THE CARPIO FORMULA

On April 21, 2009, the Supreme Court of the Philippines ruled on a new formula for the allocation of seats for the party-list system of the Philippines.The new Supreme Court ruling on the Party-list system is penned by Justice Antonio Carpio. In the said ruling he articulated a new formula which we call as the Carpio Seat Allocation Formula.

The conduct of the party-list election in the Philippines is now based on Republic Act 7941, the Philippine Party-List System Act,  and the Supreme Court Ruling of 21 April 2009. It is mandated in the party-list law as guided by the 1987 Constitution that twenty-percent (20%) of the total number of members of the House of Representatives including the party-list representatives must come from the party-list system. It also imposed a maximum of 3 seats that a party-list organization may obtain.

In the election for members of the House of Representatives, a ballot provides for two votes. One vote is for a name of candidate in a congressional district and the other vote is for a name of party-list organization for the party-list system.

The votes obtained by each registered party list groups is summed up nationwide. The total party list votes is the sum of all the votes of these registered party list groups. The percentage vote share of each party list groups is computed by dividing the number of votes each party list groups obtained by the total party list votes. Those party list groups that obtained two percent of the total party list votes are called as the two-percenters.

The Supreme Court of the Philippines (sc.judiciary.gov.ph) 

The Carpio Formula provides three stages of seat allocation.

In the first stage of the Carpio Formula, it allocates one seat to each of the two-percenters.

In the second stage, additional seats for each of the two-percenters is computed in the following manner.

1. The remaining number of seats is determined by subtracting the number of seats allocated in the first stage from the total number of available party list seats.
2. The remaining number of seats obtained in (1) is multiplied to the vote share of each of the two-percenters.
3. The whole number of the product obtained in (2) is equivalent to the additional number of seats that a two-percenter shall receive. Note that a two-percenter cannot receive more than two additional seats.

If there are seats unfilled after the second stage, a third stage of seat allocation is implemented. Those party list groups that do not receive a seat in the second stage including those two-percenters that obtained a product in (2) that is less than 1 shall be ranked from the highest to the lowest based on their vote shares. One seat shall be allocated to the highest ranking party down to the next until all the unfilled seats are distributed.


by Felix P. Muga II
Associate Professor, Mathematics Department, Ateneo de Manila University
Senior Fellow, Center for People Empowerment in Governance

The Mathematics of Politics