No one is in charge, and that's the point
A bank's ledger is easy to keep consistent because there's one bank, and it decides what counts. A blockchain has no such authority. Thousands of independent computers, run by people who have never met and have no reason to trust each other, all need to end up holding the exact same record of every transaction, in the exact same order. Nobody is appointed to referee disputes, because appointing a referee would just recreate the central authority the system was built to remove.
This is what makes consensus the central problem of blockchain design rather than a minor implementation detail. Anyone on the network can go offline at a bad moment, send conflicting information to different peers, or try to spend the same coins twice before anyone notices. A working consensus mechanism has to produce one agreed-upon history anyway, using nothing but the messages participants send each other and the rules everyone has agreed to follow in advance.