Redistricting is getting a lot of attention as the Census wraps up its data processing and we head into the 2021 redistricting cycle. And with good reason—between the gutting of the Voting Rights Act, pandemic-related data delays, and ever-increasing partisanship, this will be an incredibly important redistricting cycle.

But after doing a lot of work on redistricting in the U.S., I thought I’d take a look at what goes on across the pond—in Northern Ireland, specifically. In a place where religious polarization is stronger than political polarization (though they are intertwined), how does the redistricting process look? Are the boundaries fair?

A Small Country, Divided

Northern Ireland consists of six of Ireland’s 32 counties, which were partitioned from the rest of the island as part of the Irish independence process. The Belfast metropolitan area, lying along the Down–Antrim border, contains nearly a third of the country’s population.

Overall, 37% of households identify as Catholic and 44% identify as Protestant, with an increasing number not identifying as religious. The geographic distribution of Catholics and Protestants is complex, to say the least. In Belfast, almost completely polarized wedges radiate outwards in a kind of pinwheel pattern from the city center.

Parliamentary Constituencies

Currently, Northern Ireland has 18 of the 650 seats in the Parliament of the UK. The boundaries for these parliamentary constituencies, which are also used to elect representatives to the Northern Ireland Assembly (5 representatives per constituency), were slated to be replaced in 2019 following the final recommendations of a review process that ended in 2018, but these new constituency boundaries were not adopted. A new review will occur in 2023. Reviews are overseen by Boundary Commissions which are “independent and impartial”.

The constituencies are made up of statistical areas called “Super Output Areas” (SOAs), and generally follow county boundaries. Ideally, they would all have the same population, but as the figure above shows (using 2011 population counts), they don’t.

How the Constituencies Measure Up

How do we go about determining the fairness of a set of parliamentary constituencies? Simple measures, like comparing the fraction of Catholics in the general population to the fraction of constituencies which are plurality-Catholic, are tempting to use but ultimately inadequate. The spatial distribution of voters can heavily skew these kinds of numbers. For instance, it is nearly impossible to draw nine congressional districts for the state of Massachusetts which result in a single Republican seat, despite Donald Trump winning nearly a third of the statewide vote. Is this unfair? Not under our first-past-the-post electoral system. It’s just a consequence of Democrats being spread fairly evenly across the state (compared to other states, at least).

So what’s the alternative? The state-of-the-art is to randomly generate a bunch of other, hypothetical, sets of constituencies (“redistricting plans”). Such a collection of random plans can form a baseline against which to measure the actual, adopted plan. If the baseline is constructed according to the proper legal standards, and the adopted plan is significantly different from it, that’s evidence that the adopted plan is unfair or possibly gerrymandered.

Generating these random plans is not straightforward, as there are vastly more ways to draw redistricting plans than there are atoms in the universe, and yet only a minuscule fraction of these plans satisfy all the relevant legal constraints.

Here, we’ll use a new algorithm I’ve developed expressly for this purpose, and we’ll enforce the following constraints:

The Boundary Commission may also take into account historical constituency boundaries and the boundaries of local wards. For the time being, we’ll ignore these other considerations.

When we generate 1,000 random plans according to these constraints, we get hypothetical plans that look like this:

For each plan, we can tally up the number of Protestants and Catholics in each constituency, and sort the constituencies by these numbers. Maybe one constituency is 85% Catholic, the next one is 81%, and so on down to the least Catholic constituency, which might be 83% Protestant. (For these comparisons, we look at the Catholic/Protestant fractions among voters that identify one way or another; that is, we exclude minor religions and the nonreligious.)

We take this set of numbers—the Catholic fraction in each constituency, across the 1,000 random plans—and plot them on the graph below. Every dot is a constituency taken from one of the simulated plans, and the constituencies are arranged by how Catholic they are. Orange dots are plurality-Protestant, and blue dots are plurality-Catholic. We see that on average, across all these hypothetical plans, the most Catholic constituency is usually around 76% Catholic.

