Thursday, July 26, 2007

Comparison of the Panganiban Formula and the Rizalist Algorithm Applied to the 2007 Party List Results

Upon the suggestion of Nicholas, I am now publishing a comparison of the Panganiban Formula versus the Rizalist Algorithm in deciding how to award House Seats to the Party List organizations that ran in the May 14 midterm elections, in which 29,984,421 ballots were cast, out of which a total of 15,703,067 or 52 percent contained a vote for one of the Party List groups. The Official Comelec Canvass shows the results for 93 Party List organizations that ran under the Party List System. Seventeen of them each garnered 2 percent or more of the 15 million votes that went to the Party List System, with BUHAY topping the race at 7.45% of the Party List votes.

As the "First Party" under the Panganiban Formula, Buhay has indeed been awarded one seat for exceeding the 2 percent threshold and two additional seats for scoring above 6%. The "PANG" column in the Table below shows how many seats are awarded to the other parties based on the Panganiban formula, which is calculated by taking the ratio of votes garnered by each party and that garnered by the First Party multiplied by the number of seats awarded to the First Party (in this case, 3). But as a result of the Panganiban Formula, only TEN of the Party Lists that ran will get seats, and SEVEN of those that met the 2% threshold WILL NOT get a seat. Under the Panganiban Formula, only THIRTEEN SEATS will be awarded to the Party List System, even though 52% of the voters chose a party list on their ballot.

1 BUHAY 1,169,165 7.45 3 3 2
2 BAYAN MUNA 976,364 6.22 2.505 2 2
3 CIBAC 755,393 4.81 1.938 1 2
4 APEC 621,092 3.96 1.594 1 2
5 GABRIELA 620,890 3.95 1.593 1 2
6 A TEACHER 486,390 3.1 1.248 1 2
7 AKBAYAN 460,968 2.94 1.183 1 2
8 ALAGAD 423,071 2.69 1.086 1 2
9 BUTIL 409,132 2.61 1.05 1 2
10 COOP-NATCCO 407,417 2.59 1.045 1 1
11 BATAS 384,961 2.45 0.988 0 1
12 ARC 373,626 2.38 0.959 0 1
13 ANAKPAWIS 369,023 2.35 0.947 0 1
14 ABONO 339,888 2.16 0.872 0 1
15 AGAP 328,600 2.09 0.843 0 1
16 AMIN 316,249 2.01 0.811 0 1
17 AN WARAY 315,527 2.01 0.81 0 1

22.47 13 26
Nb: 29,984,421 ballots were cast on May 14, out of which a total of 15,703,067 or 52 percent voted for a party list candidate.

Nb: The figure in red 22.47 represents the mathematical number of seats that should go to the Party List System under strict proportionality, but of course it cannot be met exactly due to the four constraints. But the number of seats awarded under the Rizalist Algorithm is closer to this "ideal" number of seats than the niggardly 13 awarded under the Panganiban Formula.

Under the Rizalist Algorithm, the first step is the calculate the TOTAL NUMBER OF SEATS that are available for award to the qualifying party list organizations, equal to the percentage of the ballots with party list votes multiplied by twenty percent of the authorized maximum number of House Seats (250 under the 1987 Constitution and never yet changed by Law). Thus for 2007, the Rizalist Algorithm would make 26 House Seats available for awarding to the party list groups, subject to the constraints of the Four Inviolable Parameters of Panganiban (proportionality, 2% threshold, 3 Seat maximum and 20% of House). As seen in the Table, the Algorithm would award 26 seats as follows: all 17 party lists with at least 2% of the vote will get at least one seat; and the Top 9 ranking parties will each get 2 seats. NO party gets three seats in 2007 under the Rizalist Algorithm.

The Table of results above clearly exposes a major shortcoming of the Panganiban Formula. Although it purports to uphold the Four Inviolable Parameters, its implementation has resulted in seven parties not being awarded seats despite having garnered 2% of the Party List Vote, and despite the fact that giving them each at least one seat, does not in fact violate any of the other three parameters.

This indicates that the Panganiban Formula is not an "optimal" implementation of what is essentially a problem in LINEAR PROGRAMMING and optimization. It actually violates the principle that a party list qualifies for a seat by gaining a threshold of 2%, and should get one if it does not cause a violation of the other parameters.




