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Notes -
Expected accuracy gain = number of viewers * probability of changing each viewer's mind * (probability the change was in the right direction - 0.5)
Performance during a debate is correlated with being correct, and having enough knowledge to know what you're talking about, and being founded on logical arguments rather than made up nonsense that breaks down immediately upon being confronted. It is weakly correlated with these things, which take a supporting role to charisma and public speaking skills, but they exist as a non-negligible part of the equation. Therefore, we expect the (probability the change was in the right direction) to be higher than 0.5 in most cases, though there can be exceptions for certain topics where the correct side is inherently difficult to understand or explain in a short time frame, or superficially distasteful despite being right if you deeply understand it.
And many more people are going to watch public debates and care about them than about written debates. Most people don't read on purpose. Many people are barely literate at all. And they and their opinions still matter, and persuading them is important. So a debate with a 70% chance of the correct side being more persuasive with 1 million views and a 5% chance of actually changing viewers' minds accomplishes more good than a debate with a 99% chance of the correct side being more persuasive with 100k readers and a 1% chance of changing each one's mind. As an individual, you're more likely to come away with accurate knowledge if you put forth the effort to read the thorough written arguments. But as a persuader you'll get more total support if you have the charisma to put forth entertaining and persuasive debates that more people will actually care about.
I intuitively understood this although I didn't put numbers on it. My point is more just that I'm surprised more people don't talk about how written debate would be better and more prestigious, like how people talk about books are usually regarded more positively than movies even if movies get way more actual views.
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