Will Manifold implement "range" markets?

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resolved May 30

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I mean something like Metaculus where you design a probability distribution representing the value that a random variable (representing some statistic in the world) would take. It would make it easier to have questions like "How many views will the new Astral Codex post get by April?" or even "When will Kyiv fall?". In this post, I'm going to propose a way to fake it by having the user pick a range and increment, (eg. [0; 100], ∆=0.5), that way we maintain discrete bins (so {[0; 0,5); [0,5; 1), ... ,[99,5; 100]}) , and the code to calculate payouts for "Free response" questions can be used, requiring only UX changes. The way it would work is that you would design your distribution like in metaculus, and the system would buy shares based on that distribution's density for each bin, like how free response works today where you can buy shares in multiple options. The payout for X = x would be (your shares in x's bin / total density in x's bin) × pool. Since under the hood Manifold stores shares and Mana amounts with decimals, we don't have an issue with splitting up a 10 mana bet among many small buckets. One could also implement a system that allows the market maker to end with a distribution of their own, similar to ending with prob, and allocate the pool amongst those. In that case the pool for each bin would be (total density between the start and end of the bin) × pool and the payouts for each bin would be: (your shares in the bin / total density in the bin) × bin's pool. Ideally of course the developers would implement a fully continuous system, but I think it would be a lot more work for a limited advantage, as most "continuous" events tend to be rounded to discrete values anyway (like dates, times, heights, weights etc.) and this will allow for more code reüse. Feb 28, 9:50pm: @EmoftheNight I didn't really know what date to put for this tbh, so I just put till the end of the year. Mar 2, 1:45pm: TBH hopefully the admins can tell me just before they enable the feature so I can close the market and avoid anyone messing with the market too much. @danielreeves I looked into it and LS-LMSR doesn't seem like it would be any easier. If anything it would be harder because you would need to rederive alpha because in the continuous model the marginal prices at any point are zero. But I do want to make it clear, that I think a continuous system is unnecessary, and having a discrete system with small intervals would work fine. I'm just interested in it from a mathematical perspective.

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Is the current implementation of numeric markets sufficient for this to resolve positive?

I assume by market close, which is EOY.

By what date?

I'm in favor of this! Unhelpful comment: presumably it'd be easier to generalize to continuous outcomes with LMSR? Meta: Is there much value in me buying a bunch of both YES and NO to add liquidity here to encourage more discussion or anything?

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