0 0 1 5
E 1 1 0 1 0 1 0 0 0 1 5
Districtwise Divisor SAINTE LAGUE MODIFIED:
B 1 1 1 2 3 0 2 2 2 0 14
A 1 1 3 1 0 0 2 3 2 1 14
C 0 0 1 0 1 2 0 0 1 2 7
F 1 1 0 1 0 1 1 0 0 0 5
D 1 1 0 0 1 1 0 0 0 1 5
E 1 1 0 1 0 1 0 0 0 1 5
Districtwise Divisor SAINTE LAGUE:
B 1 1 1 2 2 0 2 2 3 0 14
A 1 1 3 1 1 0 2 2 2 1 14
C 0 0 1 0 1 2 0 1 0 2 7
F 1 1 0 1 0 1 1 0 0 0 5
D 1 1 0 0 1 1 0 0 0 1 5
E 1 1 0 1 0 1 0 0 0 1 5
Districtwise Divisor EQUAL PROPORTIONS:
B 1 1 1 2 2 0 2 2 3 0 14
A 1 1 2 1 1 0 2 3 2 1 14
C 0 0 1 0 1 2 1 0 0 2 7
F 1 1 1 1 0 1 0 0 0 0 5
D 1 1 0 0 1 1 0 0 0 1 5
E 1 1 0 1 0 1 0 0 0 1 5
Districtwise Divisor DANISH:
B 1 1 1 1 2 1 2 2 2 1 14
A 1 1 2 1 1 0 3 2 2 1 14
C 0 0 1 1 1 1 0 1 1 1 7
F 1 1 1 1 0 1 0 0 0 0 5
D 1 1 0 0 1 1 0 0 0 1 5
E 1 1 0 1 0 1 0 0 0 1 5
DIST. TOTALS: 5 5 5 5 5 5 5 5 5 5 50
NATIONWIDE DIVISOR: SAINTE LAGUE MODIFIED to EQUAL PROPORTIONS:
Districtwise Divisor D'HONDT:
B 1 1 0 2 3 0 2 2 3 0 14
A 1 1 3 1 0 0 3 2 2 1 14
C 0 0 1 0 1 2 0 1 0 2 7
F 1 1 1 1 0 1 0 0 0 0 5
D 1 1 0 0 1 1 0 0 0 1 5
E 1 1 0 1 0 1 0 0 0 1 5
Districtwise Divisor SAINTE LAGUE MODIFIED:
B 1 1 1 2 3 0 2 2 2 0 14
A 1 1 3 1 0 0 2 2 3 1 14
C 0 0 1 0 1 2 0 1 0 2 7
F 1 1 0 1 0 1 1 0 0 0 5
D 1 1 0 0 1 1 0 0 0 1 5
E 1 1 0 1 0 1 0 0 0 1 5
Districtwise Divisor SAINTE LAGUE:
B 1 1 1 2 2 0 2 2 3 0 14
A 1 1 2 1 1 0 3 2 2 1 14
C 0 0 1 0 1 2 0 1 0 2 7
F 1 1 1 1 0 1 0 0 0 0 5
D 1 1 0 0 1 1 0 0 0 1 5
E 1 1 0 1 0 1 0 0 0 1 5
Districtwise Divisor EQUAL PROPORTION:
B 1 1 1 2 2 0 2 2 3 0 14
A 1 1 2 1 1 0 3 2 2 1 14
C 0 0 1 0 1 2 0 1 0 2 7
F 1 1 1 1 0 1 0 0 0 0 5
D 1 1 0 0 1 1 0 0 0 1 5
E 1 1 0 1 0 1 0 0 0 1 5
Districtwise Divisor DANISH:
B 1 1 1 1 2 1 2 2 2 1 14
A 1 1 2 1 1 0 2 2 3 1 14
C 0 0 1 1 1 1 1 1 0 1 7
F 1 1 1 1 0 1 0 0 0 0 5
D 1 1 0 0 1 1 0 0 0 1 5
E 1 1 0 1 0 1 0 0 0 1 5
NATIONWIDE DIVISOR: DANISH only:
The seat distribution is identical to the above, except when the district
divisor is Sainte Lague modified, when the distribution is similar to the
first one given on this page.
