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RobinZ comments on Less Wrong Polls in Comments - Less Wrong
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That makes sense - I had imagined doing something similar, but I had never heard of Dirichlet priors.
Happy this helped. The Dirichlet-multinomial model gets relatively little attention because it adds nothing really new to the beta-binomial model for polls with just two responses. It's easy to find lots of introductory, chatty introductions to the beta-binomial like this one or this one if you want to learn more...