Thursday, July 26, 2007

Proportionality--A Critique of the Panganiban Formula for the Party List System


HOW MANY MEMBERS OF THE LOWER HOUSE ARE THERE?

This is a surprisingly tricky question to answer with any sort of precision because while the maximum number of Party List Representatives is more or less fixed, it is always possible for there to be ZERO party list reps if none of them meet the 2 percent threshold. The Lower House has two kinds of Members: District Representatives who are elected by voters in local Congressional Districts and Sectoral Representatives elected by the voters at large under the Party List System. During the 13th Congress there were 230 Members in all, with 23 Party List Reps (10%) and 212 District Reps (90%).

The main point of this post is that the TOTAL NUMBER of seats in the Lower House that ought to be awarded to the Party List System should be proportional to the number of voters that participate in the Party List System by casting a vote for it. As it stands under the Panganiban Formula the total number of seats awarded doesn't depend on whether 1,000 voters or 10 million cast ballots for the Party List!

The 1987 Constitution states:

Section 5. (1) The House of Representatives shall be composed of not more than two hundred and fifty members, unless otherwise fixed by law, who shall be elected from legislative districts apportioned among the provinces, cities, and the Metropolitan Manila area in accordance with the number of their respective inhabitants, and on the basis of a uniform and progressive ratio, and those who, as provided by law, shall be elected through a party-list system of registered national, regional, and sectoral parties or organizations.

(2) The party-list representatives shall constitute twenty per centum of the total number of representatives including those under the party list.

Unlike the number of Congressional Districts which is known before the elections and fixed by law, the actual number of seats awarded to the Party List is variable and depends on how well they do against each other.

Here is a curious fact. The NUMBER OF SEATS in the House of Representatives that will actually be occupied by Party List representatives after each election is NOT KNOWN until after the election results are tallied, under the present system which is called the Panganiban Formula. Curioser, under the Panganiban Formula the total number of Congressional seats awarded to the Party List System does NOT depend on the total number of votes cast at-large for the Party Lists but only on their relative performance against each other.

In Law, Mathematics and the Party List System former Chief Justice Artemio V. Panganiban gives an authoritative summary of the procedure now in use for implementing the Party List System in the Philippines:

The Panganiban Formula: Simply stated, the initial step, under this methodology, is to determine the additional seats to be given the party obtaining the highest number of votes. If the topnotcher or “first party” obtains four or more but less than 6 percent of the total votes cast, it gets one more seat. If it garners six or more percent, then it gets the maximum two seats. The additional seats to be given the rest of the qualified parties can be “proportionately” computed by dividing the number of votes of the concerned party by the number of votes the topnotcher garnered, multiplied by the number of seats allocated to the topnotcher.
Those four parameters are derived from both the 1987 Constitution's pertinent provisions and R.A. 7941 (The Party List Law):
First, the twenty percent allocation—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; “Second, the two percent threshold—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; “Third, the three-seat limit—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; (and) “Fourth, proportional representation—the additional seats which a party is entitled to shall be computed ‘in proportion to their total number of votes.’”

To see that the Panganiban Formula does not take into account the total number of votes cast for the Party List System, consider a very simple example. In Election Year No. 1 a total of 100 million voters cast ballots. Of this number only 10 million voters or 10% of the electorate cast votes for the Party Lists. Suppose that during this election only one Party List group breaks the 2% threshold, garnering let us say 2.1% of all the votes cast for the Party Lists, while all the others get less than 2%. In this case it is very clear that the total number of seats awarded to the Party List System in that election will be ONE SEAT.

Now suppose in a subsequent Election No. 2, that again 100 million voters turnout to cast ballots, but this time 20 million of them, or 20% of the electorate, decide to vote for a Party List group of their choice, twice as many in absolute numbers and percentage wise as in the previous election.

Suppose further that in Election No. 2, EXACTLY the same results obtain: the same party list gets 2.1% of the votes cast for the party-lists, whilst all the others garner 1.9% of the votes cast for the party lists.

Thus in Election No. 2, despite the fact that every single party list got twice as many voters casting ballots for it , despite the fact that twice as many voters cast ballots for the Party List System in Election No. 2, the Party List System will still only get ONE SEAT under the Panganiban Formula, same as in Election No. 1!

I think that this result puts into serious doubt the claim made by the former Chief Justice Art Panganiban that his Formula obeys the Principle of Proportionality in an optimum way. One curious consequence of his Formula, for example, is that it gets EASIER to win a Party List seat as the number of votes for the Party List System as whole goes down because it needs a smaller absolute number of votes to get 2% of the smaller total number of votes cast for the Party List System. In other words, it gets easier to be elected through the Party List System the LESS the electorate participates in it! Conversely, qualifying party lists are not rewarded proportionally under the Panganiban Formula for even 100% improvement in their actual vote totals from one election to another.

