The Raiblocks crypto currency approaches the DCS challenge by a couple of mechanisms. (ps: This is my reading of it, which may be wrong, see the RaiBlocks white paper for the details and the correct view)
Instead of a single block chain, each coin holder maintains their own chain, and only they may write to it (as verified by public key)
Each account assigns a representative to vote for them when a conflict arises between accounts.
The representatives are weighted by Proof of Stake rather than Proof of Work on the basis that those with the highest stake in RaiBlocks are least likely to undermine it’s value.
Proof of Work is only used to stop spam.
Warning. I have no skin in this game so my reading of the paper is purely casual.