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Why Democracy Is Mathematically Impossible

VeritasiumCited 6× on HN, 2024-2026
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10.1M views · 2 years ago · explainer · evergreen

Veritasium explains why no voting system can be perfectly fair, drawing on Arrow's theorem and the work of Eric Maskin. It looks at problems with systems like first-past-the-post and ranked-choice voting.

Linked when someone needs a quick accessible source for the claim that every voting method has flaws.

Probability & game theoryPure mathematicsUS politics & elections#arrow'stheorem#votingsystems#rankedchoice#socialchoice#democracy

6 comments from Hacker News

@perching_aix2026 · in “U.S. exempts oil industry from protecting Gulf animals, for 'national security'”

There is actually extensive mathematical history to fair voting, the output of which is super not in use, and of which I do find plenty of the alternative systems more representative: ▶ this video I do think regular variety elections are generally representative though. I just also see value in keeping these asterisks in mind.

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@alecco2025 · in “Want to sway an election? Here’s how much fake online accounts cost”

Yeah. It's complicated. See Veritasium's "Why Democracy is Mathematically Impossible" ▶ this video And also Idiocracy. This one is becoming more relevant. In all countries and all races.

CitesView on HN
@thisisit2025 · in “EPA tells some scientists to stop publishing studies”

FPTP is bad but other methods are similarly flawed: ▶ this video Keeping a democracy requires people to understand it as well. At least in US it seems they'd rather elect a dictator wannabe who clearly said he wanted to be dictator for a day than elect a woman.

CitesView on HN
@perching_aix2025 · in “EU age verification app to ban any Android system not licensed by Google”

> EU citizens voted for this. I'm growing pretty tired of this rhetoric / rhetorical sleight of hand, but maybe this is a reasonable opportunity to discuss it: - not all citizens of a jurisdiction are eligible for voting: in this case, cursory search suggests only 400M (88.8%) of 450M were eligible - seems a bit too high to me, but let's roll with it regardless - not all who are eligible actually vote: voting in the EU parliamentary elections, which is what EU citizens can actually vote on, like most elsewhere, is not mandatory; it's a right, not a duty: turnout was 50.74%, and that is of the eligible population, so really just 45.1% (203M) - most voting systems are mathematically unfair [0]: extensively researched, doesn't quite apply necessarily in this case though as per the next bit - several key positions in the various bodies are elected indirectly: same here in the EU, at which point all bets are off - laws, regulations, and policies are not voted for or against by citizens: same here in the EU too, nobody could have even possibly voted for this in the literal sense It's a run of the mill representative system and I think it'd serve discussions a great deal if this was acknowledged properly. Surely it's agreeable at least that this wouldn't be such news if people were all just completely on board as the sentence "EU citizens voted for this." implies when read naively and literally. I really don't see a point to this phrase other than inciting others. And before anyone

CitesView on HN
@perching_aix2025 · in “Britain's police are restricting speech in worrying ways”

I'm not so sure if putting down a vote for one candidate over many others every few years suffices as democracy though to begin with. [0] [0] ▶ this video

CitesView on HN
@slowmovintarget2024 · in “Megastudy testing 25 ways to reduce antidemocratic attitudes, partisan animosity”

The Pollyanna view of ranked-choice voting presented on TV doesn't really work out in the real world. Veritasium video on voting systems: ▶ this video link

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