Is there a viable alternative to the Panganiban Formula? Yes! Here it is...

RIZALIST'S ALGORITHM for the PARTY LIST

STEP 1. The first step in this procedure is to determine from the election results HOW MANY seats in Congress have been won by the Party List System. The number of seats won by the Party List System shall be equal to one-fifth of the maximum number of seats in Congress (as of 2007 this maximum number is 250 as set by the 1987 Constitution and has not been increased or decreased by Congress since.) MULTIPLIED BY THE PERCENTAGE OF THE VOTERS WHO ALSO VOTE FOR A PARTY LIST CANDIDATE. Thus the Party List System will be entitled to the full twenty percentum or fifty seats only when 100% of the voters cast ballots for a Party List candidate. If less that 1% of the voters cast ballots for a Party List Candidate, then there will be less than one seat won by the Party List System, in which case NO SEAT will be awarded even if some party list gets say 50% of the miniscule vote. Step One automatically guarantees compliance with the Twenty Percent Rule, which is Panganiban's First Inviolable Parameter.

STEP 2: From the election results the Qualifying Party List Candidates are those that garner at least two percent (2%) of all the votes cast for the Party List System and become qualified for a Party List Seat in Congress, subject to availability and the Steps below. Step 2 fulfills the Two Percent Threshold Rule, Panganiban's Second Inviolable Parameter.

STEP 3: The number of Seats available to the Party List System found in Step One will now be distributed to the Qualifying Party List Candidates found in Step 2. The first available Seat is awarded to the Qualifying Party List which garnered the highest number of votes in the election. The second seat to the next highest vote getter, and so on until either all the Seats have been awarded or all the Qualifiers have received their first seat during a first round of seat assignments. Whereupon, if there are still Seats available a second and subsequent round of assignments is undertaken until all the Seats have been assigned, or all the Qualifiers have received the maximum of 3 Seats.

The third step imposes the 3 seat maximum limit, Panganiban's Third Inviolable Parameter. And of course a stronger version of Proportionality is implemented by all three Steps, built right into Step 1, which makes the total number of Seats given to the Party List System directly proportional (within rounding errors) to the number of voters who participate in the Party List System.

Under the present Panganiban Formula the total number of Congressional seats awarded to the Party List System does NOT depend on the total number of votes cast at-large for the Party Lists. It only depends on the RELATIVE PERFORMANCE of the party lists running against each other.

Under Rizalist's Algorithm, and compared to Panganiban's Formula, what would have happened to our putative First Party Topnotcher who gets 2.1% of the votes cast for the Party List System in both of two successive elections but in which twice as many voters vote for Party Lists in the second election compared to the first? Suppose that in Election No.One, 5% vote for Party Lists and in Election No. Two, 10% vote for Party Lists.

Under the Panganiban Formula this First Party will get the same ONE SEAT in both elections, despite garnering say 20,000,000 votes in the second one and only 10,000,000 in the first one (not a population growth effect!).

Under Rizalist's Algorithm, the total number of seats available to the Party Lists in Election No. 1 will be 5% of 50 seats or 2.5 seats, which rounds up to three seats or rounds down to two seats. To be conservative let's just call this 2 seats. In Election No. 1, the First (and only qualifying party above 2%, by assumption), would get 2 SEATS. In Election No. 3, the same party would get 3 seats.

In both cases the Rizalist Algorithm awards more seats than the Panganiban Formula, yet it employs a "stronger" tenet of proportionality.

And I think it is a far more elegant and likely to produce a "more optimum" solution.

In order to compare the Panganiban Formula with the Rizalist Algorithm, imagine that (1) the number of ballots cast in a given election is 100 million votes; (2) 100 party list groups run and each one gets 2% of the votes cast for the Party List. In other words, let us imagine a series of election scenarios in which 100 party list groups qualify for a House Seat by making the 2% threshold. Tthe only variable is how many voters participate in the Party List System out of an assumed total of 100 million ballots cast. Now let us compare how SEATS will be distributed under the two systems under varying degrees of voter participation in the Party List System:


Number of Votes Cast for the Party List System out of 100 million

Percent Turnout for Party Lists

NO. SEATS FOR THE PARTY LISTS Panganiban Formula

NO. SEATS FOR THE PARTY LISTS Rizalist Algorithm

1

10,000,000 10% 50 5
2 20,000,000 20% 50 10
3 30,000,000 30% 50 15
4 40,000,000 40% 50 20
5 50,000,000 50% 50 25
6 60,000,000 60% 50 30
7 70,000,000 70% 50 35
8 80,000,000 80% 50 40
9 90,000,000 90% 50 45
10 100,000,000 100% 50 50

In this thought experiment, the Party List groups all do equally well and one hundred of them actually qualify for a Congress Seat. Under the Panganiban Formula all the Party List groups get the same one seat each no matter how well the Party List System itself does with the electorate.

