April 25, 2005
Dr. Felix P. Muga II
Mathematics Department
Ateneo de Manila University
Introduction
In the present Congress, 6 House Bills are proposed to amend RA 7941, otherwise known as the Party-List System Act. The amendments aim to correct its imperfections so that it will be true to its purpose of broadening the representation of the marginalized and under-represented sectors of our society.
RA 7941 declares that the party-list system is a mechanism of proportional representation in the election of members to the House of Representatives and reserves 20% of the total seats of the House to the party-list system.
This means that in the 2004 party-list election, 53 seats in the House of Representatives are reserved for the party-list. However, only 24 are proclaimed by the COMELEC. The entire party-list seats were not filled up also in the 1998 and the 2001 party-list elections.
The problem lies in the seat allocation method of RA 7941.
The Seat Allocation Method of RA 7941The seat allocation method of RA 7941 is a variant of the Largest Remainder Method (LR Method) used by some countries with a party-list system like Germany, Republic of Korea, Russia, Taiwan, Ukraine, Germany, Mexico, Czech Republic, Iceland, and Slovenia.
In the LR Method, the allocation of seats consists of two rounds. The first round computes the automatic number of seats that a party will win. It is based on the integral part of the quotient where the number of votes received by the party is divided by a minimum quota. The second round distributes the remaining number of seats not allocated by the first round using the remainders that are arranged from the highest to the lowest. The parties with the largest remainders win one seat each until the remaining seats are allocated.
The minimum quota can be expressed as an informal threshold in percent or as a winning minimum percentage. The natural value of the winning minimum percentage is given by
Natural Winning Minimum Percentage = 1/Total No. of Party-List Seats Available
The quotient is multiplied by 100%.
In most of the countries that have a party-list proportional system, a formal vote threshold is instituted. This formal threshold is the minimum share of the vote required by law to qualify for a seat. Note that the two thresholds are distinct. It is a possible that a party may pass the formal vote threshold but may not win a seat.
In the seat allocation method of RA 7941 the informal vote threshold is 2% but there is no formal vote threshold. Based on the 2% winning threshold, a party that garners 5% of the total votes wins 2 seats and a party that obtains 6% of the total votes is awarded 3 seats. But because of the 3-seat cap, a party that obtains 11% of the total votes only receives 3 seats.
The number of seats that can be allocated by the seat allocation method of RA 7941 is up to 50 since 1/2% = 50.
Hence, the 2% winning minimum percentage and the 3-seat cap distort the principle of proportional representation of the party-list system and cause the failure to broaden the representation of the marginalized and the under-represented sectors.
Hence, there is a need to amend the existing party-list law and find the best seat allocation method for the party-list system.
Our search for the best method must be guided by three parameters called the index of representation, index or proportionality, and the index of elasticity.
The Three Parameters for AnalysisWe shall analyze the 6 proposed amendments using 3 parameters that we call as the index of representation, index of proportionality, and the index of elasticity.
1) The Index of RepresentationThe index of representation is the amount in percent that is relative to the total number of seats allocated for the party-list system. Its value ranges from 0% to 100%. A 100% index of representation implies that the seat allocation method fills up the total number of party-list seats.
The index of representation of an allocation produced by a seat allocation method applied on a given party-list election is equal to the quotient when the total number of seats allocated by the method is divided by the total number of available seats for the party-list. The quotient is multiplied by 100%.
The seat allocation method of RA 7941 has one round of seat allocation. The number of seats obtains by a party is the integer portion of the quotient when the share of votes of the party is divided by 2%. The share of votes of the party is obtained by dividing its number of votes by the total votes of the party-list.
In the 2004 party-list election as shown in COMELEC Report no. 20, the seat allocation of RA 7941 produced 24 seats. This means that the index of representation of the seat distribution based on RA 7941 is 24/53 x 100% = 45.283%.
2) The Index of Proportionality
The party-list system is based on the principle of proportional representation. This is emphasized in section two (Declaration of Policy) of RA 7941.
The principle of proportional representation means that a party with 1% of the total votes receives 1% of the total seats; a party with 2% of the total seats gets 2% of the total seats; a party with 3% of the total seats obtains 3% of the total seats; and so on.
