In general, weakening the consistency guarantees is not done to improve scalability, but rather to improve the partition tolerance. There are replication techniques (e.g. chain replication) that allow very high performance without sacrificing consistency.

But what I'm saying here is: You cannot have ACID transactions without the C in CAP.

Theorem 1. It is impossible in the asynchronous network model to implement a read/write data object that guarantees the following properties: * Availability, * Atomic consistency, in all fair executions (including those in which messages are lost).

But can it also manage simultaneous writes (of possibly conflicting data) to multiple masters, to achieve write scalability? Won't it get slowed down, checking every master for conflicts before committing?

Having multiple masters will most likely add overhead for conflict resolution and should be avoided, but it's really orthogonal to the whole CAP stuff. If you allow writes to multiple masters without conflict resolution at write-time, then you will need to do the conflict-resolution at read-time, which is going to be much more complicated, because your read may yield multiple versions.

The point of database partitioning is that a transaction that doesn't span partitions only touches a constant number of servers (usually 2 or 3).