Appreciate your presentation greatly. I think I've finally understood a little more of how this party list "seating arrangement" in the House functions.

For years, to me there seemed to be changes all the time that I just gave up trying to understand.

My brother was the manager of a party list but don't see his party among your the party winners so I reckon his party won less than 300,000 votes. (I didn't ask my brother last time I spoke to him - family thinggy - we avoid discussing politics, he knew I was opposed to his plan of creating a party list.)

In any case, my question is why did the Panganiban Formula award only 10 of the party lists that ran and won a minimum of 2% of the vote for a total of 13 seats if it could be mathemathically proven that seats should be awarded to 17 party lists for, as you showed, a total of 26 seats? After all, this no. of seats I reckon does not even reach the 20% quota for party listers in the House?

Was the application of the so called Panganiban formula some kind of a political decision as opposed to legal decision?

Nicholas Kister said...

Your algorithm seems to be correct. But as I have said, no amount of Algorithm will fix the inherent flaws within RA 7941. I believe still, that the framers of both The Constituion and RA 7941 had 20% not as a quota, but as a specific allotment... The framers of RA 7941 failed in its implementation..

Otherwise, why would they start out with the statement,

Sec. 11. Number of Party-List Representatives. - The party-list representatives shall constitute twenty percentum (20%) of the total number of the members of the House of Representatives including those under the party-list.

Jaxius said...


You have it wrong.

If a party-list gets 2% of the total votes cast in the party-list elections, it automatically qualifies for a seat.

The Panganiban Formula deals only with the additional seat/s a party-list may get after qualifying for a seat under the 2% threshold.

DJB Rizalist said...

It cannot possible true that a party which gets 2% of the Party List Vote automatically gets a seat because that is only one of four conditions. Besides getting 2% only means that a party is "qualified" for a seat given that it is available.

True the Panganiban Formula is applied specifically for the additional seats, but it's part of a procedure or algorithm that figures out how all the seats are allocated.

And remember, even if only 1000 votes are cast in total for the Party Lists, they still get their seats.

Regarding the 20% business, that would be impossible today because there are only 250 max members allowed, but already 212 district reps.

Btw, there is some confusion over whether it is 20% of the max 250, or 20% of the ACTUAL members as long as it is less than 250.

finally, the framers could not have meant that there should always be 20% of congress from the party lists.

What if 100 of them run and they all get 1% of the vote and none qualify under the 2% threshold?

How would you fill up the 20% quota?

DJB Rizalist said...

please note that for 2007, the rizalist algorithm DOES award at least one seat to all 17 who got 2%, and 2 seat to some of them, because the party list system should have had 26 seats available to it.

But my algorithm would not ALWAYS give a seat to anyone with 2%. This depends on whether the party list system has indeed won enough votes to GET any seats at all. Whenever the party list turnout (percentage of votes for party list over the total votes) is less than 2%, the system gets ZERO seats and its doesn't matter whether anyone gets 2% or 100% no one gets seats.

Also if there are 17 with over 2% as they do today, but if again the whole system does not produce enough seats, then they won't all get a seat -- only the top rankers untill al the seats are gone)

DJB Rizalist said...

I have already presented an argument to Jaxius that 20% is not possible if not enough party lists qualify to fill up the seats.

It would be a vast violation of "proportionality" to give them 20% no matter how many votes they get from the electorate!

DJB Rizalist said...

BTW Nick, thanks for pointing out Muga's work. As I said in comments on your blog, it's not right for him to get rid of one or more the four parameters just to get a mathematic solution.

The R.A. is like the P.F. in that it fulfills ALL four conditions. but unlike PF, all 2% qualifiers get seats, if the Party List System has won enough seats in the overall election.

Jaxius said...


1. Read Sec. 11 (b) of RA 7941. It is very clear that once a party-list group gets 2% of the total votes cast, it is entitled to 1 seat.

2. The pertinent constitutional provision on the matter of the number of seats in the House reads, "The House of Representatives shall be composed of not more than two hundred and fifty members, unless otherwise fixed by law..."