The degree in which proportionality is achieved is measured by the index of proportionality. Its value ranges from 0% to 100%. If the index of proportionality is 100% this means that full proportionality is reached.
Since the total number of party-list seats is less than 100, full proportionality may not be achievable. Hence, an index of proportionality that is at least 90% for an allocation produced by a seat allocation method is desirable.
To compute for the index of proportionality, we shall adopt the formula proposed by Richard Rose, Neil Munro and Tom Mackie in 1998. This formula is known as the Rose Index of Proportionality and is a standardized version of the Loosemore-Hanby index, see “Electoral Engineering Voting Rules and Political Behavior” by Professor Pippa Norris.
The (Rose) index of proportionality is computed by finding the absolute or positive difference between the shares of votes and the corresponding shares of seats, added up together multiplied by 0.5 and the product is subtracted from 1. The result is multiplied by 100%.
In the paper “On the Seat Allocation Method of the Philippine Party-List System”, this author shows that the index of representation and the index of proportionality are related by the formula
Index of Proportionality = (1 + Index of Representation)/2 × 100%
Hence, index of proportionality based on RA 7941 is (1 + 24/53)/2 × 100% = 72.642%.
3) The Index of Elasticity
A second-chance party is a small party-list organization or group whose share of votes is below that of the actual winning minimum percentage but passes the formal threshold and wins a seat in the second round. A seat allocation method is elastic if it is flexible enough to give smaller parties a chance to win a seat. This is consistent with the purpose of the 1987 Constitution to give a chance to the marginalized and the underprivileged sectors of the society a voice in congress.
The index of elasticity is equal to the number of second-chance parties divided by the number of first round winning parties. The quotient is multiplied by 100%.
A value that is equal to 0% means that the system is inelastic, but this will imply a very high index of proportionality when the index of representation is almost perfect.
A value that is equal to 100% or more means that the number of second-chance parties is at least equal to the number of winning parties in the first round of seat allocation. However, the index of proportionality may suffer even though the index of representation is almost perfect.
In the last party-election, the seat allocation method of RA 7941 produces no second-chance parties. Hence, the index of elasticity of the allocation produced by RA 7941 is 0%.
Analysis of the 6 House Bills
1) House Bill 341House Bill 341 authored by Rep. Aimee Marcos proposes to entitle each voter 13 votes for the party-list election, one vote for a candidate in the national or regional political party and one vote for a candidate for each of the 12 sectors.
However, House Bill 341 does not provide a mechanism to allocate the total seats available for the party-list system. It cannot use the seat allocation method of RA 7941 because of the differences in the ballot structure where RA 7941 has one second vote while the Marcos Proposal has 13 second votes for the House of Representatives.
Because of the absence of a clear mechanism for the allocation of seats, we cannot analyze the Marcos Proposal based on the three parameters that we presented.
2) House Bill 409
The seat allocation method of House Bill 409 introduced by Rep. Roseller L. Barinaga provides a 2% formal vote threshold and a 10-seat cap for a winning party-list party.
The seats are allocated mainly in two rounds. The number of seats that are distributed to a given party in the first round is equal to the integer portion of the quantity calculated in the following formula:
Total No. of Available Seats × Party’s Share of the Total Votes of all Qualified Voters
where the party’s percent share of the total votes is equal to the number of the party’s votes divided by the total number of votes to be tallied.
If there are remaining seats after the first round, these remaining seats are allocated in the next round similar to the second round of the Largest Remainder Method using the decimal fractions of the quotient obtained in the formula above.
If in case of equal decimal fractions, the assignment of last seat shall be decided by the COMELEC using drawing lots.
If there are winning parties affected by the 10-seat cap, then there are unfilled seats left and a third round will take place to distribute the remaining seats to the highest ranking parties based on the number of votes each party garners.
The Barinaga Proposal uses the natural value of the winning minimum percentage in the allocation of seats, since the total number of party-list seats available is the reciprocal of the natural value of the winning minimum percentage.
