“partial resolution seems like it would be useful” I hadn’t thought of this originally, but Nuno added the category of “Resolve with a Probability,” which does this. The idea of iterated closing of a question as the bounds improve is neat, but probably technically challenging. (GJ Inc. kind-of does this when they close answer options that are already certain to be wrong, such as total ranges below the current number of CVOID cases.) I’d also worry it creates complexity that makes it much less clear to forecasters how things will work.
Here’s how I imagine it working.
Suppose a prediction market includes a numerically-valued proposition, like if we forecast COVID numbers not by putting probabilities on different ranges, but rather, by letting people buy and sell contracts which pay out proportional to COVID numbers. The market price of such a contract becomes our projection. (Or, you know, some equivalent mechanism for non-cash markets.)
Then, when we get partial information about COVID numbers, we create a partial payout: if we’re confident covid numbers for a given period were at least 1K, we can cause sellers of the contract to pay 1K’s worth to buyers. As the lower bound gets better, they pay more.
Of course, the mathematical work deciding when we can be “confident” of a given lower bound can be challenging, and the forecasters have to guess how this will be handled.
And a big problem with this method is that it will low-ball the number in question, since the confidence interval will never close up to a single number, and forecasters only have to worry about the lower end of the confidence interval.
I think we agree on this—iterated closing is an interesting idea, but I’m not sure it solves a problem. It doesn’t help with ambiguity, since we can’t find bounds. And earlier payouts are nice, but by the time we can do partial payouts, they are either tiny, because of large ranges, or they are not much before closing. (They also create nasty problems with incentive compatibility, which I’m unsure can be worked out cleanly.)
Here’s how I imagine it working.
Suppose a prediction market includes a numerically-valued proposition, like if we forecast COVID numbers not by putting probabilities on different ranges, but rather, by letting people buy and sell contracts which pay out proportional to COVID numbers. The market price of such a contract becomes our projection. (Or, you know, some equivalent mechanism for non-cash markets.)
Then, when we get partial information about COVID numbers, we create a partial payout: if we’re confident covid numbers for a given period were at least 1K, we can cause sellers of the contract to pay 1K’s worth to buyers. As the lower bound gets better, they pay more.
Of course, the mathematical work deciding when we can be “confident” of a given lower bound can be challenging, and the forecasters have to guess how this will be handled.
And a big problem with this method is that it will low-ball the number in question, since the confidence interval will never close up to a single number, and forecasters only have to worry about the lower end of the confidence interval.
I think we agree on this—iterated closing is an interesting idea, but I’m not sure it solves a problem. It doesn’t help with ambiguity, since we can’t find bounds. And earlier payouts are nice, but by the time we can do partial payouts, they are either tiny, because of large ranges, or they are not much before closing. (They also create nasty problems with incentive compatibility, which I’m unsure can be worked out cleanly.)