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Ah yes my favorite authoritative source on the mathematics of democracy: a YouTube video.
Fuck off
Veritasium is legit, they cite their sources and explain concepts exceptionally well.
However, I don't think the conclusion of the video is "Democracy is mathematically impossible", but rather "perfect representation in a democracy" is mathematically impossible (but can still be much much better than FPTP).
The video basically goes through all the top voting systems and explains their pros and cons and the history of the mathematicians who invented the systems.
It's not even that. The more accurate title would be "Ranked voting types cannot mathematically meet all of the requirements of democracy this one guy made"
The whole video I wanted to yell out "so switch to approval voting".
The dude makes some pretty legit videos. He has a PhD in physics education research. Using YouTube is just a sign of the time we live in. Imagine if your professor quit their job to become a YouTuber because they thought it'd be a more effective medium for education than a whiteboard.
Mathematics is, in a sense, about abstraction and generalization, and the video covers an ideal, or set of axioms, you'd want from a voting system. This perfect system was proven to be impossible and the researcher was granted the Nobel prize in economics. In short, there can be no perfect voting system, and we must accept a compromise (much like an engineer). You can also say mathematics is about proofs, and, no matter how unintuitive something might seem, it leaves no room for doubt. It doesn't hardly matter if the source comes from a YouTube video.
Edit: I don't agree with the context the video was posted, but I was bothered by this response to it.