The Topological Problem with Voting

When your favorite tool is a topological hammer, every problem starts to look like a higher dimensional nail.

I reckon continuity is broken since the elction outcome is discrete and not a dense space. That means the function cant be continuous

Not sure how continuity makes sense as a requirement. At a certain point, there has to be a discrete winner, and so there MUST be a point at which flipping one vote will change who/which set of candidates wins, and that just makes sense.

"We don't care about the magnitude of someone's opinion" goes so hard

I like how you delivered "here's a big twist" without fanfare and carried on as if it wasn't amusing or planned.

I would be honored to have my opinions mapped to a topological space

10:00 "I personally think that the most likely condition to fail is continuity".  Theoretically, I think you're right: pragmatically, I think the most likely condition to fail will be that the ballots are of the form "Pick a point on a circle".

I find it ironic that video about voting in two party system emerges to be about a shape with one side.

Yes! When I first saw your Möbius strip synth I knew you'd be able to do something really cool with my Synth-a-Sette. Thanks for making with MicroKits!

This video is kinda unique

2:04 "it is one of the most unexpected uses of a mobius strip, and here's the big twist" XD

I actually think the most likely condition to fail is 'ordinal voting'. If you have only two voters with exactly equal and opposite preferences, the optimal election result would be no change at all, rather than a change in a completely orthogonal direction.

Assuming continuity of results is so flawed it's hilarious. "The result of the vote is that we want 11% of candidate A and 89% candidate B" "Sir, that's... not..." "MAKE IT WORK"

I saw a Google Tech Talk about this years ago and somewhat understood it. They also went into details about which voting systems broke which fairness principles. But I have to say your topological explanation makes more sense and I think the reasoning will stick with me longer. Alas, I still can't properly explain it to people at parties. Unless I carry around props.

Never thought I'd see a video on the physics of voting

I was so distracted by the anthem played on a two-axis keyboard that I had to replay the intro multiple times! Such a great execution of an odd concept!

At the part with the two "ch" sounds in a row I noticed you pronounce "ch", "dj" "sh", "zh" in a completely different way than most people. I think your "sh" is a voiceless velar lateral fricative, with "zh" being a voiced velar lateral fricative, "ch" a voiceless velar lateral affricate and "dj" a voiced velar lateral affricate. I think they all have audio files on Wikipedia. For the common pronunciation of these you can swap "velar lateral" with "postalveolar" or "postalveolar sibilant", those also have audio. Cheers

The continuity cannot be met: The output will always switch from option A to B directly, discontinuous. You could have 1000 votes on A, and 1000 votes on B, and then just adding 1 vote is enough to select either A or B - the last vote will always have a lot more weight. To solve that your system would need to be able to output 49.5% A + 50.5% B. Some voting systems do this by assigning seats, but because the output is still an integer number and not a full real number, it would still not be continuous.

Perfect timing! I just watched every video on this channel a couple days ago.

I came here expecting a discussion of the topographical analysis of voting. With some conclusion being along the lines of "put your polling center at sea level or lower to get the best turnout for your district. Nobody wants to go uphill to vote."