3. As to the number of votes cast in the party list elections, suffice it to say that Congress deemed it not important to impose a mandatory number of votes cast in the party-list elections to make it valid. As a favorite by-line of yours, there is no “controversy” regarding the matter that the Supreme Court should take that into consideration.

The problem lies in the law itself, not in the way the Supreme Court interpreted it.

The conflict lies between the constitutional provision that says:

"The party-list representatives shall constitute twenty per centum of the total number of representatives including those under the party-list"

and Section 11(b) of RA 7941 which says:

"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..."

If 50 party-list groups get a 2% share of the votes each, it would only amount to 50 seats. As you said, there are already 212 district seats in the House of Representatives.

If what is written in the Constitution be strictly adhered to, there should be 53 seats allocated for party-list groups. However, the 2% threshold established by RA 7941 makes this an impossible feat. By imposing a 2% threshold, Congress basically limited the number of party-list in Congress to 50.

The SC affirmed the constitutionality of RA 7941 because the Constitution vested Congress with the broad power to define and prescribe the mechanics of the party-list system of representation. Thus, the matter of statistical improbability because of the 2% qualifying threshold should be squarely laid on the doors of Congress which has the prerogative to determine whether to adjust or change this percentage requirement.

As you so succinctly put a number of times, the Supreme Court should not read into the law what is not there.

DJB Rizalist said...

Thanks for your thoughtful comments, but how can you make this claim:

By imposing a 2% threshold, Congress basically limited the number of party-list in Congress to 50.

Seems to me it is the 20 percentum provision in the 1987 constitution that does that, plus the 250 seat limit. which you correctly point out the congress can change.

Also, why do you say that there should be 53 seats allocated to the Party List? The 20 Percent Provision in the 1987 says that the party list shall constitute 20 per centum of all the House Members, including the party list members.

The ACTUAL number of House Members in the 13th congress was 230: 212 district and 23 pl. but in the 14th congress there will still be 212 district reps, but only 13 party list reps. The House will have 225 members.

In neither case are they 20% but as the SC explained, that is the result of the operation of the other parameters of the law.

We cannot favor one parameter over the other, unless we want to amend the law.

I am approaching this whole problem with the starting assumption that any system I come up with MUST obey the Four Inviolable Parameters.

The interesting thing is to find a system that minimizes the error from the "ideal".

It's no fair to say the problem has no solution, because I know of at least TWO, even if I am prejudiced towards one of them.

Jaxius said...


The number of party-list allocation is dependent on the number of district representatives. The constitutional provision was translated by the SC into a mathematical formula:

No of district reps/.8 * .2 = no. of party list


212/.8 * .2 = 53

53 is the current allocation, which is a mere ceiling and not to be mandatorily filled up, of party-list seats if we would follow the 1987 Constitution.

The 250 maximum-limit in the 1987 Constitution has already been amended by the "gerrymandering" legislation of some of our congressmen so that they or their relatives can have more positions. In 1998, there were already 208 district reps.

However, because of the 2% threshold introduced by RA 7941, theoretically only a maximum of 50 of the allocated 53 seats can be filled up, i.e. 50 party-list groups get 2% each. We know this is almost impossible as some party-list groups get more than that. Thus, if Bayan Muna get 10% of the vote, it already eats up two seats that cannot be filled up because it is limited to a maximum of 3 seats (i.e., if it is the party that gets the most votes).

Your computation is erroneous. Under the Panganiban system (basing on your table), there should be 20 party-list seats that should be proclaimed. You failed to qualify the 7 parties that got 2%.

After figuring out the 20% threshold, the next threshold is the 2%. All parties that get that is entitled to one seat.

Now, to figure out whether these parties who qualified are further entitled to additional seats, only then will you use the "Panganiban Formula" (actually, the multiplier of the ratio is not the total number of seats (3) but only the additional seat entitled to the first party (2), as clarified by the SC in the recent CIBAC vs COMELEC). Thus, if the first party got only 3% of the vote and is not entitled to an additional seat, it follows that other parties are not entitled to additional seats.

Actually, the formula you devised seems arbitrary and does not fit RA 7941, which by the way Congress needs to amend. I just find it strange that you awarded 2 seats to Butil which only has 1,715 more votes more than Coop-Natcco. Yet, Butil has the same number of seats as Buhay which has more than 760,033 votes!

