Contrary to my initial
upthread enthusiasm, I am leaning towards this DAG concept can not work because it appears to attempt to defeat the CAP (Brewer's) Theorem. Before I was thinking the multiple branches are orthogonal, but it becomes clearer from the game theory issues quoted above, that there are complex dependencies. Analogous issues as the following appear to apply to DAG:
Hard to tell what you mean without knowing what you have sacrificed - C, A or P.
For example to deal with the double-spend attack stdset has been discussing, to maintain consistency and access you must do something to "fence off" partitions (branches) and give up P.
The block chain creates one partition which is the longest chain. Thus it can maintain C and A. You will have to give up one of C, A, or P. The promise of DAG was to not give up any of those.
I think you can make DAG work but you will end up with divergent partions that can't be remerged (thus losing global consistency of value), same as what will happens to Bitcoin if it is forked (even by network partitioning).
This is a serious fundamental theorem that all of us designing consensus algorithms face.