A Mathematical Way for Clustering a City into Administrative Districts

Every Filipino would know that Binondo in Manila will always be associated with Chinatown but they don’t know that it is not a barangay. Photo by Michael Buillerey on Unsplash

Can you think of a word when you see the word “Binondo”? You would say it’s Chinatown. Now, how about “La Paz”? You would associate it with batchoy.

Now, mentioning the two place names, I ask: Are both of them barangays?

If you answer “yes,” I’m sorry to say, they are officially not.

Although I can’t blame you since those place names are more recognizable than the barangays it encompassed.

In fact, both Binondo, Manila and La Paz, Iloilo City are administrative (geographical) districts.

Unlike those districts that are intended for elections (Congress and city councils), administrative districts (ADs) are clusters of barangays established for administrative, statistic-gathering and planning convenience.

This is where the problem arises.

There are few cities in the Philippines where they have more than hundreds of barangays but no clusters. As such, the city’s services (e.g. fire stations, waste disposal) will find it much difficult to serve and manage efficiently in a certain part of the area.

Is there a magic formula? I won’t claim for having an ideal formula but I can try it out.

Finding the formula

Before we could set up the formula, there are criteria that we need to consider (other than finding the best fit):

• There must be no negative numbers on either variables; there are neither -1 and less barangays as there are neither -1 and less administrative districts.
• If there are no numbers of barangays, there must be zero districts. Therefore, the intercept must be zero (0).
• The number of districts must be not be too large, so as not to give burden on the city’s planning department to spend much of their time comparing and monitoring each other.

With the three conditions set, the power model will be taken.

The following cities have already defined their districts based on their relevant laws (Republic Acts or city ordinance):

• Manila: 897 brgys, 16 districts
• Pasay City: 201 brgys, 7 districts
• Legazpi City (Albay): 70 brgys, 2 districts
• Sorsogon City: 64 brgys, 2 districts
• Iloilo City: 180 brgys, 7 districts
• Davao City: 182 brgys, 11 districts
• Island Garden City of Samal: 46 brgys, 3 districts

Input the dataset and you get this graph and regression analysis:

Based on these points, the R-squared under the model in play is 0.8458 (strong) and the formula devised is (in four decimal places):

Where x is the number of barangays (in 100s) and y is the expected number of ADs.

Putting the formula to the test

In order to test out the formula, we’ll try to find one city with many barangays without the official administrative districts.

Thus, I decided to put Caloocan as the prime example. Despite the geographic separation, they are divided (in aggregate) into 188 barangays and currently has no defined ADs.

Based on the formula we have devised, the city’s expected number of administrative districts to be carved would be 7 (actual calculation: 7.038).

The city’s development and planning department will conduct further study before sending out their recommendations to the Sangguniang Panlungsod in order to craft an ordinance.

How (potentially) many?

With the formula, we can interpolate the cities’ expected number of ADs according to their respective number of barangays or closer to that:

• 2 ADs: 19 barangays
• 3 ADs: 40 barangays
• 4 ADs: 68 barangays
• 5 ADs: 101 barangays
• 6 ADs: 141 barangays (one short of Quezon City)
• 7 ADs: 186 barangays (two short of Caloocan)
• 8 ADs: 237 barangays
• 9 ADs: 293 barangays
• 10 ADs: 355 barangays
• 11 ADs: 422 barangays
• 12 ADs: 494 barangays
• 13 ADs: 571 barangays
• 14 ADs: 653 barangays
• 15 ADs: 740 barangays
• 16 ADs: 831 barangays (66 short of Manila)

Conclusion

Finding an actual number of administrative districts to carve may not match with expected calculation. It will be based due to geographic, economic and social reasoning.

However, it’s a start as it can help the empower a part of local governance — a promise set by decentralization and soon, by federalism.

Footnotes on Raw Data

1. Pasay: As stated on their government website but they are not named and thus, not classified by the Philippine Statistics Authority.
2. Legazpi City’s districts are based on Presidential Decree 125 (1973). Daraga was supposed to be included but it is currently a separate municipality.
3. Sorsogon City’s districts are based on the merger of two municipalities under Republic Act 8806 (2000).
4. IGaCoS’ districts are based on the former municipalities before the city merger under Republic Act No. 8471 (1998).