Math Exposition on YouTube
dustingmixon.wordpress.com
dustingmixon.wordpress.com
Solve problems. Prove things. Etc.
The visual walkthrough of their proof was elegant in its exposition.
I understand the humor makes it more fun to work on and self effacing, but you hooked me with this novel tool to analyze political districts, and rather than process all of them and report on the findings, it was merely used to “own the libs”?
Are all the claims of gerrymandering false based on this metric?
What happens when you change the 40% for the minority metric?
I guess I discovered I would rather dwell on the abstraction of “arbitrarily extreme constants”.
I think my preference would be districts defined by geographic features and boundaries paired with a different set of elected officials determined by the type of proportional representation without any limits on geographic boundaries.
This is true but then there are other buckets as well. Why should location be the only organizing principle, when we know there are a bunch of concerns that aren't tied to it?
Why not have virtual districts across dimensions? You get a vote for your birth year cohort, a vote for your geographical district, and a vote for your income bracket group. Parliament will be this weird 3D set of people chosen to represent various interests.
Or we just do proportional representation. I find it hard to justify FPTP, it causes wild distortions.
But you should, since proprortionality as a property has strong evidence of being practically producing better piblic satisfaction with government, as well as having a strong theoretical argument for being the best measure of the degree to which a “representative” body actually is representative.
> Approval voting and score voting look especially good and they wouldn't require a change to the constitution.
Approval voting and score voting look especially bad for public elections in a multicultural society, since they call for abstract ratings that where there are well-established cultural variations in assignment for the same actual sentiment, and treat them as having consistent meaning.
And rough PR in the House (e.g., by STV) doesn't require a Constitutional amendment, either, only a statutory change.
and besides, you won't get PR at any scale beyond a handful of cities without first escaping duopoly, which requires score voting or approval voting as a prerequisite.
Proportional representation isn’t a method, its an axis of measurement, and there is very good evidence that better performance on that axis produces better outcomes in terms of satisfaction with government among the citizenry.
There is neither evidence nor even a theoretical reason to think that what you call “good” single winner methods (which are “good” only by abstract mathematical criteria only applicable to single-winner methods which themselves have no empirical link to good outcomes, and which make assumptions like that ballot markets have some consistent meaning across voters that are known false for the kind of rating systems they use) either would in practice perform good (or even better than FPTP) on that measure or defy the observed relation of that measure with satisfaction.
> and besides, you won't get PR at any scale beyond a handful of cities without first escaping duopoly, which requires score voting or approval voting as a prerequisite
This first part of that sentence is a ludicrous claim offered with no support. If you mean “you can't establish a better voting method without buy-in from those elected under the current methods”, that’s false in any jurisdiction with citizen initiatives (as many US states have). Whether states adopting this can be sufficient to create political pressure to negate the problem on a national basis is... well, that's certainly a question.
If you mean “no matter what voting method you adopt, it won’t produce very proportional results as long as there is an existing duopoly for incumbent officeholders in the same body”, perhaps because of some kind of partisan/media momentum effect, then there is probably a kernel of truth there, in that it will probably take more than one electoral cycle to transition to producing results close to the natural degree of proportionality of the new voting method if it is radically divergent from the former one, but that's a frictional effect, not a binary switch.
The second part, though, is even worse. There is neither evidence nor even a good theoretical argument to suggest that there is some scale where you can’t get from FPTP to something producing more proportional results without the first step being score or approval voting. And your link provides neither evidence or argument on this point, only the bare claim that the author(s) “very much doubt you are going to get it” without range (i.e., Score) voting (apparently rejecting your claim that Approval is viable) as a “preparatory step”.
How it is supposed to work is that 50% of representatives are 'local' representing a region (of roughly 300.000 people) and the remaining 50% of representatives ensure proportionality.
So, imagine the CDU (centre-right party) wins 40% of the voting share, but 60% of the seats, the SPD (centre-left) 30% of both voting share, and seats, the Greens 20% of the share but only 10% of the seats, and the FDP 10% of the share and no seats. The seats to ensure proportionality would be distributed 20%, 30%, 30%, 20% respectively.
There are a lot of subtleties to the system to ensure true proportionality that I won't go into right now, and tend to lead to the parliament growing (if things work perfectly there should be 598 seats, but currently there are 736), but broadly the system works.
In proportional representation it is still possible to vote for a local candidate, depending on how it is organized. Voting for a party is the common thing, but allowing people to vote explicitly for a candidate lower on the list allows getting a local candidate straight into parliament. Not that that is ideal, but it is definitely not impossible.
Nobody cares how districts are shaped when there is no advantage in having them shaped a certain way.
I think the US system is undemocratic as it fails on some very fundamental levels to assure representation that honors the voter's will.
Yes, it would make much more sense to define the districts by any of various obvious methods and then not worry about whether they have equal population.
but it bothers me that the solution to this problem is to redraw voting districts. and for a while i could not figure out why or what to do about it, but then i wondered, why not simply have multiple representatives for each district. say a dozen or so. that way there is enough room for each minority to be proportionally represented by candidates of their choice.
to make it more interesting, give each voter more than one vote, up to the number of representatives. then you add up all the votes and pick the top 12.
make the districts larger or add a second layer of voting to keep the total numbers of elected representatives down. with a second layer all elected would again elect a smaller number amongst themselves again allowing minorities to be represented.
There's no reason the 60% should have thier will ignored just because thier votes are split between two or three parties and the remaining major party ekes out an extra 5-10% of the population than the next highest voted candidate (see canada for exactly this happening).
Each person should also be able to have thier will about a bill included in the voting at any time instead of having to hope whoever you voted to rep you actually does what they said let alone what you want.
That's way more important than the issue of districts (though that is an issue needing addressing its just not remotely as impactful in both the short and long term).
So what? FPTP is objectively the worst voting method, across pretty much all metrics (others may do slightly worse at local representation).
Also, proportional representation is a class of voting methods (my personal preference being STV).
Maybe this submission can use a more specific title? Referencing the topic -- the math behind ugly voting districts / gerrymandering.
i've got nothing to do with anything related to math but i really want to find a niche topic to delve into detail just to join in the sharing.
As an example: One that stuck in my head from decades ago was solving the Fibonacci recurrent relation. At some point the professor wrote down “r^n” and somehow “r^2 + r + 1 = 0” shows up.
When asked where r^n came from he said it was just a guess. When asked how or why not guess something completely different, he said “that’s how we solve these problems”.
And that was that. Nobody in his class understood this and myriad other areas in math where the answer seems to be “and then a miracle occurs”.
There are many YouTube math teacher who are massively better than most university (and below) instructors. My guess is this is because they actually love what they do.