With some help from demoncrat I came up with a much better weightings algorithm than the one I gave yesterday.

Simply set the weight of each node to the probability that there will be an uncompromised path from that node to an attester. This technique obviously meets the increasing confidence criterion I gave, and is much simpler and easier to analyze. I also find it much more intuitively compelling.

Unfortunately it might not be possible to efficiently compute, or even approximate, said probability. I hope it is.

A probability of compromise of 1/2 seems to square with my own judgements of graphs imagining the nodes as people I know personally.