Sunday, January 24, 2021

A Redistricting Toy Problem

This is a non-gaming post.

I've been thinking about drawing electoral districts and gerrymandering lately. I came up with a simple toy problem that I cannot decide on an answer for. So I'll throw it out for any readers to comment on.

Imagine we have a small, square town. There are two parties here, the Blues and the Greens. Most people lean Blue or lean Green. However, partisanship is not extreme, and some people will vote for a particularly charismatic or competent candidate from the other party. For various reasons about 2/3 of the people lean Blue and live on the west side of town. 1/3 lean Green and live on the east side. Like so:

B | B | G

B | B | G

B | B | G

The city has a council with 3 councilors. What's the best way to draw three districts for this town?

If you slice vertically, then you guarantee representation. There will be 2 Blue councilors, and 1 Green. However, the districts are not competitive at all, and there's no real possibility that Green will ever get a majority.

If you slice horizontally, then you guarantee competitiveness. However, it's quite possible that Green will lose all three elections, and have no representation at all. But if the Green party is particularly good one year, then they could take 2 or even 3 seats and have a majority.

So I don't know what the best solution is. Maybe the solution is to ignore district composition entirely and use strictly geographical borders.


  1. Hmmmm, "yes of course"? I mean, if in a country you're for representative democracy, then the distribution of the representatives must match that of the people's opinion, i.e. pure proportional system, country-level. The reason countries abandon this in favour of other voting systems is to sacrifice some democracy to gain more stable majorities.

  2. What is your goal? See, the problem with Gerrymandering is that districts are (in general) not drawn to abstract principle, they are drawn by people in the legislature who are themselves members of Blue or Green who also expect to face elections. So, real districts are drawn up to be "stable" and to not mess up the majority party that voted them in.

    This gets into the interesting question of what should the goal be? Here you have a 2/3rds 1/3rd split, but real world problems can be thornier. What if you have a minority that is only 10% or less, and is also diffuse throughout? Would they ever get representation? Should they? I don't see an inevitable answer here. This sort of depends on what you think the legislature should be. Which circles back to the original question -- what is your goal?

  3. This reminded me of a video I saw a while back:

    Not sure I can help with an answer beyond "it's complicated," as I think there can't be a single correct answer without first biasing the question.

  4. Whats the goal? That green never can get power? That its proportionate to population? That its 50/50 even if the people are not? It's also stating that only 2 parties can ever exist.

    Many "modern" countries have just moved to proportional representation that doesn't have any zones, or had a 50/50 split of zones and popular vote. It does mean majorities are unlikely, and groups therefore are bound by central alliances.

    Netflix has a decent video on this topic, goes over your example too.