We also mark the fraction of Catholics in the current constituencies with black lines. If this line falls below its corresponding set of points, that means that that constituency has fewer Catholics than would be expected based on our baseline of randomly generated plans.

The pattern here is one of polarization. Compared to neutrally-drawn random plans, the existing constituencies have fewer Catholics in the plurality-Protestant constituencies and fewer Protestants in the plurality-Catholic constituencies, while the constituencies in the middle are about average. Voters in each religious community are packed in with similar voters, compared to what might otherwise be expected. (Some polarization is expected of course, given the geographic distribution of religions—that’s why the graph has an upward slope.)

Percentages are well and good, but how does this translate into seats? Voting patterns in Northern Ireland are far from straightforward, with several political parties that appeal to overlapping constituencies. But it’s easy to convert the information in the above graph to a count of the number of constituencies which are plurality Catholic and plurality Protestant. Given the population numbers across the whole country, a proportional breakdown would be 8 Catholic-plurality constituencies and 10 Protestant-plurality constituencies.

As the histogram below shows, that 8–18 split is indeed what should happen on average, according to our baseline. But instead there’s a 7–17 split. At the same time, that isn’t too unusual—about 16% of the time, we’d expect to see 7 or fewer plurality-Catholic constituencies.
But it is one seat fewer than the average.

Why this discrepancy? Part of it could be population change since the boundaries were last adjusted (in 2007, based on the 2001 census). And the population has changed further since the 2011 census. But another possible explanation lies in the Boundary Commission’s mandate to consider the traditional boundaries of the constituencies.

We can explore this by generating another set of 1,000 baseline plans, but adding one additional constraint: that the geographic “core” of each constituency remain the same. What is the geographic “core”? For our purposes, it will be the set of SOAs (the building blocks for constituencies) which do not border another constituency. This means that roughly 67% of voters are guaranteed to stay in the same constituency. The effect of all of this is to create hypothetical plans that are close to the existing boundaries.

The graph below is the same as the one as above, but uses this new baseline. And the pattern above—that constituencies were more religiously polarized than we would expect—mostly disappears.

Going from here requires less math and more philosophy. Is it a good thing to have more religiously homogeneous constituencies? If not, are the existing boundaries a religious gerrymander or just drawn to reflect the old boundaries? How did those boundaries get to be the way they were? How would we move towards more integration while respecting traditional boundaries, anyway?

Conversely, if religious homogeneity is a good thing—after all, it tends to reduce the number of wasted votes (Catholics in Protestant constituencies, and vice versa)—how far can we push it? Is more polarization possible?

There are other redistricting tools that are better suited to answering questions like this, but we can gain an idea of what’s possible by generating yet another set of baseline simulations. This time, we’ll explicitly group together Catholic and Protestant areas, so that these areas aren’t split by the redistricting process.

The results of this simulation are shown in the graph below. While the overall shape doesn’t show much more polarization than what is already seen under the current boundaries, we now see a couple plans which yield 11 Catholic-plurality constituencies and only 7 Protestant-plurality constituencies.
Compared to a proportional split of 8–18, this is rather a lot, and we don’t see the same possibility for more Protestant-plurality constituencies beyond 12.

One of these 11–7 split plans is shown below. The general strategy is to merge Belfast East and Belfast South, while adjusting the boundaries of Belfast West and mopping up the remains with Belfast North. Upper Bann and Lagan Valley are shifted northwards, adding enough Catholics to tip them into a Catholic plurality. With the leftover constituency created by merging Belfast East and South, the constituency of South Down, a Catholic stronghold, can be split into two more closely divided constituencies that cover the areas left by Upper Bann and Lagan Valley.

An interesting exercise, for sure. But voting patterns and ultimate constituency winners are not so easily predicted from religious affiliation alone. Not to mention that Sinn Féin MPs don’t take their seats in Parliament anyway.