Our analysis shows that a seat allocation based on the House Bill 409 or the Barinaga Proposal as applied to the 2004 party-list election results in 16 winning parties that occupy 53 seats. This gives a perfect (100%) index of representation, a very high (96.327%) index of proportionality, but a 0% index of elasticity.
3) House Bill 2451
The seat allocation method of House Bill 2451 introduced by Reps. Edgar L. Valdez, Ernesto C. Pablo, and Sunny R.A. Madamba, provides a formal vote threshold that is equal to the natural value of the winning minimum percentage, a 6-seat cap and two rounds of seat allocation.
In the first round, all parties that qualify, that is, those parties whose shares of votes pass the formal vote threshold, are guaranteed one seat each. The remaining number of seats is distributed in the second round.
The number of seats that a party may win in the second round is equal to the integer portion of the product calculated as follows:
Remaining No. of Seats × Party’s Share of the Total Votes of all Qualified Parties
This round may not distribute all the seats remaining from the first round. Hence, it is possible that the Valdez et al Proposal may not fill up the entire number of seats available for the party-list.
The seat allocation based on the Valdez et al Proposal on the 2004 party-list election produces 44 seats. This means that the allocation has an 83.019% index of representation, an 87.997% index of proportionality and 0% index of elasticity.
Two seat allocation methods are equivalent if the number of seats of a party in the first method is equal to the number of seats in the second method.
If there are no winning parties affected by the cap or limit on the number of seats that a party may win, the Valdez et al Proposal and the Barinaga Proposal are equivalent with the following adjustments:
1. The quantity below shall be added to the product in the second round of the Valdez et al Proposal
No. of Guaranteed Seats × Party’s Share of the Total Votes of all Qualified Parties - 1
2. The two proposals shall have the same cap on the number of seats, and
3. The two proposals shall have the same formal vote threshold
4. A new round of seat allocation similar to the second round of the Barinaga Proposal will be added to the Valdez et al Proposal to allocate the remaining number of seats.
4) House Bill 2734House Bill No. 2734 proposed by Reps. Satur C. Ocampo, Teodoro A. Casiño, Joel G. Virador, Crispin B. Beltran, Rafael V. Mariano, and Liza L. Maza has two rounds in the allocation of party-list seats, a 6-seat cap, a 2% actual winning minimum percentage and no formal vote threshold.
In the first round of seat allocation, the number of seats that a party may win is equal to the integer portion of the quotient when the party’s share of votes is divided by 2%.
The remaining number of seats after the first round is allocated in the second round to those parties that received less than 6 seats including those parties that do not win a seat in the first round. The allocation in this round is similar to the second round of the Barinaga Proposal.
In case of equal fraction, the allocation of the last seat shall be decided by the COMELEC by drawing lots.
The allocation based on the Ocampo et al Proposal results in 37 winning parties occupying 53 seats. 16 of the parties are first round winners while 21 are second-chance parties. This results in a perfect (100%) index of representation, 86.203% index of proportionality and a very high 131.250% index of elasticity.
If there are no winning parties affected by the cap or limit on the number of seats that a party may win, the Ocampo et al Proposal and the Barinaga Proposal are equivalent with the following adjustments:
1. the Ocampo et al Proposal shall adopt the natural value of the winning minimum percentage,
2. the two proposals shall have equal formal vote threshold, and
3. the two proposals shall have the same cap on the number of seats.
5) House Bill 3302
House Bill Number 3302 introduced by Reps. Loretta Ann P. Rosales, Mario Joyo Aguja and Anna Theresia Hontiveros-Baraquel has three rounds of seat allocation, adopts 1.8% both as a formal vote threshold and the actual winning minimum percentage and a 6-seat cap for the number of seats that a party may win. The parties who are qualified to win are called the winning minimum percenters. These parties receive one guaranteed seat each in the first round.
The remaining number of seats from the first round is allocated to the qualified parties in the second round. Each party is awarded a number of seats equal to the integer portion of the quotient when the party’s share of all the votes of the winning minimum percenters is divided by 1.8% less 1.
If there are remaining seats after the second round, these are allocated in the third round similar to the second round of the Barinaga Proposal.
In case of equal fractions, the assignment of the last seat shall be decided by the COMELEC based on the comparison of actual votes.
