Appendix A - Logic Check Experiment: Why Democracy Is Mathematically Impossible by Veritasium
Table of Contents
Source
Case Study: (Inadvertently) Scaffolded Prompt
🔍 Prompt
I’d like to discuss the logical quality of the conclusion of a YouTube transcript. This is the core of the argument, without conclusion:
… (Ommitted for brevity; transcript remains available on Youtube) …
Now the conclusion:
“So is democracy mathematically impossible? Well, yes, if we use ranked choice methods of voting, which is what most countries in the world use to elect their leaders. And some methods are clearly better at aggregating the people’s preferences than others, the use of first past the post voting feels quite frankly ridiculous to me, given all of its flaws. But just because things aren’t perfect doesn’t mean we shouldn’t try. Being interested in the world around us, caring about issues, and being politically engaged is important. It might be one of the few ways we can make a real difference in the world. Like Winston Churchill said, ‘Democracy is the worst form of government except for all the other forms that have been tried.’ Democracy is not perfect, but it’s the best thing we’ve got. The game might be crooked, but it’s the only game in town.”
Does the conclusion actually follow from the previous content? Is it logical? Do you detect specific fallacies?
🤖 GPT Response
The unabridged response is lost in the ether, but the exact content that impressed me, manually organized in a single table (copy/paste only), follows:
Fallacy Name Explanation in Context of the Transcript Conclusion Equivocation The word “democracy” is used in two different senses: (1) a political system of collective decision-making, and (2) a voting method that aggregates individual ranked preferences. The conclusion claims “democracy is mathematically impossible” based on the second meaning, while implying a broader political critique using the first. Category Error Arrow’s theorem demonstrates limits of preference aggregation mechanisms, not of democracy as a political institution. The conclusion incorrectly treats a limitation in one technical component as a flaw in the overall concept. Appeal to Authority / Sentiment The Churchill quote (“Democracy is the worst form…”) is invoked to justify staying engaged with democracy, but it bypasses logical argumentation. Churchill is not a mathematical authority, and his aphorism is used to close a technical argument emotionally, not analytically. Non Sequitur The conclusion jumps from “perfect preference aggregation is impossible” to “therefore, we should stay politically engaged.” This leap is not logically justified by the body of the argument, which focused narrowly on voting system mechanics, not civic virtue or political participation.