Proportionality, anyone?

Under the Rizalist Algorithm, the Constitutional dictum to use a "uniform and progressive ratio" for the Party List System is explicitly fulfilled. If only 10% of the voters cast ballots for the Party Lists, then only 10% or 5 of the maximum of 50 seats available will actually be awarded to the Party Lists, and only the Top Five party lists will get a single seat. All 100 of them get seats only if 100% of the electorate participates in the Party List System.

This extreme case reveals the essential non-proportionality of the Panganiban Formula.

Under this extreme case, the Rizalist Algorithm may also be criticized, of course, because not all the party list groups that actually meet the 2% threshold will be awarded a seat in the Lower House.

But this extreme case is highly unlikely to occur and is presented merely to illustrate the point about proportionality. Under more realist scenarios, however, the Rizalist Algorithm still beats out the Panganiban Formula, IMHO.

Consider for example a second scenario. Suppose that in an election where again 100% of the electorate votes for a Party List candidate so that the full twenty percentum or 50 House seats are available to be awarded to them. But instead of 100 party lists each getting precisely 2% of the 100 million votes, what we have is the following distribution of votes garnered by just ten parties:

PARTY LIST GROUP
Percent of PartY List Vote
Seats Won (Panganiban Formula)

Seats Won (Rizalist Algorithm)

(PLS Turnout 100% 50 seats available)

Seats Won (Rizalist Algorithm)

(PLS Turnout 50% 25 seats available)

Seats Won (Rizalist Algorithm)

(PLS Turnout 30% 15 seats available)

Seats Won (Rizalist Algorithm)

(PLS Turnout 10% 5 seats available)

1

6%
6*3/6=3
3
3
2
1
2
5.5%
5.5*3/6=2
3
3
2
1
3
5.0%
5*3/6=2
3
3
2
1
4
4.5%
4.5*3/6=2
3
3
2
1
5
4.0%
4*3/6=2
3
3
2
1
6
3.5%
3.5*3/6=1
3
3
2
0
7
3.0%
3*3/6=1.5
3
3
1
0
8
2.5%
2.5*3/6=1
3
3
1
0
9
2.0%
2*3/6=1
3
2
1
0
10
1.5%
1.5*3/6==0
0
0
0
0

In this thought experiment we now have ten party list groups running in the election, with all but one of them garnering 2% or more of the votes cast for the Party List System. Notice that under the Panganiban Formula the party list groups get the exact same number of seats no matter what their overall performance at the polls measured by the total number of votes they all get.

CONCLUSIONS:

1. The Panganiban Formula does not implement an "optimum" version of Proportionality. In fact, it could be asserted that the Formula actually violates Proportionality by being independent of the parameter that seems to be the natural candidate to be the PROPORTIONALITY PARAMETER that determines the TOTAL NUMBER of seats won by the Party List System, namely, the percent of the ballots cast that have votes for a party list group.

2. The Panganiban Formula actually gives parametric primacy of place to the 3-Seat Maximum Rule, and guarantees compliance with it by assigning all groups qualifying under the 2 percent threshold seats in proportion to their votes RELATIVE to the number of seats given to the "First Party". This however, only maximizes the "quantization error" associated with the fact that only an integral number of seats can ever be awarded.

The Rizalist Algorithm suffers from none of these criticisms and explicitly obeys the Four Inviolable Parameters of the Constitution and the Party List Law.

9 comments:

Nicholas Kister said...

DJB, I've been trying to follow the Party list this election, I've tended to agree with Felix Muga's work.

If you have time, however, please try to calculate the 2007 Party List results, so that I can compare your results with that of Felix Muga's work..

Clearly The Panganiban Formula should never even have existed, I know Panganiban is a bright guy, but I would have hoped he could have at least consulted with a Mathematician as well as the Constitution when he made his formula.

Nicholas Kister said...

If you aren't aware of Felix's work. Please visit CenPeg for Felix Muga's work, or you can visit Tingog.com (my blog) and search for Felix Muga which should give you the articles that I have written on the subject..

Nicholas Kister said...

When I said calculate the party list results for the 2007 election, I meant to use your algorithm...

DJB Rizalist said...

Hi Nick,
Comelec's results for the party list in 2007 elections are found
here
In which we find that the turnout for the party list was 15 million plus votes out of 29 million or the equivalent under my algorithm of 26 seats for the party list.

And it looks like there are 23 party lists that met the 2% threshold. That means they all get one seat, except for the Top 3 ranking party lists, who each get 2 seats. No one gets 3 seats.

