How many distinct schemes are there for predicting a number on Manifold?
Two or three

Sometimes you want to predict a number but don't know ahead of time what buckets to use. Maybe you don't even know what a reasonable upper bound might be. For example, yesterday I created a market to predict how many people will follow Scott Alexander's example and donate a kidney. I realized, after it was too late for that market, that there are better ways to do it and started taking notes for future reference. Then I thought to dogfood it, which is what this market is doing. As I learn about new schemes, I'll add them to the following list.

1. Pre-decided partition

By partitition I mean mutually exclusive and exhaustive buckets. This is what I did in the kidney market. There's technically an "Other" option but it's impossible to be chosen unless the answer is somehow a negative number or something. (It just now occurs to me that technically/theoretically that is perfectly possible!)

2. Overlapping thresholds

Use thresholds for the answers and allow them to overlap ("any number of answers chosen"). Then you can start with a guess at the median and make two answers, e.g., "less than 10" vs "10 or more". For every answer that has enough probability mass to be interesting, refine it by adding a new answer. Maybe you end up with "less than 10", "10 or more", and "100 or more". If the final answer is, say, 200 then both "10 or more" and "100 or more" are chosen as correct. HT @JamesGrugett

3. Branch from "Other"

That's what this market is doing! Stick to "only one answer can be chosen" but keep branching off from the "Other" option. So start with just "One" (or "Zero" if that's a possibility) and "Other" and see how the probability mass gets apportioned. Add new options as desired, always keeping them mutually exclusive and exhaustive. HT evanbd on the Manifold Discord.

4. Remap [MIN, MAX] to [0,1]

Make a standard NO/YES market and resolve-to-PROB based on where the outcome falls between MIN and MAX, interpolating linearly.

Resolution Criteria

I plan to only add new schemes on the Pareto frontier. In other words, if there's no possible scenario where anyone could prefer a proposed scheme to the ones already on the list, then I won't add it. If a proposed scheme is a special case of an existing one then we'll argue about it in the comments. For example, scheme 1 above is in some sense a special case of scheme 3. But unless I hear a good counterargument in the comments, I'm deeming it to deserve a distinct place on the list as a baseline scheme that a normal person would think to use. This is based on my own judgment. Pointing to a real-world use of a scheme on Manifold will probably convince me. The goal is to make a useful list. Only things that actually work on Manifold by the close date count.

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It just now occurs to me that Manifold could (and maybe should!) introduce a new numeric market type that subsumes all of these. Then the answer could end up being 1!

bought Ṁ20 of Other YES

Oh ho, I just learned that there's a pseudo-numeric market type not available via the UI but available like so:{"q":"Template+for+a+numeric+market","closeTime":0,"description":"{\"content\":[{\"type\":\"paragraph\"}],\"type\":\"doc\"}","outcomeType":"PSEUDO_NUMERIC","visibility":"public","min":100,"max":1000,"initValue":500,"groupIds":[]}

But turns out there are good reasons that that's not available in the UI:

Will Manifold remove numeric markets within a week?
Resolved YES. Manifold's current implementation of numeric markets allows users to bet on a scalar value within a numerical range. Under the hood, it operates using the same mechanism as a binary market, with the low and high points of the range mapped to 0% and 100%, respectively. Many of our users have reported being confused by numeric markets, in particular by the concept of HIGHER and LOWER shares, the fact that you can only bet within a given range, and the low payouts that result if there isn't significant price action. Given the added complexity to our platform, we're wondering if we should scrap this type of market entirely. This market resolves YES is we remove numeric markets as a choice from the "create a market" page at any point within the next 7 days. (We almost certainly won't remove or delete existing numeric markets, regardless of what we decide, at least until they've resolved.) You can influence this market by posting your thoughts below! Resolution I have decided to remove numerical and multiple choice markets from the create page. (This decision is not necessarily final and may be reversed.) While there is clearly demand for markets on scalar values, our current implementation is a poor experience for everyone and a source of confusion for newer users. Removing numerical markets as an option pushes users to create binary markets, which is a much better experience for traders (as evidenced by the higher trading volumes and fewer complaints). We are actively considering reworking numerical markets and hopefully will introduce a new and improved form in not too long.

Ah, I immediately regret putting "open-ended" in the title. Because there's a useful scheme for the case that you do have clear bounds: Use a standard NO/YES market and resolve-to-PROB with a renormalization.

I think that deserves to be on the list. Since no one has traded yet, I think I'll go ahead and edit the question! [And done.]

I think off the bat we have 2 as a lower bound, even if schemes 1 and 3 are deemed non-distinct. But I'm inclined towards 3 so far. I have no idea if any additional schemes will be proposed!