DJB Rizalist said...

But I am only quoting the official results. I recalculated the results based on the Panganiban Formula and got exactly the same results as announced in the newspapers.

The reason that the seven party list candidates were not given seats under the Panganiban Formula is that when you multiply 3 by the ratio of their votes to that of the First Party Buhay, they get a number smaller than 1,which the PF rounds DOWN to zero.

this is precisely my criticism of the PF: it does not award seats to those that meet the 2 percent threshold even if doing so would not violate any of the other parameters.

I agree with you on that.

However, as I've said, it is not AUTOMATIC that in some future election, if a party list gets 2% that it would have a seat under the R.A.

RA is based on first calculating the proportion of the House Membership the PL is entitled to, based on the number of votes they get in total divided by all the ballots cast.

That is the only real way of implementing PROPORTIONALITY.

bUT I AGREE, all those 17 parties who got more than 2% in 2007 should be given seats since it would not violate any of the Four Parameters to do so. ONly the PF would be violated but NONE of the 4 params.

DJB Rizalist said...

53 times 5 equals 212.
That's 20% of the Number of District Representatives, not "20 percent of the House Membership including the Party List" as the Constitution provides.

See, I think that the number of party list reps that are serving cannot possibly be a FIXED number like 50 because it is always possible for there to be no qualifying party list groups if none of them get 2% or more.

But help me understand your point of view by answering this simple question:

Should the number of party list representatives be a constant 20% of the House Members? What nga if none or not enough qualify under your own 2% rule?

DJB Rizalist said...

another thing: the Districts have to grow with population because the constitution also provides that a city or province with 250,000 or more citizens in it is qualified for a seat in the House.

The fact that the party lists are not always at their full complement of 20%, I claim, comes from the fact that they have never gotten 100% of the vote at large.

In the same way, the District Representatives are also not at their full possible complement which will all change with the next census.

I think 20% is an upper limit, not a fixed point.

Jaxius said...


53 multiplied by 5 is 265. 212 (number of district reps) + 53 allocated seats for party list. 80% district and 20% party-list. The latter is merely a ceiling, not to be mandatorily filled-up.

The maximum of 50 seats, as i said, is a mere ideal under the RA 7941 because of the 2% threshold. Only 50 parties can possibly get 2% out of the 100% votes cast, right?

If there are no parties that reach the 2% threshold, then there would be no party-list that would qualify.

While the Constitution says 20% of the House of Represetatives shall be composed of party-list, it gave Congress the power to enact a law that would give the parameters for their qualification and selection.

Let me reiterate that the Panganiban Formula is only used to determine if a party-list group that qualified under the 2% threshold is entitled to an additional seat. You do not use it to determine if a party-list is entitled to a seat. Qualification for a seat is still the 2% threshold.

DJB Rizalist said...

i stand corrected on my arithmetic. but let me read the rest of your comment!

DJB Rizalist said...

have you written a complete analysis and alternative scheme yourself. I'd like to read it.

Jaxius said...


Been trying to figure out a system that should be better than the current as outlined by RA 7941. Still on the drawing board. Will send you when done.

LEX MUGA said...


1.Section 11 of RA 7941 allocates one seat each to the party-list groups (two-percenters) with at least 2% of the total party-list votes. Since 17 parties (Party-List Report No. 29 as of July 11, 2007) have satisfied this requirement, in the first round of the Panganiban Formula, 17 seats are allocated.

2. If the first party has at least 6% of the total party-list votes it will be given two additional seats.

3. The additional number of a two-percenter is determined by finding the integral part of the product of its total number of votes and the additional number of seats of the first party (2 seats in the case of Buhay 2007) and divided by the total number of votes of the first party.

This actually means that if a two-percenter has at least 50% of the total votes of the first party, then it will be given one additional seat. Otherwise, no additional seat is given.

Hence, BAYAN MUNA, CIBAC, APEC and GABRIELA will be given one additional seat each.

Threfore, a total 6 seats is awarded by the Panganiban Formula in the second round including that of Buhay.

