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How the seat allocation formulas make all the difference

How the seat allocation formulas make all the difference

"When it comes to decision-making,

it is the majority which counts, but when it comes to representation, it

is the proportion which matters." - Victor Considerant, French Socialist

politician, 1808-1893

After the recent elections for the National Assembly, quite a number of

articles on the controversial formulas of the allocation of seats have appeared

in the media.

However, there still seems to exist quite a lot of confusion and misunderstanding

about this issue among many people, even "experts", and a large

number of diplomats. This article tries to bring some light to a subject

which has all the potential to create a serious constitutional crisis if

it is not properly addressed.

The preamble and Article 51 of the Constitution as of Sept 21, 1993, prescribe

"a multi-party liberal democratic regime" and "a policy of

liberal democracy and pluralism" for Cambodia, thus creating the foundation

for an electoral system of proportional representation in Cambodia.

Proportional representation implies that the number of seats allocated to

a party should be proportional to the number of votes that party has received.

According to Article 76 of the Constitution the deputies of the National

Assembly "shall be elected by a free, universal, equal, direct and

secret ballot". With regard to the seat allocation formula the constitutional

principle of the equality of votes is of utmost importance because it demands,

amongst others, that each vote should have the same value as expressed in

the number of seats.

Or, to put it another way: each seat in parliament should represent about

the same number of votes, regardless to what party it belongs.

The Law on the Election of the National Assembly as of Dec 19, 1997, prescribes

that "the electoral system shall be proportionalrepresentation, with

provincial/municipal constituencies" (Article 5). Apart from that,

the electoral law stipulates that "remaining seat(s) for a constituency

shall be allocated in accordance with the greatest (highest) average formula"

(Article 118).

Unfortunately, the provision of Article 118 is not clear at all, because

there is no internationally recognized standard view on what constitutes

the highest average formula.

One group of experts (Cotteret/Emeri; Martin; et al) pretends that the "highest

average formula" or "method of the greatest divisors" comprises

only the so-called "Jefferson method" which, in turn, gives the

same result as the d'Hondt divisor system.

Another group of experts (IDEA; Farrell; O'Neal; et al) subsumes a number

of divisor systems to the notion of the "highest average system",

ie: the Jefferson formula which is, in its results, equivalent to the d'Hondt

system of the greatest divisors, the Sainte-Lague formula (or Webster formula

of major fractions), and, three modified Sainte Lague versions.

Overall, the Jefferson or d'Hondt formula is judged to be the least proportional,

while use of the pure Sainte-Lague highest average formula and the largest

remainder system using the Hare quota (equivalent to the UNTAC system) produce

the greatest proportionality (Lijphart; Farrell; O'Neal; Gauglhofer; et


Few authors (eg M Gauglhofer) and experts have taken notice of the so- called

"quota method" of two North American scholars ML Balinski and

HP Young which they have proposed since 1975 in a considerable number of

outstanding academic papers.

The reason for that might well be that the "quota method" is rather

youngin comparison to the other methods of seat allocation, most of which

date back to end of the 19th or beginning of the 20th century.

The Balinski/Young method clearly belongs to the category of the highest

average system because it establishes, like the Jefferson method, the highest

average according to the formula Vv/(Ns+1) for the allocation of remaining

seats. In contrast to the Jefferson method, Balinski/Young then allocate

the remaining seats in one step whereas the Jefferson method allocates the

remaining seats in several steps.

The reason why Balinski/Young proposed their "quota method" is

that no party should get more seats than its upper quota. Table 2 shows that in Kampong Chhnang

the CPP, with a quota of 1.87 seats, would get 3 seats according to the

Jefferson method. However, according to Balinski/Young, a party with a quota

of 1.87 seats should get a maximum of 1 + (0.87=)1 = 2 seats because 0.87

seat can only be rounded up to 1 seat and definitively not to 2 additional


In Kampong Cham where Funcinpec won most of the votes that party, with a

quota of 6.92 seats, would be allocated 8 seats according to the Jefferson

method whereas under Balinski/Young Funcinpec would only get 7 seats in

Kampong Cham in due respect for the upper quota 6 + 1 = 7.

Therefore, according to Balinski/Young and other authors, the Jefferson

method of the highest average does not satisfy quota and tends to be disproportional

in favor of the winning party. The figures provided in Table

1 prove this assessment to be correct.

From the above-mentioned we can conclude that the concept of the "greatest

(highest) average formula" of seat allocation contains at least two

methods: the Jefferson method which is equivalent to the d'Hondt system,

and the Balinski/Young method.