FICTITIOUS ELECTION. National threshold of 12%.
Parties D, E, F eliminated.
ALL NATIONWIDE DIVISORS ALL give:
PARTY: B A C
SEATS: 20 20 10
NATIONWIDE DIVISOR: D'HONDT only:
DISTRICTS: 1 2 3 4 5 6 7 8 9 10 TOTAL
District divisors: D'HONDT only:
B 2 3 1 3 3 1 2 2 3 0 20
A 3 2 3 1 1 1 2 3 2 2 20
C 0 0 1 1 1 3 1 0 0 3 10
District Divisors: SAINTE LAGUE MODIFIED to EQUAL PROPORTIONS:
B 2 3 1 2 3 1 2 2 3 1 20
A 3 2 3 2 1 1 2 2 2 2 20
C 0 0 1 1 1 3 1 1 0 2 10
District Divisor: DANISH only:
B 3 3 1 2 3 1 2 2 2 1 20
A 2 2 3 2 1 1 2 2 2 3 20
C 0 0 1 1 1 3 1 1 1 1 10
NATIONWIDE DIVISORS: SAINTE LAGUE MODIFIED to DANISH; all same:
DISTRICTS: 1 2 3 4 5 6 7 8 9 10 TOTAL
Districtwise divisor: D'HONDT:
B 2 3 1 3 3 1 2 2 3 0 20
A 3 2 3 1 1 1 3 2 2 2 20
C 0 0 1 1 1 3 0 1 0 3 10
Districtwise divisor: SAINTE LAGUE MODIFIED:
B 2 3 1 2 3 1 2 2 3 1 20
A 3 2 3 2 1 1 2 2 2 2 20
C 0 0 1 1 1 3 1 1 0 2 10
Districtwise divisor: SAINTE LAGUE:
B 2 3 1 3 3 1 2 2 2 1 20
A 3 2 3 1 1 2 2 2 2 2 20
C 0 0 1 1 1 2 1 1 1 2 10
Districtwise divisors: EQUAL PROPORTIONS to DANISH:
B 3 3 1 2 3 1 2 2 2 1 20
A 2 2 3 2 1 2 2 2 2 2 20
C 0 0 1 1 1 2 1 1 1 2 10
DIST. TOTALS: 5 5 5 5 5 5 5 5 5 5 50
APPENDIX VI.
COMPARISON OF PARTYWISE AND PRIORITY METHODS
WITH NATIONWIDE D'HONDT DIVISORS
FOR DIFFERENT DIVISORS IN THE DISTRICTS.
ELECTIONS 1962-1992.
NB: ALL THE FOLLOWING COMPARISONS ARE BETWEEN METHODS WITH THE
D'HONDT DIVISOR FOR THE NATIONWIDE CALCULATIONS. THESE METHODS
ARE COMPARED WHEN DIFFERENT DIVISORS ARE CHOSEN FOR THE DISTRICTS.
ELECTION OF 1962. No Threshold.
District divisor:
Partywise: d'Hondt to Danish.
NOT =
Priority : d'Hondt, Modified St Lague; Sainte Lague to Danish.
All three groups of distributions are different.
D'Hondt priority concentrates 2 seats of the PCP in District 7,
and 2 seats of the DNP in District 10. This is not done in the
Sainte Lague priority method. This method also gives a better
distribution for the DNP and the PN than does the partywise method
for any choice of divisor. It gives a seat to the DNP in the 6th
rather than the 9th district, and gives 3 seats to the PN in the
9th rather than the in the 6th district, making it fairer than its
counterparts.
