The geometric mean gives 0 an advantage over 1, which makes it not symmetric in general. If we trust EY and NB the same, then f(p,1-q) should equal 1-f(q,1-p) (in both cases, one person thinks they get p of the dollar and the other thinks they get q.)
Your variant of 2 does not satisfy this, which I think is the feature I think is the most important.
The geometric mean gives 0 an advantage over 1, which makes it not symmetric in general. If we trust EY and NB the same, then f(p,1-q) should equal 1-f(q,1-p) (in both cases, one person thinks they get p of the dollar and the other thinks they get q.) Your variant of 2 does not satisfy this, which I think is the feature I think is the most important.