On the Philippine Party-List System and the 4 Inviolable Parameters

by Felix P. Muga II 
July 17, 2007

In his article, “Law, Mathematics and the Party-List System” (PDI, July 15, 2007, page 15), former Supreme Court (SC) Chief Justice Artemio Panganiban enumerated a system of 4 inviolable parameters that determines the seat allocation method of the Philippine party-list system.

1. the twenty percent allocation (0.2TOTAL) —the combined number of all party-list congressmen shall not exceed twenty percent of the total membership of the House of Representatives, including those elected under the party list;

2. the two percent threshold (0.02THRESH) —only those parties garnering a minimum of two percent of the total valid votes cast for the party-list system are ‘qualified’ to have a seat in the House of Representatives (sec. 11 of the Party-List Law, RA 7941);

3. the three-seat limit (3SEATCAP) —each qualified party, regardless of the number of votes it obtained, is entitled to a maximum of three seats, that is, one ‘qualifying’ and two additional seats (sec. 11 of RA 7941); and

4. proportional representation (PR) —the additional seats which a party is entitled to shall be computed ‘in proportion to their total number of votes.’ (secs. 2 and 11 of RA 7941).

Chief Justice Panganiban failed to mention, however, whether the four inviolable parameters are consistent with each other.

A system is consistent if and only if there is at least one solution. On the other hand, a system is inconsistent if and only if it has no solution.

I believe that the system of four inviolable parameters mentioned by Chief Justice Panganiban is inconsistent. Hence, no formula can be designed to give a correct solution.

0.2TOTAL Parameter Rephrased

The 1987 Constitution mandates that “the party-list representatives shall constitute twenty per centum of the total number of representatives including those under the party list ....”

The 0.2TOTAL parameter does not faithfully follow this formulation. I believe the said parameter was rephrased so that the 0.2TOTAL and 3SEATCAP parameters will be consistent.


Inconsistent PR and 3SEATCAP Parameters

The PR parameter is based on the principle of proportional representation which is the public policy of the Party-List Law or RA 7941. This principle asserts that the qualified party’s share of the total seats is equal to its share of the total votes of all qualified parties.

The qualified party’s share of the total seats is computed by dividing the number of seats it received by the total number of seats.

The qualified party’s share of the total votes is determined by dividing the number of votes it garnered by the total number of votes of all qualified parties.

Hence, by the PR parameter, the (ideal) number of seats that a qualified party shall be entitled to receive is equal to its share of the total number of votes of all qualified parties multiplied by the total number of party-list seats.

For example, in the 2007 party-election, the total number of party-list seats is 55. Thus, if a qualified parties has 10 percent of the votes of all qualified parties, then by the PR parameter, its (ideal) number of seats is 10% x 55 = 5.5. This means that the said party is entitled to at least 5 seats but not more than 6 seats.

If the 3SEATCAP parameter is imposed, then the said party cannot have more than 3 seats.

Since the two parameters are inviolable and both parameters produce inconsistent solutions where the 3SEATCAP parameter demands a number of seats that cannot exceed 3 while the PR parameter demands a number of seats that is either 5 or 6, it follows that the 3-SEATCAP and the PR parameters are inconsistent.

As a result, a formula that adheres with the 3SEATCAP is bound to violate the PR parameter.
The Panganiban Formula Violates the PR Parameter

If the Panganiban Formula is applied to the latest Party-List Tally (Canvass Report No. 27), a “solution” is obtained with 21 seats where Buhay has 3 seats. The solution is consistent under the 0.2TOTAL, .02THRESH and the 3-SEATCAP parameters.

By the PR parameter, Buhay with 14.2643% of the total votes of all qualified parties will get about 14.2643% × 55 = 7.84536495 seats.

The Panganiban Formula which assigns 3 seats to Buhay violates the PR parameter on Buhay by at least 4 seats.

The formula also violates the PR parameter on Bayan Muna by at least 4 seats also, on Cibac by at least 3 seats, on Gabriela, APEC, A Teacher and Akbayan by at least 2 seats each, on Alagad, Butil, Batas, Anakpawis, COOP-NATCCO, Abono, Agap, ARC and An Waray by at least 1 seat each.

Thus, the total number of seats violated by the Panganiban Formula over all the qualified parties is at least 28 seats. This is equivalent to at least (28/55) × 8,070,680 = 4,108,701 disenfranchised voters.

Since the system of parameters is inconsistent, no seat allocation formula can be designed to produce a correct solution. Thus, a formula that adheres to the 3SEATCAP parameter will disenfranchise a number of party-list voters if the PR parameter produces more than 3 seats for a qualified party.

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Felix P. Muga II teaches mathematics at the Ateneo de Manila University and is a Fellow of the Center for People Empowerment in Governance (CenPEG). His homepage is at http://www.math.admu.edu.ph/~fpmuga.