ELECTION OF 1962. 5% Threshold.
PCP eliminated.
District divisor:
Partywise: d'Hondt to Danish.
NOT =
Priority : d'Hondt, Modified St Lague; Sainte Lague to Danish.
All three groups of distributions are different.
The partywise method (with any district divisor) concentrates 2 seats
of the PCP in district 7, whilst the priority method with the d'Hondt
divisor awards 2 seats to the DNP in the tenth district. The Sainte
Lague priority method does not do this. This method also gives a better
distribution for the CWP, the DNP and the PN. It gives a seat to the
CWP in the 3rd rather than the 9th district, it transfers one DNP seat
from the 7th to the 6th district, and awards 3 seats to the PN in the
9th rather than the 6th district.
ELECTION OF 1962. 9.3% Threshold.
DNP eliminated.
District divisor:
Partywise: d'Hondt ; Modified Sainte Lague to Danish.
NOT =
Priority : d'Hondt, Modified St Lague; Sainte Lague to Danish.
There are four groups of methods, all different from each other.
All the partywise methods concentrate 2 CWP seats in the 10th district,
and award a seat to this party in the 7th District, where it is not so
strong. Conversely, the priority methods move one Gozo seat and the seat
in the seventh district to the 2nd and 3rd districts, where the CWP is strong.
The d'Hondt partywise method gives an inversion in the 4th District,
whilst the d'Hondt priority method gives an inversion in the 7th District.
The Sainte Lague priority method does not yield any inversion. It is also
interesting to note that this method awards one seat to the MLP in the
tenth District.
ELECTION OF 1962. 10% Threshold.
CWP eliminated.
District divisor:
Partywise: d'Hondt to Danish.
NOT =
Priority : d'Hondt, Modified St Lague; Sainte Lague to Danish.
There three groups of distributions all different from one another.
The partywise methods yield an inversion in the 4th and 7th Districts.
The priority d'Hondt produces an inversion in the 7th District.
By contrast, the Sainte Lague priority method does not give rise to
any inversion, and seems to be the best option.
ELECTION OF 1966. No Threshold.
District divisor:
Partywise: d'Hondt ; Modified Sainte Lague to Danish.
NOT = =
Priority : d'Hondt ; Modified Sainte Lague to Danish.
There are three groups of distributions all different from one another.
Partywise d'Hondt : CWP awarded seats in districts 2, 7 and 8;
Partywise Priority: CWP awarded seats in districts 6, 7 and 8;
Mod St Lague to Danish: CWP awarded seats in districts 7, 8, 10.
(Partywise or priority)
The relevant districts in descending order of CWP strength are:
7, 8 and 6, all closely followed by district 10. The CWP has only
a moderate following in the second district. There are no inversions
in this district for any of the three groups of methods.
ELECTION OF 1966. 6% Threshold.
CWP eliminated.
District divisor:
Partywise: d'Hondt ; Modified Sainte Lague to Danish.
NOT = =
Priority : d'Hondt ; Modified Sainte Lague to Danish.
There are three groups of distributions all different from one another.
The difference between these methods lies in Districts 2, 7 and 10
as follows.
Method Party District
2 7 10
Partywise d'Hondt PN 2 2* 4
MLP 3 3 1
Priority d'Hondt PN 1 3 4
MLP 4 2 1
Mod Sainte Lague-Danish PN 2 3 3
(Partywise or Priority) MLP 3 2 2
* signifies an inversion.
All methods give an inversion in the 8'th district for this election.
ELECTION OF 1971. No Threshold.
District divisor:
Partywise: d'Hondt ; Modified Sainte Lague to Danish.
NOT =
Priority : d'Hondt to Danish.
All three groups of methods are different from one another.
Partywise d'Hondt gives an inversion in the 1st district.
Partywise Sainte Lague modified to Danish give an inversion in 1st and
10th districts.
