Posting here the discussion that we had with Alex and MarX.
Since our network is sharded it is possible by a sheer chance for the adversaries to have a significant voting power in some shard. Therefore, our system is designed to be robust in the situations when the adversaries have >1/3 of the voting power in some shard. However, when the adversaries have >2/3 of the voting power in some shard they can compromise the system. However, if we assume that the adversaries have less than <1/3 of the voting power across all shards then the chance of the adversaries having >2/3 of the voting power in some shard is negligibly small, as shown in the informal spec of TxFlow.
We, however, would also prefer to avoid the case when the adversaries that have <1/3 of the overall voting power gain >1/3 voting power in a significant number of shards.
The following is a small script that can be run to plot the distribution of the number of shards that would be controlled by the adversaries if they have a significant voting power: https://gist.github.com/nearmax/86cb984392749a08c0c2876d944407ec
For instance for the overall number of voting seats = 10K, number of shards = 100, and the overall voting power of an adversary equal to 25%, such adversary would on average have control (>1/3 of seats) of 2-3 shards, out of 100. The following is the plotted distribution: