UPDATE: Eric Neyman recently wrote about an extra assumption that I believe cleanly cuts into why this example fails.
The assumption is called the weak substitutes condition. Essentially, it means that there are diminishing marginal returns to each forecast.
The Jack, Queen and King example does not satisfy the weak substitutes condition, and forecast aggregation methods do not work well in it.
But I think that when the condition is met we can get often get good results with forecast aggregation. Furthermore I think it is a very reasonable condition to ask, and often met in practice.
I wrote more about Neyman’s result here, though I focus more on the implications for extremizing the mean of logodds.
UPDATE: Eric Neyman recently wrote about an extra assumption that I believe cleanly cuts into why this example fails.
The assumption is called the weak substitutes condition. Essentially, it means that there are diminishing marginal returns to each forecast.
The Jack, Queen and King example does not satisfy the weak substitutes condition, and forecast aggregation methods do not work well in it.
But I think that when the condition is met we can get often get good results with forecast aggregation. Furthermore I think it is a very reasonable condition to ask, and often met in practice.
I wrote more about Neyman’s result here, though I focus more on the implications for extremizing the mean of logodds.