Will Manifold Markets/Metaculus have built-in support for reflective latent variables by 2025?post by tailcalled · 2022-12-10T13:55:18.604Z · LW · GW · None comments
Prediction markets and similar systems are currently nice for soliciting predictions for outcomes where there is a clear, unambiguous objective resolution criterion. However, many phenomena in the real world are hard to directly observe, but tend to have multiple indirect indicators. A familiar example might be aging/senescence, where you have indirect indicators like muscle weakness, gray hair, etc. that someone is aging, but you do not have a directly observable Essence Of Aging.
There exists a type of math which can be used to statistically model such variables, called reflective latent variables. There are a number of specific implementations for specific contexts (factor analysis, latent class models, item response theory), but they are all mostly based on the notion of having several indicator variables which are supposed to be independent conditional on the latent variable.
Essentially, a prediction market could implement this by allowing people to create questions with multiple resolution criteria, and allowing people to make correlated predictions over those resolution criteria. Then people could be scored based on their overall accuracy across these resolution criteria. If sufficiently many correlated predictions have been made, people might not even need to have specific opinions on the resolution criteria, but might just be able to bet on the probabilities of the abstract latent variables, and have the market infer what the corresponding bets on the resolution criteria would look like.
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