Thursday, February 2, 2017

Redistricting in Alberta

Every eight to ten years, the Alberta Electoral Boundary Commission meets up to reconfigure the riding boundaries for upcoming elections. This is a fairly important part of our democracy, as cities are often growing, people tend to move around a lot, and keeping our boundaries updated to reflect current population distributions is a good way to ensure that everyone is equally represented in our legislature.

Fortunately enough, Alberta isn't like many US states where it is elected politicians themselves who decide where these boundaries will be drawn, which can tend to lead to gerrymandering as I've discussed before. So although in Alberta districts are determined by a neutral committee and appear to avoid obvious signs of manipulation for political purposes, they aren't really all that good at making sure everyone's vote counts the same no matter where they live. For instance, the Electoral Boundaries Commission Act specifies that the maximum population deviation from the average per riding is 25%. As well, provided the area is sparsely populated enough, up to 4 districts can have populations that are as much as 50% below the average population of a riding in the province.

This led to a situation where, based on the 2011 census, the largest district had a population of 51,800 people, more than twice the size of the smallest district at 23,050. Someone living in Dunvegan-Central Peace-Notley has nearly twice the voting power of the average Albertan when it comes to provincial elections, at a population a whopping 45% below provincial average. (As a side note, this still isn't as bad as on the federal stage, where Labrador is 73% below average, and five times less than the highest populated riding in Brantford-Brant, but that's a different story.)

So, as an infomercial might say at this point, "There must be a better way!"

The Electoral Boundaries Commission is accepting submissions now while they begin their redistricting process, and this seems as good a time as any to determine a better solution. What is a fair way to split the province up into 87 sections each with the same population?

One of the coolest solutions is to use the shortest splitline algorithm. As explained by CGP Grey, the shortest splitline algorithm is a repetitive process that searches for the shortest line that splits an area perfectly in two by population. Each half is then split again with the shortest line that produces equal halves, until ultimately we stop when we've gotten the desired number of sections split up, which are necessarily of exactly even population.

So lets try this for Alberta. The first thing we need is a population distribution of Alberta, which Statistics Canada helpfully has lying around on their website. It looks like this:



This is Alberta broken up into 5,711 census dissemination areas based on the 2011 census.

Next up, we would normally find the shortest line that crosses Alberta in such a way that exactly half of the population is above the line, and exactly half is below the line. Since Alberta has 87 districts, though, we actually want to find the shortest line that has 44/87 of the population above it, and 43/87 of the population below it. In my (slightly optimized) model, that looked like this:


Then we split each half again. The top half is an even number, so we can split it in two easily, whereas the bottom has to be split into 22/44 and 21/44 segments. That gives us this:


And so on and so forth until we've split all of Alberta up into equal segments. The final result of this ends up being this lovely stained glass window:




Of course, things can't always be perfect no matter how hard you try, so this is a solution for Alberta that has a maximum population in each riding of 0.38%. The largest riding has 42,052 people in it, and the smallest has 41,752. This is a solution to split up Alberta that has a maximum voter variance that is 118 times smaller than we have now, and a coefficient of variation that is 68 times smaller.

Also, just because the map was drawn with straight lines doesn't mean it has to stay like that. If we go back to our census dissemination area shapes from Stats Canada, we can convert an Edmonton distribution from this:


To this:

Which is actually starting to look pretty reasonable. Neighborhoods are kept together, and the areas are looking relatively compact.

The shortest splitline method is an objective and fair way to distribute votes such that everyone's votes are counted equally. I was able to redistrict all of Alberta using Excel - no fancy programming skills are needed. There's no reason that we can't have redistricting being as boring as updating census data and having a computer spit out a single solution each time we need it.

That being said, there are still some objections people could have with it - for instance, it doesn't necessarily give a hoot about municipal boundaries. Take Red Deer for example: after applying the algorithm to Alberta, Red Deer got sort of unfortunately split into four districts, each of which includes substantial amounts of surrounding countryside:

Oh no.
This would have people in Innisfail voting alongside southwest Red Deer, and people in Saskatchewan River Crossing voting alongside west Red Deer. That's probably a bit messed up. In cases like this, I think it's probably fair to use the splitline algorithm to get to a starting point, and then massaging the districts as needed to make sure they make a bit more sense. Because the algorithm got within a 0.38% maximum population variance to start with, it is likely quite straightforward after to swap around some areas as needed to keep the popluation variance still small. For instance, Public Interest Alberta recommends a maximum population deviation of 5%, which I'd suggest is reasonably easy to achieve if we're starting from a point where our deviation is essentially 0%.

So if I've convinced you that using algorithms to redistrict our population can lead to fairer, objective, even distributions of our political districts, and that those are things worth having in our democracy, head on over to the Commission's website and leave them a submission before February 8th!

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