@tom My usage is based on empirical results, geometric mean of the probabilities for ensembling predictions from a NN has produced better results for me on many occasions.
I searched for theory once, as the intuition didn’t sit well, especially when thinking about the case when one ensemble member has a near 0 output. In practice though, it works. I suppose a ‘try both’ answer might be more appriopriate.
In my theory search, the papers that provided some insight in the context of NN were about dropout

https://arxiv.org/abs/1312.6197 8
http://papers.nips.cc/paper/4878-understanding-dropout.pdf 7