3. The total number of seats that will be allocated by the Panganiban Formula (based on Party-List Report No. 29, as of June 11, 2007) is 17+6 = 23. This allocation is 3 seats short of the allocation of the Rizalist Algorithm as computed.


Lex Muga

LEX MUGA said...


The system of 4 inviolable parameters are inconsistent.

Consider the 3rd parameter.
"a qualified party can have at most 3 seats."

Consider the 4th parameter. Suppose that a party has at least 10% of the total votes then by the principle of the proportional representation it will have 10% of the total seats.

If there are 55 available seats, then by this Principle it is entitled to 5.5 seats. This means that the party is entitled to either 5 or 6 seats.

There is no point of points of intersection. Hence, the system of 4 inviolable parameters are INCONSISTENT. Therefore, there is no correct solution.

If a formula claims to have a solution, then there are votes that are DISENFRANCHISED. As in our example, the number of disenfranchised votes of the concerned party is
between (5-3) x (total votes/total seats) and (6-3) x (total votes/total seats).


Lex Muga

DJB Rizalist said...

Hello Lex,
I've blogrolled your weblog here at Philippine commentary.

It is obvious you've been thinking about this interesting problem of the party list for some time and much more than me. So thanks for indulging me.

First of, let me just say that I don't agree with questioning ANY of the four parameters. We have to take the word problem as stated.

It is not correct to say that there is no correct solution, because the real problem is that there are MANY correct solutions!

I think it is misleading to say that the four parameters are inconsistent with each other, because if we think of these things as piecewise functions they end up defining a solution space, which I claim has some solutions that are better than others.

Indeed, you can construct a kind of error function over the pertinent domains of interest which can be a mathematical measure of how good any solution is.

In other words, if you set up the exact and ideal number of seats that any qualifying party gets and take the difference with whatever solution set is used, the better solution sets are the ones with the smallest integrated error.

In my algorithm, the total number of seats awarded to the PLs is 26. Under the Panganiban Formula it is 13. Exact ideal is 22.47. What does your system produce, if you work one out that OBEYS all 4 parameters as both RA and PF do.

LEX MUGA said...


In the Bagong Bayani vs Comelec ruling of the Supreme Court where the Panganiban Formula was given, Justice Mendoza provided an alternative formula.

The Mendoza formula is stated as follows:

1. Following section 11 of RA 7941, those with at least 2% of the total votes cast for the party-list shall be awarded 1 seat each.

2. The additional number of seats for each two-percenters is determined by:

2.1 multiply the total number of votes of a two-percenter by the remaining number of seats and divide the result by the total number of votes of all the two-percenters.

3. The total number of seats of a two-percenter is equal to the integer party of the result in (2.1) plus one seat, if the sum is less than 3. Otherwise, the total number of seats is 3.

If we apply the Mendoza formula to the latest Party-List Tally (Report No. 29), the computation for (b) on Buhay is

1,169,165 * (55-17) / 8,757,756 =

Thus, the sum for Buhay is 6 and
by the Mendoza formula, Buhay will actually receive 3 seats.

Computing the number of seats of the two-percenters we have the following:

a) party-list BUHAY down to the 7th ranked party AKBAYAN will receive 3 seats each.

b) 8th ranked party ALAGAD down to the 17th ranked party AN WARAY will receive two seats each.

The total number of seats
allocated by the Mendoza Formula in the 2007 elections is
7(3) + 10(2) = 41 seats.

The allocation is 14 seats short of the total number of seats available.

This is better than the Panganiban Formula or the Rizalist Algorithm.

However, it violates the principle of proportional representation by at least 8 seats or at least 1,273,855 votes will be disenfranchised.

Lex Muga

LEX MUGA said...

Dear DJB,

I'm using the Largest Remainder method at 2% formal vote threshold.

If the 3rd parameter is imposed (3-seat cap), we have:
a) 3 seats each for BUHAY down to the 10th ranked COOP-NATCCO;
b) 2 seats each for BATAS down to the 17th ranked AN WARAY.

The total allocation is 3(10)+ 2(7) = 44.

This is better than the Panganiban Formula (23 seats), the Rizalist Algorithm (26 seats), and the Mendoza Dissenting Opinion (41 seats).