Priority d'Hondt to Danish does not yield any inversion. Also the
distribution is identical to the actual election.
ELECTION OF 1976. No Threshold.
District divisor:
Partywise: d'Hondt to Danish.
=
Priority : d'Hondt to Danish.
All methods are identical and equal to the actual election.
ELECTION OF 1981. No Threshold.
District divisor:
Partywise: d'Hondt ; Modified Sainte Lague to Danish.
NOT = =
Priority : d'Hondt ; Modified Sainte Lague to Danish.
There are three groups of distributions all different from one another.
The difference between these methods lies in Districts 2, 6 and 10 as follows.
Method Party District
2 6 10
Partywise d'Hondt PN 1 2 4
MLP 4 3 1
Priority d'Hondt PN 1 3* 3
MLP 4 2 2
Sainte Lague Mod-Danish PN 2 2 3
(Partywise or Priority) MLP 3 3 2
* signifies an inversion.
It is interesting to note that all methods give an inversion in the
first district for this election. This is equivalent to a seat swap
to restore a districtwise result to nationwide proportionality.
ELECTION OF 1987. No Threshold.
District divisor:
Partywise: d'Hondt ; Modified Sainte Lague to Danish.
NOT = =
Priority : d'Hondt ; Modified Sainte Lague to Danish.
There are three groups of distributions all different from one another.
The difference between these methods lies in Districts 2, 7 and 10 as follows.
Method Party District
2 7 10
Partywise d'Hondt PN 1 2 4
MLP 4 3 1
Priority d'Hondt PN 1 3* 3
MLP 4 2 2
Sainte Lague Mod-Danish PN 2 2 3
(Partywise or Priority) MLP 3 3 2
* signifies an inversion.
All methods give an inversion in the first district for this election.
ELECTION OF 1992. No Threshold.
District divisor:
Partywise: d'Hondt ; Modified Sainte Lague to Danish.
NOT = NOT =
Priority : d'Hondt ; Modified Sainte Lague to Danish.
There are four groups of distributions all different from one another.
In this election the MLP cedes one seat to the AD in a district depending
on the method and divisor used. The d'Hondt partywise awards the seat in
the second district - this is the least satisfactory of all. The other
methods award this seat in the 9th, 10th or 11th districts, where the
AD is strongest with 2% of the relevant district's total vote. It is
clear that when the district percentages are very near each other as in
this case, it is mainly a matter of chance which of the three districts
will get the AD seat!
ELECTION OF 1992. 5% Threshold.
AD eliminated.
District divisor:
Partywise: d'Hondt ; Modified Sainte Lague to Danish.
= =
Priority : d'Hondt ; Modified Sainte Lague to Danish.
There are two groups of distributions which are different from each other.
D'Hondt for both methods gives MLP: PN = 4 : 1 in second district,
and MLP: PN = 1 : 4 in tenth district;
Modified Sainte Lague to Danish for both partywise and priority methods
give the corresponding ratios in these two districts as 3 : 2 and
2 : 3 respectively.
FICTITIOUS ELECTION. No Threshold.
District divisor:
Partywise: d'Hondt to Danish: all different.
NOT =
Priority : d'Hondt to Danish: all different.
All ten methods are different from one another.
The partywise methods all give two seats to party E in the 9th District,
where it is of only average strength.
The priority Sainte Lague method gives a better distribution for
parties D and E. Party C has one seat transferred from District 4 to
District 8, where it is of comparable strength. Distributions of
parties A and B are reasonable for both partywise and priority methods.
FICTITIOUS ELECTION. 12% Threshold.
Parties D, E, F eliminated.
District divisor:
Partywise: d'Hondt ; Modified St Lague to Danish.
NOT = = NOT=
Priority : d'Hondt ; Mod St Lague to Eq prop; Danish.
There are four groups of methods, all different from one another.
The partywise and priority methods with Sainte Lague divisors give
identical distributions in this case.