On June 24, the Philippine Daily Inquirer published an article, “Party-List System: Mathematical Absurdity” (page 14) where the author, lawyer Oscar Franklin B. Tan, proposed a seat allocation formula to correct the mathematical absurdity of the party-list system. The proposed formula yields 55 seats which is the total number of party-list seats available in the 2007 party-list election as mandated by the 1987 Constitution.
Is Tan’s formula a solution to the seat allocation problem that has plagued our party-list system since 1998?
I believe that the proposed formula is an unacceptable solution to the seat allocation problem of the party-list system in the Philippines. The proposed formula violates the principle of proportional representation as provided for by the Party-List Act (R.A. 7941).
Instead, I propose another seat allocation formula that, I believe, affirms the policy of the Party-List Act and complies with the mandate of the 1987 Constitution that the party-list shall constitute 20% of the total members in the House of Representatives.
Vote threshold clarified
Almost all of the party-list systems in the world impose a formal vote threshold to determine which parties are entitled to a legislative seat. For example, the party-list systems in Germany, Republic of Korea, Russia, Taiwan, Hungary, New Zealand, Thailand and Ukraine have a formal vote threshold of 5%. In Mexico and Denmark, the formal vote threshold is 2%. If a party does not reach the formal vote threshold, then it has no right to receive a seat.
In her book on Electoral Engineering: Voting Rules and Political Behavior (ISBN: 0521536715, Cambridge University Press, 2004), Pippa Norris says
“The formal vote threshold is the minimum share of the vote (in the district or nation) required by law to qualify for a seat, and this is distinct from the informal threshold or the actual minimum share of the vote required to win a seat.”
In Germany, the law mandates the Bundestag parliament to have at least 598 members. Its informal vote threshold is 1/598 or 0.167224%. Thus, a qualified party in Germany that obtains at least 5% of the total party-list votes is assured of at least 29 party-list seats, as measured by 5% x 598 = 29.9, based on the principle of proportional representation. In fact, the Alliance90/Greens Party with 8.119883% of the total party-list votes was awarded 50 party-list seats in 2005.
In the Philippines, is the 2-percent threshold in the Party-List Act a formal or informal threshold? Or both? Section 11 of the Law states:
“xxx
The parties, organizations, and coalitions receiving at least two percent (2%) of the total votes cast for the party-list system shall be entitled to one seat each:
provided, that those garnering more than two percent (2%) of the votes shall be entitled to additional seats in proportion to their total number of votes:
xxx”
In his proposed formula, Attorney Tan believes that the 2% is an informal vote threshold. Hence, he is right in rejecting its implementation because the real informal threshold in the 2007 election is 1/55 or 1.818182%.
What if the Supreme Court interprets the 2% to be a formal threshold? Then the proposed formula shall be applied to the top 15 party-list groups that obtained at least 2% based on the Party-List Canvass Report No. 25 of the Comelec. Even if all the 15 parties shall be awarded 3 seats each, the total number of party-list seats (55 in 2007) cannot be filled since 15x 3 = 45. This will be contrary to the claim of the proponent that the proposed formula will be able to allocate the 20% mandate of the 1987 Constitution. It is in this vein that the proponent calls for the rejection of the 3-seat cap.
Features of the proposed formula
Tan’s proposed formula will generally work if there is no formal vote threshold. This is the first feature of the proposed formula. There are party-list systems in the world that have zero formal vote thresholds such as in Belgium, Peru and Switzerland.
The proponent may argue that the 2-percent formal threshold should be junked since it is restrictive and will allow a few party-list groups to win a seat. Thus, the 2-percent formal vote threshold defeats the purpose of allowing the marginalized and the underrepresented sectors to be represented in Congress.
Another argument is that the 2-percent formal threshold will disenfranchise the voters of An Waray (1.97%), FPJPM (1.89%) and AMIN (1.84%) since one seat in the 2007 party-list election is equivalent to 1/55 or 1.818182%.
The second feature of the proposed formula is the nth-party rule with 3-seat cap. In the 2007 election, this is called as the 32nd-party rule since it uses the 1.03% of the 32nd ranked party-list AGHAM as the basis of the proportionality. This is in contrast to the Panganiban Formula which uses the first-party rule where the basis of the proportionality is the party with the highest number of votes.
