e.g.
A<-B<-A*<-C<-D
A* is the double spend. Why must C and D get orphaned?
If we can get over this point, I'll describe the entire idea.
If you keep using "orphaned" talking about DAG you'll never get the core idea of this new concept. Even those transactions that reference "double-spends" are useful, because they also reference legit transactions. I'll repeat again, if you send a normal payment and a double-spending then you increase security of the system. Validation of transactions is similar to
https://en.wikipedia.org/wiki/Billet_reading, you mess with very young transactions but secure elder ones.
Again per the upthread discussion, I allege this is only true if all participants are using the same probabilistic selection algorithms for paying and acceptance. I actually believe the natural state of the system is to devolve into chaos. I will in the future (perhaps) endeavor to show this mathematically (if it can be so reduced).