Collective Epistemics: Napkin Math on Independent Errors

Part of a larger series I want to put together on some of the basic equations and models of collective epistemics from the more mathy side of the social sciences. LLM Status: Pictures + Picture descriptions are LLM-assisted. Introduction Today we're going to do some napkin math on some fun little equations around collective epistemics. You can see this as an exercise in trying to become more collectively rational. If we want to improve the epistemics of a community, is that the same thing as improving our own? How much should you explore versus exploit, given the role you have and the community you're in? These are all good questions that I probably won't answer today. Instead I'll give you an introduction to some of the math behind the jury theorems, plus a hodge podge of simpler, approximate collective intelligence theorems. We’ll then talk a little bit about tape readers, model selection and finally antifragility. See it as a somewhat coherent buffet of different things within collective epistemics all pointing towards how it is likely better for you to create an inside view of a field compared to just delegating it if you care about the epistemics of the field you are in. Shared outside views can become an inside view The first move is to look at ourselves as a collective agent. Condorcet's Jury Theorem says that if you have n voters, each with probability p > 0.5 of being correct, and their errors are independent, then as n grows the probability that the majority is cor…