Higher-Order Forecasts

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I think 0th-order, 2nd-order and 3rd-order forecasting should be called threecasting, fivecasting and sixcasting respectively. This easily lets speakers differentiate between layers; also, imo, names which are bad puns tend to stick.

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.## Examples

Here are some examples:

0-Order Forecasting (i.e., the ground truth)1st-Order Forecasting (i.e., regular forecasting)2nd-Order ForecastingWhat is the chance that a Republican will win the 2028 Presidential Election?” was posted to Manifold, with a subsidy of 100k Mana, what would the prediction be, after 1 month?”3rd-Order ForecastingHow many forecasts will the question "What will be the GDP of the US in 2024?" receive in total?’]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.

## Benefits

Some potential benefits of higher-order forecasting include:

Identify Overconfidence"How overconfident is [forecast/forecaster] X"Prioritize Questions"How valuable is the information from forecasting question X?"Surface Relationships"How correlated will the forecasts for questions X and Y be over [time period]?"Faster Information Aggregation"What will the forecast for question X be on [future date], conditional on [other forecasts or events]?"Leverage Existing InfrastructureWe've already seen some early examples of higher-order forecasts on platforms like Manifold Markets. For example, with the recent questions:

## Challenges

Of course, there are also challenges and risks to consider with higher-order forecasts:

## Alternative Names

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:

Derivatives:In the financial market, "markets about markets" are called derivatives. However, "derivative" is often understood as a term specific to markets, which could make it more confusing for forecasting.Meta-forecasts:I used this term before. It's a catchy term, but it doesn't differentiate between layers easily. There's no straightforward way to refer to "meta-layer 1."Higher-Layer:Similar to "higher-order," but less precise.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.

## Conclusion

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.