The only thing I can think of is to start with the districts we have and then produce an algorithm that uses a random number generator to redraw lines. The algorithm can fuzz the current boundaries making a district larger or smaller or it can choose to split a district or combine two districts. Just keep randomizing the districting for each election starting with the output of the last time it was randomly fuzzed.
Sometimes the randomness will work in favor of one party, sometimes against it. In the long term, it adds in some non-partisan non-determinism, which is probably good for justice long-term.
Fuzzy circles! Great idea. That, or repeated boundary drawing that brute forced every possible district combination and gave a probabilistic result of elections based on where districts were drawn.
A pretty common downside is a lack of adherence to historical boundaries and groupings - some neighborhoods that legitimately formed a district and a unified block due to strange geographic features could be broken up.
But actually - there are two classes of algorithms out there: one can determine how to fairly divide up a state and another measures how unfairly a state is divided up - instead of going full into computers-determine-everything it might be nice to just have a requirement that the result of the election in the state is relatively statistically probable given the proportions of votes for each party. So people could still draw districts we would just have a manner to prove their districts are acceptably fair.
The algorithmic determination of districts is attractive, but there
can still be the problem of accidental "gerrymandering"---that the
voters are so thoroughly mixed that the 40% party loses to the 60%
party almost everywhere.
There is another interesting way to solve this. Divide the land into
even-population districts in any way. Then, let the population vote
on the candidates. Finally, in each district, choose one vote at
random to determine the winner. The distribution of the
representatives' party allegiations will be statistically very close
to the actual distribution in the population. (This is not my idea; I
read it somewhere some time ago.)
I wonder if similar math could lead to a way of setting up voting districts, as a fair alternative to gerrymandering. Of course you wouldn't want to cut people into pieces, so it would have to be an approximation of some sort.
I caught part of a discussion on NPR this morning regarding California's newly drawn districts. There seem to be many complaints (most from different groups feeling like they were split, or combined unfairly).
While it's an improvement to have been done by an independent commission, the way these maps are drawn still seems archaic. Redrawing district lines, to me, seems like a problem that could pretty easily be solved algorithmically.
What do you think? What sort of inputs would you need? What factors would you take into account? Any good articles on this sort of thing? Any existing partitioning algorithms suitable for this? Would simply randomising districts be preferable?
Makes me wonder, is there a fairer, algorithmic way to carve up a geographical area into election districts so we can apply the same solution to every state?
This is an active area of research for sure. One idea is basically to come up with a few rules for what the districts must look like (as unions of precincts) and use Markov chain Monte Carlo to sample from a probability distribution on the possible districting plans. Several court cases have featured expert evidence from math researchers asked to quantify how crazy the districting is using this methodology (ish). Wesley Pegden's expert witness report in one such case is readily findable, for example.
One of the main difficulties is that we don't have much rigorous theory telling us how long to run the Markov chains.
I believe that a fairer method of districting would be to generate a Voronoi graph where the size of each cell is based on population data. Each cell should be centered around a population centroid and should contain approximately the same number of citizens.
I was thinking that there would be an overlay of squares, each identical, like graph paper. As long as the squares contain a relatively small population as compared to the rest of the state, then the two parties are forced to make real choices. And that's the real goal - for both partoes to make real choiced, and not to simply game the system via gerrymandering.
It's kind of a half-assed idea at this point. But I was thinking that, by forcing identically drawn boundaries, then it would force both parties to choose.
Now that I think about it more, it probably wouldn't work. Both parties would just grab squares that guaranteed their victory. It would end up ultra-gerrymandered.
Perhaps the sizes (number of eligible voters, and also number of people who actually voted) of the voting districts follows the law? Then you could take the total vote counts, and distribute them back to the candidates in a lot of artificial ways (e.g. always 50-50, a random percentage between 30 and 70, say) and probably obtain data that still follows the law.
I think this article is more damning of a simple two-party system than it is of re-districting. How does the math change if you simply draw arbitrary boundaries of roughly equal size but have multiple parties and ranked-choice voting?
Could you use a cake slicing algorithm? I.e. you get one party to choose a fraction, and the other party chooses whether it's theirs or not, until the number of fractions is gone? Does this scale to n parties of different shares and allegiances splitting a 2d plane?
Or maybe just generate the borders with a heat map after elections with PR?
So then without making other more fundamental changes we would have to gerrymander. In fact a number of strange looking districts are gerrymandered with creating a majority minority district as the stated goal.
I believe we need structural changes to really solve this problem but absent that, I think having a computer algorithm that has the following priorities in the following order:
1) Compact (ie smallest circumference)
2) Least number of axis points and smallest difference in the sides.(ie a square is the goal)
3) Least number of wasted votes (ie use the proposal from the supreme court case)
4) Least change from a previous district (maybe not for this first run)
The author of this site seems to think that in the ideal world, districts would be decided up with clear straight lines.
This is not the case. Districts should represent distinct groups of people. Ideally, with well drawn districts, political representation will be accurate to the popular vote.
I'd recommend you all read the following article if you haven't yet.
I think if you wanted to solve districts algorithmically, you would need a neural network.
It doesn't have to entrench the political parties, depending on the system used. For example the people tasked with drawing each district could be selected from the general public by sortition, i.e. like jury duty.
These people would be given access to every tool and expert help they need, and if they wanted to just rubber-stamp the suggestion of whichever party they support, then they would be free to do so.
A slightly more deterministic process would be to generate a list of all parties (or independent candidates) who received more than 10% of the vote at the last election, and allow each of them to draw a number of districts in proportion to the share of the vote they received.
Oh I think I see. A kind of adversarial map-drawing process. You are given a fine-grained grid ahead of time and then let the parties fight over how the squares will be merged together into districts. Each side tries to draw the map to favor themselves but is countered by the adversary. Neat idea.
I like the idea of a mathematical formula for determining politicization of redistricting. I'm not sure if SCOTUS would really impose a mathematical limit to wasted vote efficiency but maybe we could use more math and technocratic solutions to political problems!
Impartial algorithmic redistricting. I wrote code to process the Census data into impartial compact districts for all the state US House districts and State Legislature districts. It's mathematically great, but politically inconvenient, but I'm proud of it.
Sometimes the randomness will work in favor of one party, sometimes against it. In the long term, it adds in some non-partisan non-determinism, which is probably good for justice long-term.
This sidesteps the question of values entirely.
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