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it’s even weirder than this - theoretically the accuracy of a poll depends only on the size of the sample in absolute terms, *not* relative. a 1000-person poll has the same predictive power no matter how large the population it’s drawn from is!

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Tim Urban

@waitbutwhy

· May 2

I used to wonder how polls that surveyed less than a percent of a population could claim to represent the views of the whole population. Running twitter polls has helped me understand. It’s amazing how well the first 300 votes predict the results after 20,000 votes.

QC (in Berlin 7/29-???)

@QiaochuYuan

May 2

what makes it all work theoretically is the assumption that you’re sampling uniformly randomly which is a very strong assumption that lets you make correspondingly very strong conclusions

QC (in Berlin 7/29-???)

@QiaochuYuan

May 2

the simplest toy model is to think about drawing, say, red or blue balls uniformly at random out of a very large bag, and computing what you can infer about the true proportion of red vs. blue balls by drawing N balls. good bayes theorem exercise

QC (in Berlin 7/29-???)

@QiaochuYuan

twitter polls obviously can’t claim to be doing this but as a poll percolates through RTs, likes, etc. you can think of its respondents as coming from a sort of random walk on the twitter network, and there are theoretical results about how well these sorts of walks “mix”

11:39 PM · May 2, 2022Twitter for iPhone

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· May 2

early results suggest that 4 out of 5 tweeters are double digits daily checkers

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The true random sample is increasingly impossible. Had its short heyday when landlines were ubiquitous. Now it's impossible with cell phones

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the shape of the graph is going to determine the sampling probabilities for each user they won't be uniform maybe it'll be the perron vector for the random walk, like pagerank