Autovacuum broken by Incorrect localhost entry

If you're seeing an error like this in your postgresql.log:

LOG:  could not connect socket for statistics collector: Invalid argument
LOG:  disabling statistics collector for lack of working socket
WARNING:  autovacuum not started because of misconfiguration
HINT:  Enable the "track_counts" option.

There's a good chance that your localhost entry in /etc/hosts is broken.  In my case, there was a typo in the IP address, which should have been 127.0.0.1:

27.0.0.1   localhost

Once that was fixed, then the PostgreSQL database started up normally and Autovacuum was running.