A potential downside is that markets about markets are generally easier to manipulate than markets about ground truth. You may even find that second-order markets create an incentive to distort first-order markets to an extent that makes the existing markets less reliable.
I think that higher-order markets definitely make things more complicated, in part by creating feedback loops and couplings that are difficult to predict.
That said, there are definitely a few ways in which higher-order markets could potentially make markets more reliable.
My guess is that useful higher-order markets will take a lot of experimentation, but with time, we'll learn techniques that are more useful than harmful.
Another simple type of 2nd order forecast is "What will [Forecaster]'s forecast be on [Date]?"
In addition to the links I provided in the other comment, people might be interested in reading about a small competition I ran on Manifold last year which tries to capture exactly this "surface correlations" concept.
Executive summary: Higher-order forecasts, which are forecasts about lower-order forecasts, could improve the efficiency and information aggregation of prediction markets and forecasting systems, analogous to the role of derivatives in financial markets.
Key points:
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Higher-order forecasting could be a useful concept for prediction markets and forecasting systems more broadly.
The core idea is straightforward:
Nth-order forecasts are forecasts about (N-1)th order forecasts.
Here are some examples:
0-Order Forecasting (i.e., the ground truth)
1st-Order Forecasting (i.e., regular forecasting)
2nd-Order Forecasting
3rd-Order Forecasting
As forecasting systems mature, higher-order forecasts could play a role analogous to financial derivatives in markets. Derivatives allow for more efficient pricing, risk transfer, and information aggregation by letting market participants express views on the relationships between assets. Similarly, higher-order forecasts could allow forecasters to express views on the relationships between predictions, leading to a more efficient and informative overall forecasting ecosystem.
Some potential benefits of higher-order forecasting include:
We've already seen some early examples of higher-order forecasts on platforms like Manifold Markets. For example, with the recent questions:
Of course, there are also challenges and risks to consider with higher-order forecasts:
I considered a few options for names, asked around a bit, and settled on "higher-order" for this term. Here are some other options I considered:
If there's contention on this later, it could be useful to have some formal discussion, to make sure that we share consistent terminology. Right now, I doubt many people care about it.
Over time, I expect higher-order forecasts to go from a niche idea to a key component of mature forecasting systems. Just as financial markets would be far less efficient without derivatives, forecasting platforms could see substantial accuracy and liquidity gains from higher-order forecasts.
An application I was expecting you to mention was longer term forecasts. E.g. if there was a market about, say, something in 2050, for example, the incentives for forecasters are perhaps less good, because the time until resolution is so long. But a "chained" forecast capturing something like "what will next year's forecast say" (and next year's forecast is about the following year's forecast, and so until you hit 2050, when it resolves to the ground truth).
This assumes that forecasters are less effective when it comes to markets which don't resolve for a long time.
Good point.
I think this sort of use case is very important. I think that this problem is probably better addressed with other methods rather than straightforward sequences of separate questions, but I imagine the latter will occasionally be useful as a solution.
I've also been thinking about this use case recently. I think I like the term "progressive" forecast, but I'm curious to get more takes!
Readers of this comment thread might be interested in this blog post from Johnathan Mann and this followup, where this concept is called "iterative markets".
I did find that interesting, thanks for the links!
What other methods do you have in mind for it?
You can imagine strategies like,
"There's just one question. However, people will get paid out over time, if the future aggregate agrees with their earlier forecasts. These payments can trigger at arbitrary times, and can feature a lot of flexibility regarding how far back the forecasts are that they reward."
The effect is very similar to doing it by formally having separate questions.
(I'm sure many would consider this a minor difference)
In principle, normal markets should work this way. That is, if there's a market that won't settle for a year, but you think next week the price is going to go up a bunch, you will want to buy it now, and then sell it when the price goes up. If lots of people do this, the price goes up now, instead of next week (and in fact, if everyone saw that coming, it went up last week instead, and so on). If the market is reasonably liquid and/or there are market makers, you're not committing yourself until settlement, you can just sell out of your position when the price corrects (or when you give up on it doing so).
If, on the other hand, the market is not reasonably liquid, then I don't think iterated markets fix your problem, because people don't have a strong reason to expect the next market forecast to match the actual probability, so they can't profit by trading on that basis.