DJB Rizalist said...

Hi Nick,
Comelec's results for the party list in 2007 elections are found
here
In which we find that the turnout for the party list was 15 million plus votes out of 29 million or the equivalent under my algorithm of 26 seats for the party list.

And it looks like there are 23 party lists that met the 2% threshold. That means they all get one seat, except for the Top 3 ranking party lists, who each get 2 seats. No one gets 3 seats.

DJB Rizalist said...

Ooops, correction Nick. There appear to be only 17 party list groups that met the 2 percent threshold. That means under my algorithm, the Top 11 will get TWO SEATS, while the bottom 6 get only one seat. But no one gets 3 seats.

Nicholas Kister said...

DJB, thank you for obliging with the calculations. It looks to me, under the current constraints, that your algorithm makes much more sense than that of Panganiban.

But clearly R.A 7941 has an inherent flaw, while at the very beginning it deems to give 20% of the seats to Party lists, it then sets out to refute itself, and set out constraints that will and have made it possible to give The Party Lists less than the alloted 20%.

And clearly, while the framers of the constitution and even R.A 7941 probably wanted 20% allocation for the Party Lists, it fell short, in understanding how to implement it.

Thus we have lawmakers acting like mathematicians.

Felix Muga's proposal, is just that, a proposal, and is not meant to conform with the present status, but hopefully will set in motion a bill to be filed by Congress in amending R.A 7941.

As per my information, a Bill of such sort was filed in the 13th Congress, read here, and because of the laziness of the 13th congress, it was not passed, but will need to be refiled in the 14th Congress.

It is my point to make clear, that 20% of the party lists may seem much, but it was basically what the framers of the constitution had in mind. Whilst we have an almost permanent number of Senators, Governors, and Congressmen, it seems to me a valid question to ask as to why we can't have a permanent number of Party List Representatives.

Nicholas Kister said...

Oops. Please read, here, for information regarding the bill.

I'm not sure what other avenue there is with regards to sorting out this mess.

domingo said...

DJB, there is a basic flaw in the enabling Act--R.A. 7941, “Party-List Systems Act.”

The constitutional provision you cited, Art. VI, Sec. 5(1), provides that the second group of Members of the House of Representatives “shall be elected through a party-list system of registered national, regional, and sectoral parties or organizations.”

The Constitution, therefore, enumerates THREE different categories of registered parties and organizations qualified to be “elected through a party-list system”: (1) national; (2) regional; and (3)sectoral.

Sec. 3 (d) of --defines a “regional party” as a political party whose “constituency is spread over the geographical territory of at least a majority of the cities and provinces comprising the region”; and Sec. 5 identifies the different sectors : “labor, peasant, fisherfolk, urban poor, indigenous cultural communities, elderly, handicapped, women, youth, veterans, overseas workers, and professionals.”

However, Sec. 12 of the Act, “Procedure in Allocating Seats for Party-List Representatives,” disregards altogether and clearly discriminates against REGIONAL parties and organizations, by providing that:

“The COMELEC shall tally all the votes for the parties, organizations, or coalitions on a nationwide basis, rank them according to the number of votes received and allocate party-list representatives 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, how can the regional parties and organizations the Constitution (and the Act for that matter) recognizes as one of the three components of the party-list system--whose constituency as defined in the Act is spread only over a limited geographical territory of a REGION--“compete for and win seats in the legislature,” if party-list votes under Sec. 12 of the Act are to be tallied, ranked and allocated “on a nationwide basis” similar to that for Senators chosen at large?

In short, is the system instituted under Sec. 12, R.A. 7941 that directs party-list votes to be tallied, ranked and allocated “nationwide”--rather than regionwide--which leaves regional parties and organizations unfairly disadvantaged, tantamount to virtually denying their access to representation they rightly deserve, constitutional?

The current approach unduly deprives the marginalized in regions the right to fair representation that otherwise would have been available to them under a different, more equitable apportionment scheme.

The Act, for instance, could have provided an allocation of, say, three seats per region. As it is now, the prevailing system creates a new breed of powerful, “OVER”-represented “marginalized TRAPOS” (with a maximum of 3 seats and the pork to boot) within the second group of House members, in the same way that the “original TRAPOS” in the first group of congressional district representatives have through the years unfairly, unjustly lorded over and bullied the truly marginalized sectors.

Thus, aside from the absurdities confronting the 20% allocation, the 2% threshold, the 3-seat limit, and the proportional representation, it is obvious that the prevailing “nationwide” seat allocation system now being implemented pursuant to RA 7941 clearly defeats the laudable purpose the Act proclaims: “the broadest possible representation.”

For it would unarguably be extremely difficult, if not impossible, for marginalized parties and organizations in any of the 13 regions to gain even one seat in the House of Representatives.