Therefore, the provision of Article 118 of the Law on the Election of the

National Assembly is unfortunately not conclusive as to what highest average

method for the allocation of remaining seats should be used. Consequently,

according to Article 16 of the electoral law, the National Election Committee

(NEC) had the responsibility to decide on the seat allocation formula and

to include it in the Regulations and Procedures for the elections.

The Khmer-language version of the Regulations as of May 6 and May 25, 1998,

both of which were not marked as "Draft" and which had been distributed

widely to political parties and interested organizations included in Annex

V a formula for the allocation of seats which was identical to the Balinski/Young

formula. This was the 1st NEC formula for seat allocation.

Then, at the end of May, that formula was apparently changed into the Jefferson

(equivalent to d'Hondt) method, and a May 29 version of the Regulations

including a new Annex V was produced and was apparently distributed to the

political parties in the beginning of June.

However, the minutes of a NEC meeting on May 29 do not include any reference

to the changed seat allocation formula or that this change had been discussed

and decided by the members of the NEC. Too, the NEC did not issue a press

release concerning the change in the formula of the seat allocation.

Most of the political parties and interested organizations became aware

of the change in the seat allocation formula only after the election when

they used the 1st NEC formula (Balinski/Young) to calculate the allocation

of seats in the new National Assembly and compared it with the projections

of the CPP, which seemed to be the only political party to be informed about

the change in formula in time.

It has been said by a number of critics of the non-CPP parties that these

parties did not do their homework properly by not carefully studying the

Regulations as of May 29. Certainly, they share some responsibility for

the present impasse. However, it should not be forgotten that many of themwere

struggling to rebuild party structures which had been destroyed during the

coup in July 1997.

In addition to that, they had received earlier versions of the Regulations

which were not marked as "Draft" and it was indeed not easy work

to study carefully each new version of a document which comprised nearly

200 pages and compare it with earlier versions.

Finally, the NEC, when it released the May 29 version of the Regulations,

should have issued at least a letter to the parties clearly pointing out

the changes in the latest version.

The formula for the allocation of seats is one of the cornerstones of any

electoral system of proportional representation. It can have vast political

repercussions. It can decide about the absolute majority in parliament,

and in the case of the elections in Cambodia in 1998 it does.

Table 1 shows that

if the 1st NEC formula of Balinski/Young is applied, Funcinpec together

with the Sam Rainsy Party would get 62 seats, whereas CPP would be allocated

59 seats (1 seat would go to the Khmer Democratic Party). However, if the

2nd NEC formula of Jefferson is used, CPP would get 64 seats and Funcinpec

together with the Sam Rainsy Party would be allocated 58 seats.

In view of these consequences of the change of formula from Balinski/Young

to Jefferson, the statement of the senior election technical adviser to

the NEC, Mr Theo Noel, that "the revision of the formula was purely

technical" is completely incomprehensible.

A change in the seat allocation formula has to be made public. It simply

cannot be done by a dead-of-night action as it appears to have been done

at the moment. The way the NEC handled this change seems to be unprofessional,

non-transparent, politically irresponsible and, perhaps, even illegal.

Table 1 shows that

there is not only a considerable difference in seat allocation between the

1st and the 2nd NEC formula but that there is also a significant difference

in proportional representation of the votes as expressed in the number of

seats for each political party.

The 1st NEC formula of Balinski/Young produces fairly proportional results:

The number of votes represented by each seat varies between 34,420 for the

CPP seats and 38,870 for the seats of the Sam Rainsy Party, which results

in a difference of 4,450 votes per seat. By far the best proportional result

is produced by applying the Sainte-LaguÎ formula with a difference

of only 1,728 votes per seat.

However, the 2nd NEC formula of Jefferson/d'Hondt produces by far the most

disproportional result and the biggest inequality of votes in favor of the

winning party (CPP) at the expense of the smallest party (SRP).

The number of votes represented by each seat varies between 31,731 for the

CPP's seats and 46,644 for the seats of the Sam Rainsy Party, which results

in a difference of 14,913 votes per seat.

This huge disproportion seems to be in contradiction to the principles of

the equality of votes and of proportional representation as stipulated in

Article 76 of the Constitution and in Article 5 of the Law on the Election

of the National Assembly, respectively. Therefore, it seems that the 2nd

NEC formula is not only in contradiction of the electoral law but also unconstitutional.

Nicaraguan dictator Anastasio Somoza once told the opposition: "You

won the elections. But I won the count."

Unless the Constitutional Council is able and willing to make a fair judgement

on the matter of the seat allocation formulas, that statement would need

to be re-phrased to "You won the elections, but I won by formula"

in order to match a situation which should be prevented from happening.

Peter Schier is the permanent representative of the Konrad-Adenauer-

Foundation (KAF) in Cambodia.


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