Problems of the Panganiban Formula: Underallocation, Nonallocation, Overallocation

The Panganiban Formula was introduced by the Supreme Court when it ruled on the case Veterans Federal Party vs. Comelec (2001). In the said formula, a party-list group is entitled to one seat if it reaches the two-percent threshold of all the party-list votes. The additional number of seats that the party-list group shall receive is determined as follows:

1. if the party-list group has the most number of votes (called as the first party) and if it obtains
a. at least 6% of the total number of party-list votes, then it shall receive two more seats; or
b. at least 4% but less than 6% of the total number of party-list votes, then it shall receive one more seat, or
2. if the party-list group obtains the same number of votes as the first party then it receives the same number of additional seats as the first party, or
3. if the party-list group obtains at least one-half but less than the number of votes of the first party, then it shall receive one more seat, or
4. if the party-list group obtains less than one-half of that of the first party, then it does not receive any additional seat.
Party-List Canvass Report No. 30, the latest Party-list Tally of the Comelec shows that there are 17 party-list groups that obtain at least 2% of the total party-list votes where Buhay is the first party with 7.418753% of the total party-list votes. If we apply the Panganiban Formula we have the following results.

The 1987 Constitution mandates that the party-list shall constitute 20% of the total number of representatives in the House of Representatives including the party-list. There are 220 legislative districts now, the total number of party-list seats available is 220/4 = 55 seats. Note that 55/(220+55) = 0.2 or 20%.

Hence, the Panganiban Formula allocates only 23/55 = 0.41818182 or 41.82% of the total number of seats available. This is a case of underallocation.

In the 2007 party-list election, ninety-three party-list groups were allowed to participate by the Comelec. Thus, there is a possibility that no party will be able to reach the 2%-threshold. If this happens, no party-list group will receive a seat and the party-list will not be represented in the House of Representatives. This is a case of noallocation.

If the first party obtains 6% of the total party-list votes and 27 party-list groups obtains 3% of the the total party-list votes, then there will be 28 party-list groups that are entitled to a seat and their combined share of the party-list votes is 27(3%) + 6% = 87%. Using the Panganiban Formula, the first party shall receive 3 seats and the 27 party-list groups shall receive 2 seats each. The Panganiban Formula will allocate 3+54 = 57 seats. This allocation is two seats over the available number of seats.

Actually, the largest possible allocation of the Panganiban Formula is 65 seats where the first party obtains 6% and there are 31 party-list groups with 3% of the total party-list votes. This allocation is 10 seats over the available number of seats.

These are cases of overallocation.

On The Two-Percent Formal Threshold: A Restrictive Mechanism for the Marginalized and Under-Represented

courtesy of www.congress.gov.ph


A formal vote threshold is the share of the total votes that a party has to obtain in order to qualify for a seat. In some countries, the formal threshold is higher to lessen the number of parties in the parliament and making it easier to form a government. In Germany, it has 5-percent, Poland has 7-percent and Turkey has 10 percent.

According to a blogger, Global Economy Matters, “the ten percent threshold was introduced by the 1980-83 military government to prevent a recurrence of the excessive parliamentary fragmentation and resulting governmental instability that characterized Turkish politics for much of the 1970s - has had a mixed record over the years.” (http://globaleconomydoesmatter.blogspot.com/2007/07/turkeys-early-parliamentary-election-of.html).


courtesy of www.congress.gov.ph

The formal vote threshold for the Philippine party-list system can be deduced from Section 11 of the Party-List System Act (Republic Act 7941). The said provision specifies that a party-list group that obtained at least 2% of the total votes cast for the party is entitled to a seat.

The party-list system in the Philippines is instituted to give the marginalized and under-represented sectors of its society representation in the House of Representatives and it comprises 20% of the entire number of representatives as specified by the Constitution. Although, it has not been reached since party-list elections have been conducted since 1998.