In the 13th Congress, I was involved in the committee of Etta Rosales to amend RA 7941. We only reached the 2nd reading because of the Garci Tapes and the Gloria Impeachment.

The seat allocation method of the amendment uses the Largest Remainder Method at 1/(total no. of seats) formal vote threshold and a 6-seat cap.

The Rosales amendment will yield 53 seats. The Amendment violates the principle of proportional representation by one seat only or at least 164,676 votes are disenfranchised.

We can improve our solution by petitioning the Supreme Court to declare the 3-seat cap as unconstitutional because this is the cause of our DISPROPORTIONATE party-list system.

The 3-seat cap is not enshrined in the Constitution. It was mentioned in the minutes of the ConCom because they were discussing the party-list in the context of the two-party system. However, the two-party system was not approved and the commissioners decided to develop an open and multiparty system according to the will of the people.


Lex Muga

DJB Rizalist said...

Under your system, how many seats would be awarded to the party lists if we assume that the turnout for the partylist in 2007 was not 15 million votes, but say 5 million votes?

Is your scheme sensitive to this parameter?

DJB Rizalist said...

what i mean is, is your system sensitive to the proportion of the votes given to party lists and the general vote total?

What happens in your system if let us say only 100,000 votes cast votes for the partylist?

LEX MUGA said...

Dear DJB,

Proportional Representation is based on the total number of votes of all the parties that are entitled to receive a seat and the total number of seats available.

We shall consider the basic guiding principle for proportional representation:

"Power or legislative seats should be distributed in proportion to people’s stakes under consideration."

"individuals with some positive stake shall have some power while individuals with no stakes shall be excluded from the decision-making process."

Thus, if individuals do no vote for the party-list then they are not given power.

Under this principle the total number of available seats is allocated even if 5 million votes for the party-list out of 100 million voters who actually voted.

This is also what we have in the election for the congressional districts. In Batanes, there are less than 10,000 registered voters. If 9,000 voters actually voted and if the leading candidate has 3,000 votes, the seat is given to him or her even if he or she does not receive all the votes.


DJB Rizalist said...

I think that is the problem with ALL the proposed alternatives as well as the Panganiban Formula.
You don't actually implement the most obvious of the proportionalities implied in the constitution. Namely, when is the party list system deserving of ALL the seats implied by 20% of the House.

In my system, I first calculate this number, which seems to be the correct way to implement proportionality.

Regarding district elections, remember that even those who vote for the losing candidate must now accept the winner and "give their power to them".

I think not voting for a party list, or voting for one, should count for something.

Regarding error function, you award 44 seats, but what is the ideal or purely mathematical result you are comparing that number against? I claim that pure proportionality and the other rules mean 22.47 seats should go to the party lists. You give twice as many but I am sure am not comparing apples to apples.

What say you of my criticism though that your system is insensitive to the turnout for the party list?


DJB Rizalist said...

sorry i haven't read all your stuff. But how do you calculate the 44 seats you award to the party list this year?

DJB Rizalist said...

There does not seem to be anything PROPORTIONAL about a system in which one party list can get 3 seats for getting 6% of the party list vote each time, but, in the first election gets 10,000,000 votes; in the second eleciton 100,000 votes; and in the third election 1 vote.

LEX MUGA said...

Dear DJB,

We differ in the concept of proportional representation.

The constitution is silent about its meaning.

However Sec 11 of RA 7941 specifies that the additional number of seats of those who are entitled to a seat is computed in "proportion to their total number of seats".

Section 12 of the same Law also said that party-list representatives are allocated "proportionately according
to the percentage of votes obtained by each party, organization, or coalition as against the total
nationwide votes cast for the party-list system."

It is clear from the Party-List Law that proportional representation is based on the number of votes cast for the party-list.

I think this is the essence of Proportional Representation.

For example in the 2005 Bundestag election, the total number of votes of the parties who are entitled to a seat is only about 84.9% of the total number of votes cast but all the number of seats available for the party-list is given (299 regular list seats plus 14 overhang seats).

Also, in the 2005 Polish Election of its lower chamber, 6 out of 19 parties were entitled to a seat. These 6 parties obtained 89.07% of the total votes cast but the total number of seats available for the party-list were given to them.