Problem with 2-digit decimal expansion
The proponent uses two-digit expansion when a party’s number of votes is divided by the chosen party’s number of votes. Since two seats are not yet filled when the formula was applied on the latest Comelec data (Canvass Report No. 25), the two unfilled seats were assigned to AKBAYAN (0.97) and An Waray (0.91).
But if eight-decimal digit expansion is used, the top 2 parties with highest ranking decimal components are Gabriela with 0.99632511 since (4.129778%)/(1.033394%) = 3.99632511 and Akbayan with 0.96890099. Since Gabriela has 3 seats already, then it cannot be awarded one additional seat.
The proponent is silent on how to award the remaining seat if this type of problem arises. Will it be given to An Waray with 0.91003223 or to the third ranking party based on decimal component Yacap with 0.92291198? In fact An Waray is 6th in the rank. The 4th and 5th ranking parties are TUCP with 0.92284144 and ANAK with 0.91557631.
Let us assume that this problem is settled and eventually 55 seats are awarded to the parties.
Proportional representation
The proponent agrees that there are two conditions to be met for a seat allocation method to be acceptable:
1. 20% of the total members of the House of Representatives must come from the party-list; and
2. The seat allocation must adhere to the principle of proportional representation.
If there is no formal vote threshold, generally the first parameter will be satisfied.
The problem lies in the second parameter. The principle of proportional representation asserts that
“The number of seats awarded to a qualified party shall be proportional to the number of votes obtained by the qualified party…”
Euclid (c. 325 BC – 265 BC) in Book V of Elements defines the following:
“xxx
3. A ratio is a sort of relation in respect of size between two magnitudes of the same kind.
xxx
5. Let magnitudes which have the same ratio be called proportional.
xxxx”
The two magnitudes that have the same ratio are:
• Number of seats awarded to a qualified party with respect to the total number of seats available for the party-list system; and
• Number of votes obtained by the qualified party with respect to the total number of votes obtained by all the parties that are qualified to receive a seat.
This means that the percentage of seats awarded to a qualified party based on the total number of party-list seats available (TPLS) is equal to the percentage of votes it garnered based on the total number of votes of all parties who are qualified to receive a seat (TQPV), or
This equation becomes
This is the ideal number of seats that a qualified party is entitled to receive based on the principle of proportional representation. The actual number of seats that a qualified party receives is the number of seats allocated by the existing seat allocation formula. Hence,
If there is no formal vote threshold then TQPV is equal to TPLV which denotes the total number of votes of the party-list.
In the latest Comelec data, TPLV = 13,719,165 and in the 2007 election, TPLS = 55.
The number of votes of Buhay in the report is 1,111,035. Hence, the ideal number of seats of Buhay based on the principle of proportional representation is 4.45412859.
The difference between the ideal number and the actual number of seats of a qualified party is called the seat allocation error of the existing allocation formula on the qualified party. It is determined by
seat allocation error = ideal no. of seats - actual no. of seats
If actual number differs from the ideal number by less than one, then the allocation formula affirms the principle of proportional representation. Otherwise, if the difference is one or more then it violates the said principle.
The integer part of the absolute value of the seat allocation error is called the degree of negation of the formula.
For example, the ideal number of seats of Buhay is 4.45412859 but it is awarded 3 seats only by the 32nd-party rule. Then the seat allocation error is 1.45412859. Thus, the degree of negation of 32nd-party rule on Buhay is 1. This is equivalent to (1/55) x 13,719,165 or about 249,439 voters of Buhay are denied of representation in Congress because of the violation of the 32nd-party rule on the principle of proportional representation.
The seat allocation error of the 32nd-party rule differs by more than one seat on Apec, A Teacher and Akbayan. See Table below.
The actual number of seats allocated by the 32nd –party rule on Apec, A Teacher and Akbayan is more than the ideal number of seats based on the principle of proportional representation. The difference is at least one in each party. This means that the voters of other parties are denied of representation in Congress since the seats that are due to the parties they voted for are transferred to Apec, A Teacher and Akbayan by the 32nd-party rule. The number of voters that are disenfranchised in this way is about (3/55) x 13,719,165 or about 748,318.