If the Rosales et al Proposal is applied to the 2004 party-list election, the index of representation is 98.113%, since a total of 52 seats out of 53. It has is a high index of proportionality of 93.987%. There are 19 winning parties and there are no second-chance parties. Hence, the index of elasticity is 0%.
If there are no winning parties affected by the cap or limit on the number of seats that a party may win, the Rosales et al Proposal and the Barinaga Proposal are equivalent with the following adjustments:
1. The two proposals shall have equal formal vote thresholds, and
2. The Rosales et al Proposal shall use the natural value for the actual winning minimum percentage.
6) House Bill 3474
House Bill No. 3474 introduced by Rep. Guillermo P. Cua has three rounds of seat allocation, adopts a 3-seat cap and uses 1.8% as a formal vote threshold.
In the first round, all parties that qualify to win a seat are awarded one guaranteed each.
The remaining number of seats is distributed in the second round where each party receives a number of seats equal to the integer portion of the product when the remaining number of seats is multiplied to the party’s share of the total votes of all the qualified parties.
If there are remaining seats after the second round, a third round similar to the second round of the Barinaga Proposal occurs.
In case of equal fractions, the assignment of the last seat shall be decided by COMELEC by comparison of actual votes where the last remaining seat is awarded to the higher votes.
The allocation of Cua Proposal produces an 86.679% index of representation, an 86.232% index of proportionality of 93.987%. Since there are no second-chance parties, the index of elasticity is 0%.
If there are no winning parties affected by the cap or limit on the number of seats that a party may win, the Cua Proposal and the Barinaga Proposal are equivalent if the following adjustments are made:
1. The quantity below shall be added to the product in the second round of the Valdez et al
No. of Guaranteed Seats × Party’s Share of the Total Votes of all Qualified Parties -1
2. The two proposals shall have the same cap on the number of seats, and
3. The two proposals shall have equal formal vote thresholds.
Recommendation
We find that a method which uses 1) an extra round to allocate the remaining party-list seats, 2) a natural value for the winning minimum percentage, and 3) a higher cap in the number of seats results in a very high if not a perfect index of representation and a very high index of proportionality. This is shown in the Barinaga and the Rosales et al Proposals.
We also find that a method which uses a zero value of the formal vote threshold and an extra round result in a very high index of elasticity, but reduces the index of proportionality. See the Ocampo et al Proposal.
As the value of the formal vote threshold is made smaller, the shares of the total seats of the highest ranked parties decrease. This means that a small value of the formal vote threshold serves as a natural cap for the number of seats that a party may win.
For example, when the formal vote threshold of the Barinaga Proposal is at 2%, the number of seats received by Bayan Muna is 8 out of 53 seats. But when it is lowered to 1%, Bayan Muna receives 6 seats only and there are 11 second-chance parties.
Hence, a smaller value of the formal vote threshold means an improve value in the index of elasticity and a substitute for the cap on the number of party-list seats.
A value that is greater than ½ of the natural value of the winning minimum percentage or ½ of the reciprocal the total number of available seats for the party-list produces a number of second-chance parties and a high index of proportionality. This claim is proven in our paper entitled “On the Seat Allocation Method of the Party-List System in the Philippines” which can be accessed at http://www.math.admu.edu.ph~fpmuga.
Therefore, we recommend the following:
1. the adoption of a formal vote threshold that is equal to
½ × (1/Total Number of Seats Available for the Party-List ) × 100%
The percentage value is round up to two decimal places, that is, the digits to the right of the decimal point starting from the third are dropped and 1 is added to the second decimal place.
2. the use of two rounds of seat allocation similar to the Barinaga Proposal.
If we apply this recommendation to the 2004 party-list election using COMELEC Report No. 20, the formal vote threshold is equal to 0.95%, since 0.5 × 1/53 =0.94340%. There are 32 parties that qualify to win a seat where 21 parties are first round winners and 11 are second-chance parties. All the 53 seats are filled up. The seat allocation based on this recommendation has a perfect (100%) index of representation, a 92.667% index of proportionality and a 52.381% index of elasticity. See Table 1.