LEX MUGA said...

Dear DJB,

It is improbable that the party-list system will get only 1 vote.

Note that this is a party-list system and and parties are composed of nominees and members.
In the 2007 elections, the total number of votes cast for the party-list is about 15M (as of the latest tally) out of 29.98M voters who actually voted.

What do you mean by pure proportionality? How do I replicate your 22.47 seats?

I think pure proportionality is based on those who are entitled to receive a seat. Why do we have to include those who are not entitled to receive a seat in the allocation? They will only make proportionality less pure.

Let us not make the party-list difficult for the marginalized and underrepresented sectors of our society.

In fact the constitution insists that one-half of the seats allocated to the party-list representatives must come from "labor, peasant, urban poor, indigenous cultural
communities, women, youth, and such other sectors as provided by law except the religious sector".

22.47 seats is less than one-half of the 55 seats.

Let us make the party-list system friendly to these sectors.

Let us rally together and call for the rejection of the 3-seat cap which is the real culprit of our DISPROPORTIONATE party-list system.



LEX MUGA said...

Dear DJB,

The Largest Remainder Method will always give the total number of party-list seats available (55 seats in 2007). See the computation in

The ideal number of seats that a qualified party is entitled to receive based on the principle of proportional representation is equal to its share of the total number of votes of all parties that are entitled to receive a seat times the total number of party-list seats.

If the 3-seat cap will be imposed on the LR Method based on the latest Party-list Tally (No. 29), the allocation is reduced to 44 seats.



DJB Rizalist said...

"Section 12 of the same Law also said that party-list representatives are allocated "proportionately according
to the percentage of votes obtained by each party, organization, or coalition as against the total
nationwide votes cast for the party-list system."

So why do you calculate the number of seats based on the proportion of the party list votes with respect to the First Party and not the grand total?

In fact there is nowhere in the calculations of Panganiban or yours where the "the percentage of votes obtained by each party, organization, or coalition as against the total
nationwide votes cast for the party-list system." is taken explicitly into account and used for something.

That of course is the reason why you would get the same result whether the total votes are 1, 10, 1000, 10,000, 10^6 or 30 million as long as the partylists get the same relative percentages.

It is immaterial that one vote is highly unlikely, the criticism is about the gross violation of proportionality exactly as you define it and in Section 12 of the law.

But without necessarily agreeing with me in toto, do you agree that in fact there is something wrong with that?

I suspect that if you merely introduced this new parameter of total number of seats based on percentage of votes relative to the total, our algorithms would come up with the same answer!

I'm looking at my procedure for calculating the seats and I can also adopt the largest remainder system, which might increase my allocation, but still have to run the numbers.

BTW, I have some EXCEL files that have simulations and all the numbers in them. We should get do some numerical experiments maybe. The solution space of the 4-parameter problem is very complex and might have some surprisingly good systems hiding in them that even the Courts might agree are better than Panganiban's Formula.

I certainly think the Muga Method would be better than PF!

LEX MUGA said...


Thank you for regarding my proposed method better compared to the Panganiban Formula.

Yes, the PF uses the "proportionality based on the first party" and not on the "proportionality based on all the qualified parties".

This is one argument against the PF.

I am not really comfortable with the 4-INVIOLABLE PARAMETERS because I believe that the system it created is inconsistent. The Supreme Court should not call them the "4 INVIOLABLE PARAMETERS" but "3 INVIOLABLE PARAMETERS PLUS A SECONDARY FOURTH" because the 4th is not really inviolable.

If the legislators insist that it is part of system, then we shall lobby to increase the number to TEN SEATS because that is really the intention of the CONCOM (although in the context of a two-party-system).

Yes, I'm very glad to do some numerical experiments with you. Why don't you post some of your EXCEL files? Maybe we can find the most acceptable APPROXIMATE solution given the 4 parameters.



LEX MUGA said...

Dear DJB,

According to some lawyers, when Congress created additional districts by legislation it's automatic that the number of seats in the lower chamber is changed.

Thus, when it created 8 legislative districts by legislation before the 2007 elections, it is also by law that the number of representatives is increased from

212+53=265 in the 13th congress to 220+55=275 in the 14th congress.