The aggregation method you suggest is called logarithmic pooling. Another way to phrase it is: take the geometric mean of the odds given by the probability distribution (or the arithmetic mean of the log-odds). There’s a natural way to associate every proper scoring rule (for eliciting probability distributions) with an aggregation method, and logarithmic pooling is the aggregation method that gets associated with the log scoring rule (which Scott wrote about in an earlier post). (Here’s a paper I wrote about this connection: https://arxiv.org/pdf/2102.07081.pdf)
The aggregation method you suggest is called logarithmic pooling. Another way to phrase it is: take the geometric mean of the odds given by the probability distribution (or the arithmetic mean of the log-odds). There’s a natural way to associate every proper scoring rule (for eliciting probability distributions) with an aggregation method, and logarithmic pooling is the aggregation method that gets associated with the log scoring rule (which Scott wrote about in an earlier post). (Here’s a paper I wrote about this connection: https://arxiv.org/pdf/2102.07081.pdf)
I’m also exited to see where this sequence goes!
Nice, thank you.