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.
This question resolves positively if (in tailcalled's judgement) Manifold Markets has added support for latent variables by the start of 2025.
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Created a mockup of how latent variable markets could function: https://files.onlinetests.me/lvar.html
This is just a hypothetical; some parts were simplified because I don't have a whole UI toolkit setup, and it might also make sense to deviate from my vision if a designer has better ideas. However it might be a start that makes it easier to understand for people who aren't familiar with the concept.
@Gurkenglas Interesting solution. Adding sandbox markets might be sufficient to implement my favored kind of latent variable system, and if the API for sandbox markets is easy enough to use, I might even implement latent variables myself using it.
Though I think one essential feature of latent variables would be that people should be allowed to bet directly on the distribution of the latent, and part of how that would be implemented would be through some corresponding bets on the criteria. (This wouldn't be all of it, there would also be some LV-specific aspects to betting on the latent.) So sandbox markets would have to somehow support using some of the Mana to bet on downstream markets in order for LVs to work.
I should probably clarify the resolution criteria in the light of sandbox markets. I would be inclined to take the current phrasing literally and say that me using sandbox markets to implement latent variables on another site does not automatically resolve the market positively, but if I make an implementation and it gets integrated reasonably seamlessly into the Manifold UI, the question would resolve positively, even if there are some technical reason why it is strictly speaking separate (e.g. if latent variables are still a separate server/codebase that I host, but Manifold has seamless links to my server in the market-creation process, that would count as positive for the purpose of this question).
@yaboi69 Kind of.
But at least in the way I imagine it, you will not just be able to bet on the latent variable, but also on the connection between the latent variable and the indicators.
So for instance you could imagine a "who's winning in Ukraine" market that has indicators like control over various cities, concessions made by either side in negotiations, war deaths, etc.. And then maybe some document is leaked which shows that Russia is super duper determined to get Crimea. In that case maybe you'd make a bet that regardless of who wins overall, Russia will get Crimea, so Crimea might not be a good indicator of the rest of the war.
@tailcalled I see. So potentially a whole pile of markets each boiling down to "estimate P(Y|X)” (“Conditional on losing Crimea, will Russia lose the war”) to tie a complex model together in examples like the one you gave. Provided together in UI as an intermingled package.
@yaboi69 Almost. You would be estimating P(X|Y) ("conditional on losing the war, Russia will lose Crimea"), not P(Y|X). Here Y ("Russia loses the war") would be an abstract variable whose meaning is determined as being whatever correlations the Xs have in common.
If you want to look at the fornal math, I recommend you look up latent class models.
@yaboi69 Oh and there would also be an unconditional market on P(Y) (that is on "Russia will lose the war"). The scoring of predictions on P(Y) would be determined by the P(X|Y) markets (since it can't be determined directly because Y is abstract).