Therefore the 32nd-party rule violates the principle of proportional representation by at least 4 seats.
The 32nd-party rule contradicts this principle because of the following factors:
1. Imposition of the 3-seat cap; and
2. Using the nth-party as the basis of proportionality.
The imposition of a cap clearly violates the principle of proportional representation when the ideal number of seats is one more than the cap.
The votes of the nth-party (or the first party of the Panganiban Formula) must not be used as the basis of proportionality. Proportional representation must be based on the total number of votes of all the parties that are qualified to receive a seat and on the total number of seats available for the party-list because the principle dictates that the
Our proposed formula
Our proposed formula has two rounds of seat allocation to the qualified parties:
1. In the first round, the number of seats that is allocated to the qualified parties is equal to the whole part of the ideal number of seats based on the principle of proportional representation;
2. If the total number of seats does not reach the total number of seats available for the party-list, then a second round of allocation is conducted, thus
a. The qualified parties are ranked from the highest to the lowest based on the decimal fractions of the ideal number of seats.
b. One seat of the remaining number of seats is given each to the highest ranking qualified parties based on the decimal fractions until all the seats are filled up.
Assuming that there is no formal vote threshold as in the case of the 32nd-party rule, the allocation of seats should be:
Our proposed formula satisfies the first condition of an acceptable seat allocation method since it earmarks the total number of seats available for the party-list.
Note that the difference between the ideal number of seats based on the principle of proportional representation and the actual number of seats allocated by the proposed formula is less than one on each qualified party. This means that the proposed formula affirms the principle of proportional representation.
If the 3-seat cap of the Party-List Act will be imposed on our proposed formula after we have allocated the seats, then Buhay and Bayan Muna will receive 3 seats each instead of 5 and 4, respectively. The degree of negation of the 3-seat cap will be 3 seats. This is equivalent to (3/55) x 13,719,165 or about 748,318 voters that are disenfranchised because of the violation of the 3-seat cap on the principle of proportional representation.
Since the total number of seats is reduced from 55 to 52 after the 3-seat cap is imposed, the 20-percent mandate of the Constitution is violated. In this case, the 3-seat cap does not only violate the policy of the Party-List Act but is also unconstitutional. Therefore, the 3-seat cap must be rejected.
Our proposed formula at 2% formal vote threshold
Suppose that the Supreme Court interprets the 2-percent threshold as formal. Then our proposed formula with 2% formal vote threshold will still satisfy the 20%-mandate of the 1987 Constitution and the principle of proportional representation. The allocation reaches 55 seats and the difference between the ideal number and actual number of seats is less than one seat. See Table 4.
Our proposed method is not the only formula with a formal vote threshold of 2% that satisfy the 20%-mandate of the 1987 Constitution and the principle of proportional representation. We claim, however, that our formula gives the “best index of proportionality” since the 7 qualified parties that were chosen in the second round to be given one additional seat have the highest decimal fractions. In this way, the seat allocation error on each qualified party is minimized, i.e. the error approaches zero, while filling the entire number of party-list seats.
The index can be computed using the formula:
where the computed value is expressed in percentage and it ranges from 0% to 100%.
The index is 100% if full proportionality is achieved. The index is 0% if a party with no votes is awarded all the available seats. The index of proportionality of our proposed formula with 2% formal vote threshold is 96.132874%. Further discussion on this topic can be obtained in my papers “On the Seat Allocation Method of the Party-List System in the Philippines, Loyola Schools Review, Vol. 4, 2005” and “Amending Republic Act 7941, Otherwise Known as the Pary-List System Act”, Matimyas Matematika, Vol 28, Nos. 1-3, 2005.
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Felix P. Muga II is an associate professor at the Mathematics Department of Ateneo de Manila University and is a Fellow of the Center for People Empowerment in Governance (CenPEG). He obtained his B.S. Mathematics (Magna Cum Laude) at Silliman University and his Ph.D. in mathematics at the University of the Philippines in 1995 and was awarded one of the Ten Outstanding Young Scientists by the National Academy of Science and Technology (NAST) in 1998. He has a written a number of articles on the proportional party-list system since 2005. These articles can be downloaded at http://www..math.admu.edu.ph/~fpmuga.
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