(by Dr. Felix P. Muga II, Mathematics Department, Ateneo de Manila University) 

The Supreme Court in its latest resolution promulgated on April 13, 2007 in Citizens’Battle Against Corruption v. COMELEC (G.R. No. 172103) which the Philippine DailyInquirer reported on Monday, April 23, 2007 denied the petitioner CIBAC for a secondseat in the House of Representatives following the 2004 party- list election. The highcourt emphasized that the seat allocation formula to compute the number of additionalparty-list seat must be in line with its decision on 6 October 2000 case of VeteransFederation Party, et al v. COMELEC ( G.R. No. 136781). 

The Supreme Court formula which we call as the Panganiban-Veterans Formulacomputes allocates one seat to the parties with at least 2% of the total party-list votes.Then the additional number of seats of a concerned is computed by dividing the numberof votes of the concerned party by the number of votes of the first party. The quotient ismultiplied by the additional number of seats of the first party. The integer part or thewhole part of this computation is the additional number of seats of the concerned party.The Supreme Court refers to the “first party” as the party-list group that obtained thehighest votes in the party- list election. The first party has one additional seat if it garnered at least 4% but less than 6% of the total number of party-list votes, or it has two additional seats if it obtained at least 6% of the total number of party- list votes. The said formula imposes a 3-seat cap consistent with the provision of the Party-List System Act (RA 7941).  

In the 2004 party-list election, BAYAN MUNA is the first party with 1,203,305 voteswhich is 9.458493% of the total party-list votes of 12,721,952. By the Panganiban-Veterans Formula BAYAN MUNA will be awarded two additional seats since it obtainedmore than 6% of the total number of party- list votes and 15 other party- list groups with at least 2% of the total number of party- list votes were entitled to 1 seat each.APEC with 934,995 votes had 3 seats in the 13th Congress due to the COMELECsimplified formula. It will be awarded a second seat by the Panganiban-Veterans Formula since (934,995 x 2)/ 1,203,305 = 1.55404 with integer part equals 1. Thus, APEC will have 2 seats in the 13th Congress instead of 3. 

AKBAYAN with 852,473 votes had 3 seats also in the 13th Congress. Using thePanganiban-Veterans Formula, AKBAYAN will be given a second seat since (852,473 x2)/ 1,203,305 = 1.41689 with integer part equals 1. Thus, it will have 2 seats in the 13thCongress instead of 3 also. 

CIBAC, the petitioner of the case, with 495,193 had 1 seat in the 13th Congress. Nosecond seat will be awarded by the Panganiban-Veterans Formula since (495,193 x 2)/1,203,305 = 0.82305 with integer part equals 0. 

The total number of seats that will be allocated by the Panganiban-Veterans Formula onthe 2004 party-list election is 21 (See Table 1). Note that the simplified COMELECFormula allocated more seats with 24.   

The 1987 Philippine Constitution mandates that 20% of the total number of members ofthe House of Representatives must come from the party-list. This means that out 5representatives, 1 comes from the party- list and 4 from the congressional districts. Hence, the total number of party- list seats is 1/4 of the total number of congressiona l districts. 

Since there are 212 congressional districts in the 2004 synchronized national and localelections, the total number of party- list seats is 212/4 = 53.With 21 seats by the Panganiban-Veterans Formula instead of 53 seats, 32 seats are not filled up. This means tha t approximately (32/53) x (12,721,952) = 7,681,179 party- list voters are not represented in the House of Representatives. 

What is the reason of the inability of the Panganiban-Veterans Formula todistribute the entire number of available of seats? Does the said formula contradict the principle of proportional representation? 

The principle of proportional representation in the party- list system asserts that the share of seats of a party- list group must be equal to the share of votes of the party-list group.

This means that the number of seats of a party divided by the total number of part- listseats is equal to the percent share of votes of the concerned party. Hence, by the principle of proportional representation, the (ideal) number of seats of a party is determined by the formula no. of seats of a party = (% share of votes of the party) x (total no. of party-list seats) 

We define call the difference of the ideal number of seats determined by the principle ofproportional representation and the actual number of seats allocated using a particularseat allocation formula as the seat allocation error of the formula. 

