1. How open are various decision-makers to actually paying attention to forecasts? 
2. How likely are they to just make the same decision anyway, referring to forecasts when they justify this decision and ignoring them the rest of the time? 
3. How does this vary for different decision-makers and contexts (e.g., politicians vs civil servants vs funders vs business leaders)? 
4. How does this vary by different approaches to forecasting (e.g. those surveyed by Beard et al.), different presentations of forecasting, and different topics? 

I’m guessing a good amount of research will have already been done on these topics, but I’ve been surprised about such things before.

I imagine these questions could be answered through a mixture of: 

• surveys of relevant people
• lab experiments
• interviews with people who’ve tried implementing forecasting in relevant settings
• literature reviews of potentially relevant work in political science and political economy (e.g., on kinds of info are drawn on in political decision-making more generally)
• probably also other approaches

It seems plausible that these sorts of questions aren't as well answered by academic research as by people just actually trying to implement forecasting in relevant institutions, get relevant decision-makers to pay attention to forecasts, etc.

(This is one of my own ideas about a cluster of questions that might warrant academic/academic-style research. I’d be interested in people’s thoughts on this cluster and the cluster I suggest in a different comment, including regarding how important, tractable, and neglected these questions are.)

Not really answering your question, but there is some recent work attempting to forecast clinical trial results that may be relevant: Can Oncologists Predict the Efficacy of Treatments in Randomized Trials? Kimmelman (the senior author) is doing other work on the topic too (e.g. here). I'm not aware of much published work in this space in a biomedical context. 

My guess is that key decision makers in medicine (e.g. funders of trials), would not be very open to paying attention to forecasts (even if shown to be accurate to some degree), as there is a very strong culture of relying on data and in particular on RCTs. 

Greenberg 2018 lists and evaluates forecasting scoring rules. Research on additionally more complex metrics that take into account e.g.:

• importance of the questions forecasted on (perhaps using an interest score such as Metaculus)
• number of questions forecasted on (brier score distorts if only few forecasts)
• relative performance as compared to other forecasters on similar sets of questions

Might be useful to set incentives right in forecasting tournaments. Prediction markets solve the first point by logarithmic subsidising.

1. How does the resolution and calibration of forecasts vary by the forecasts’ “range” (e.g., whether the forecast is for an event 6 months away vs 3 years away vs 20 years away)?
2. How does this vary between topics, types of forecasters, etc.?
3. Do people who are superforecasters for short- or medium-range questions (e.g., those that resolve within 3 years) still do better than average for long-range forecasts?
4. Are there approaches to forecasting that are especially useful for long-range forecasts? (Approaches that could be considered include those surveyed by Beard et al.)
5. All the same questions, but now for “extreme” or “extremely rare” vs more “mundane” or “common” events (e.g., forecasts of global catastrophes vs forecasts of more minor disruptions).
6. All the same questions, but now for forecasts that are long-range and about extreme/extremely rare outcomes.

Background for this cluster of questions: How Feasible Is Long-range Forecasting? 

One rationale for this cluster of questions would be to improve our ability to forecast global catastrophic and existential risks, and/or inform how we interpret those forecasts and how much weight we give them.

This research could use very similar methodologies to those used by Tetlock, just with different forecasts. However, a very important practical limitation is that the research may inherently take many years or decades.

(This post says "Fortunately, we might soon be in a position to learn more about long-range forecasting from the EPJ [Expert Political Judgement] data, since most EPJ forecasts (including most 25-year forecasts) will have resolved by 2022". This might reduce the marginal value of further work on this, but I imagine the marginal value could remain quite high.)