How to Draw Sri Lanka’s New Electoral Map
The Electoral Map Mapping Algorithm (EMMA)
We concluded Proportional Representation, First-Past-the-Post or Both? with the three questions including,
“What would the Electoral Map look like if we returned to FPTP or adopted some mixed system?”
In 5 Properties of Good Electoral Maps, we answered a meta-question needed to answer the above, namely,
“What properties make a Good Electoral Map?”.
In this article, we describe an “Electoral Map Mapping Algorithm” (EMMA) that will programmatically generate a new Electoral Map for Sri Lanka that both obey the “5 Properties” and might be suitable for FPTP or mixed elections.
How EMMA works
EMMA takes the Old Electoral Map as input and modifies it step-by-step, gradually making it more and more optimal in terms of the “5 Properties”. Once “sufficiently optimal”*, the New EM is output.
[* More on this vague statement later]
Next, we will analyze this in more detail by examining each property (though not in the same order as the original article).
1. Population Balance
Each PD has roughly the same population. Since Sri Lanka has about 20.3M people*, each must contain about 130K. If a PD is significantly larger than this ideal (e.g. Nuwara-Eliya with 420K people), it must be split into smaller PDs. If it is significantly smaller (E.g. Kayts with 40K people), it must be merged with other smaller PDs to form a larger PD.
[*All population statistics quoted in this article are from the 2012 census.]
In this way, with each modification, EMMA achieves progressively better population balance.
3. Respect for other Region Boundaries
“Always respect the boundaries of Old EDs. I.e. No new PD will split across more than one Old ED.”
Rather than generate one EM for the whole of Sri Lanka, EMMA generates one EM each for each of the 22 EDs.
This way, it implicitly respects old ED boundaries.
“Whenever possible, a new PD will be equivalent to some old PDs”
EMMA leaves it unmodified if some PD is the right size (or at least not significantly the wrong size).
We will refer to this as the “Do Nothing” strategy.
[Going forward, we will use a few examples from EMMA’s output. These assume a 160 seats proportioned according to population across 160 polling divisions, and contested FPTP. We will discuss “Sri Lanka’s New Electoral Map” in the next article in more detail.]
Example. In our 160 seats-FPTP scenario (see note above), the Vanni ED gets 3 seats. Conveniently, it has three PDs, which, while not ideal in size, are all within 50% of the ideal. Hence, we could choose to “Do Nothing” and leave the Vanni as it is. Note, we could favour “Population Balance” against “Respecting Old PD Boundaries”, and apply the “Merge and Split” strategy described below. As we conclude later, there is no right, “scientific” answer to this question.
“If not, a new PD is a collection of two or more old PDs.”
If a PD is too small (like Kayts), EMMA will merge it with other smaller PDs to form a larger PD with a more balanced size.We will call this the “Merge” strategy.
Example. In our 160 seats FPTP scenario, the Jaffna ED gets 5 seats. However, in the Old Electoral Map, it has 11 PDs, and hence several (all except Kilinochchi) would need merging.
“If not, an old PD is split into two or more new PDs.”
If a PD is too large (like Nuwara-Eliya), EMMA will split it into smaller PDs with a more balanced size.
We will call this the “Split” strategy.
Example: In our 160 seats FPTP scenario, The Batticaloa ED gets 4 seats. Currently, it has 3 PDs, two (Batticaloa PD and Kalkudah PD) with almost ideal populations, and the third (Paddiruppu PD) almost 2x the ideal. The latter is an ideal candidate for a split
“If none of the above is possible (i.e. we cannot respect the boundaries of Old PDs), we will make sure that we respect the boundaries of GNDs, by making sure no Grama Niladhari Division (GND) splits across multiple PDs.”
Finally, there might be cases where a PD is the wrong size, but the most optimal strategy is neither a split nor a merge.
For example, suppose we have three contiguous PDs, each with a population of 85K (or roughly 2/3 of the ideal 130K). In such a case, we can merge all three into a giant PD with 255K people and then split it into two PDs with roughly 127K people — almost equal to the ideal 130K.
We will call this the “Merge and Split” strategy.
Example: In our 160 seats FPTP scenario, the Matara ED gets 6 seats. With 7 PDs, we need to “loose” one PD through some form of merge. We could, for example, merge Kamburupitiya PD and Devinuwara PD. Alternatively, we could Merge Kamburupitiya PD, Devinuwara PD and Matara PD, and split the resulting area in two. The latter favours population balance over respecting Old PD boundaries.
For each ED, EMMA will use one or more of the “Do Nothing”, “Merge”, “Split”, and “Merge and Split” strategies.
2. Contiguity
Since the only modifications we make are merges, splits or combinations thereof, contiguity is implicitly guaranteed.
5. Compactness
EMMA will have multiple different ways of performing a merge or a split. For example, a PD can be split into two smaller PDs across the vertical, the horizontal, or infinite other ways.
In these cases, EMMA will favour modifications that result in more compact (i.e. more similar width and height, e.g. squares and circles) shapes instead of less compact ones (e.g. narrow strips).
4. Respect for Ethnic, Religious and other groups
As with compactness, EMMA will favour modifications that result in fair PD boundaries and avoid favouring one group over another.
Concluding Thoughts: Art vs Science
Practitioners of Computer Science would notice that EMMA is not an Optimal Algorithm but rather a Greedy Algorithm. It makes small modifications, step-by-step, resulting in a progressively optimal but not perfectly optimal result.
There are two reasons why we chose a “greedy algorithm” over an “optimal algorithm”.
The first reason is computer scientific. Generating Electoral Maps (also known as the “Redistricting” Problem) has no known optimal solution beyond the most trivial cases.
The second reason is more complicated. As we saw above, EMMA has to optimize across many tradeoffs. On the one hand, we optimize for population balance; on the other hand, for respect region boundaries; on a third hand for respecting ethnic and religious groups; and so on. There is no way to determine what the optimal tradeoff is.
Hence, we observe the results, and when we have a solution that is “sufficiently optimal”, we output the result. There is no scientific way to determine “sufficiently optimal”. Hence, at some point, science has to defer to art; as with so many things…
In the next article, we will look at EMMA output. Or more simply, “Sri Lanka’s New Electoral Map”.
[Disclaimer: I am a Computer Scientist, specialising in Artificial Intelligence, and no expert in Politic and Political Science. My interest in Sri Lankan Elections is purely one of a interested citizen and hobbyist.]
