I've always thought the Linux way of everything auto-updating for you, albeit after asking you first, was the best way forward so it always felt kind of wrong having to run
composer self-update manually.
What better tool is there to periodically run a script than cron. It's as simple as adding the following to a file located, at least on Ubuntu, here:
# Update Composer to the lastest version
It's probably a good idea to redirect the output to a log file with a timestamp but i'm not that worried. Composer complains at you if it's older than 30 days anyway:
Warning: This development build of composer is over 30 days old.
It is recommended to update it by running "composer self-update" to get the latest version.