With the two-percent threshold only a small number of parties are able to obtain a party-list seat. In the last election, there are 17 out 93 participating party-list groups are represented.

If the formal vote threshold is removed and the Largest Remainder Method will be used, about 40 parties will gain seats for the 2007-2010 House of Representatives. If the formal threshold is fixed at one-half of the informal threshold which is 1/(total number of party-list seats) about 36 parties can make it. See our computations below.


 Formal Threshold at Four-Percent


Formal Threshold at Two-Percent



Formal Threshold at 0.9091-Percent



No Formal Threshold

The 2007 Party-List Election in Japan

courtesy of http://www.sangiin.go.jp/eng/index.htm

Last Sunday, July 29, 2007, Japan held an election for the House of Councillors (Senators) which is the upper chamber of the Japanese Parliament or the National Diet.

A total of 121 seats were contested where 73 seats will be filled in forty-seven prefectural districts and 48 seats will be allocated by proportional representation on a national basis.

Every voter has to cast two votes for the National Diet. The first vote is for a single candidate in a prefectural district. The candidates with the largest number of votes in each district, up to the number of seats to be filled, are elected to office. The second vote is for the party-list system. The 48 seats will be allocated by the Highest Average Method devised by the Belgian Mathematician Victor D’ Hondt.

All the elected Senators will serve for 6 years. The total number of members in the upper chamber is 242 and half of them are elected every three years.

Seven parties are qualified to receive a party-list seat. These are:

1. Democratic Party of Japan (DJP) with 23,256,242 votes
2. Liberal Democratic Party (LDP) with 16,544,696 votes
3. New Komeito Party (NKP) with 7,762,324 votes
4. Japanese Communist Party (JCP) with 4,407,937 votes
5. Social Democratic Party (SDP) with 2,637,716 votes
6. People’s New Party (PNP) with 1,269,220 votes
7. New Party Nippon (NPN) with 1,770,697 votes

The total number of votes of all qualified parties is 57,648,832 representing 97.853050% of all the votes cast for the party-list. The qualified parties received all 48 party-list seats available.

The Highest Average Method

In the Highest Average Method, successive quotients or averages are calculated. It is determined by dividing the number of votes of each party by a sequence of integer divisors 1, 2, 3, 4, and so on.

The list of successive quotients for each qualified party using the divisors from 1 up to 25 is given in the table below.




The top 48 quotients shall determine the 48 seats to be allocated. Hence,

1. Democratic Party of Japan (DJP) shall be awarded with 20 seats,
2. Liberal Democratic Party (LDP) with 14 seats,
3. New Komeito Party (NKP) with 7 seats,
4. Japanese Communist Party (JCP) with 3 seats
5. Social Democratic Party (SDP) with 2 seats
6. People’s New Party (PNP) with 1 seat, and
7. New Party Nippon (NPN) with 1 seat

The table below shows the rank of each quotient corresponding to the seat number that each party obtained.


Analysis

The Highest Average Method allocates the total number of available party-list seats. The seat allocation error  is zero as well as the degree of negation. This means that the Highest Average Method affirms the principle of proportional representation on the parties participating the 2007 Japan party-list election. See table below.

where
TQPV is the total number of votes of all qualified parties,
Actual Number of Seats is the actual allocation of the
                 Highest Average Method,
Ideal Number of  Seats is the obtained by the product
                  of the  % Based on TQPV and 48, 
Seat Allocation Error is the Ideal Number of Seats 
                    minus the Actual Number of  Seats, and the
Degree of Negation is the absolute value of the integer 
                    part of  the Seat Allocation Error.

The index of proportionality of a given method is determined by dividing the sum of the absolute value of the seat allocation error by 96 and the result is subtracted from 1. A value of 1 or 100% means full proportionality and a value of 0 means a disproportionate method. The index of proportionality of the Highest Average Method on the 2007 Japan party-list election is equal to 97.088495%.