The seat allocation error of the formula can be computed as follows: error = (% share of votes x total no. of party-list seats) – (actual no. of seats allocated) For example, in the 2004 party-list election, COCOFED obtained 1.288733% of the total party- list votes and failed to get a seat by the Panganiban-Veterans Formula. Hence, the seat allocation error of this Formula is equal to 1.288733% x 53 – 0 = 0.68302852. 

CIBAC had 3.892429% of the total party-list votes and awarded 1 seat by the Panganiban-Veterans Formula (see Table 1). Hence, the seat allocation error of thisformula on CIBAC is 3.892429% x 53 – 1 = 1.06298758. 

Using this method the errors of the Panganiban-Veterans Formula on BAYAN MUNA,APEC, AKBAYAN, ANAKPAWIS, ABA-AKO and ANAD are given in Table 2. 

If we sum up all the computed seat allocation error of all the parties in the 2004 party- listelection, it is equal to 32. This explains why the actual number of seats allocated by theCOMELEC Formula in the 2004 party-list election is 53 – 32 = 21. 

The seat allocation of the Panganiban-Veterans Formula on COCOFED is not significantsince the error is less than 1.   

The absolute error is defined as the value of the error considered as a positive number. The seat allocation error of the Panganiban-Veterans Formula on COCOFED is not significant since the absolute error is less than 1. It is immaterial to allocate a fraction of a whole seat.

However, the seat allocation error of the Panganiban-Veterans Formula on 7 parties in Table 2 is significant since the absolute error is at least 1 seat.Hence, a seat allocation formula contradicts the principle of proportional representation ifthe absolute seat allocation error is greater than or equal to 1. We consider the integerportion of the absolute error as the degree of negation of the seat allocation formula.The degree of negation is equivalent to the number of seats being denied by the formulato the concerned party. if the degree of negation is 0 then the seat allocation methodaffirms the principle of proportional representation. 

This implies that the degree of negation of the Panganiban-Veterans Formula on BAYANMUNA is equivalent to 2 seats, while the degree of negation on APEC, AKBAYAN,ANAKPAWIS, CIBAC, ABA-AKO and ANAD is equivalent to 1 seat each. This givesus a total of 8 seats. This means that (8 x 12,721,952)/53 = 1,920,295 voters are denied of representation in the House of Representatives directly by the Panganiban-VeteransFormula. 

The negation on BAYAN MUNA is due to the imposition of the 3-seat cap, the negationon APEC, AKBAYAN and CIBAC is due to the use of the first party’s additionalnumber of seats and number of votes as the basis for computing the additional number of seats for those parties with at least 2% of the total party-list votes and the negation ofABA-AKO and ANAD is due to the use of 2% as the minimum number of votes neededto be awarded a seat.  

The following theorem traces the root of the negation of the Panganiban-VeteransFormula on the principle of proportional representation. 

Theorem

Suppose that the seat allocation method used in a given party- list election is thePanganiban-Veterans Formula and let 1/(total no. of party- list seats) be called the simple quota. Then the Panganiban Formula negates the principle of proportional representation on a party- list group if the total number of party- list seats is greater than 50 and 

1. if the percent share of votes of the party- list group is greater than or equal to thesimple quota but is less than 2% of the total votes;

2. if the percent share of votes of the concerned party- list group is at least twice as largeas the simple quota but is less than one- half of the percent share of votes of the firstparty.

3. if the percent share of votes of the concerned party- list group is at least three times as large the simple quota but is less than the percent share of votes of the first party.

4. if the percent share of votes of the concerned party- list group is at least four times aslarge as the simple quota. 

For the proof of this theorem please see my article “On the Negation of the Party-ListSystem Act on the Principle of Proportional Representation” in the book on politicalparties and party-list groups to be published by the Center of People Empowerment inGovernance (CenPEG) in May 2007 or visit my web page inhttp://www.math.admu.edu.ph/~fpmuga.