The composer is still under development. Alpha versions have been released, but there is still no forecast date for the first stable release.
Thus, running composer self-update always sets the most recent commit from the Github repository. Expect these commits to be broken! If you can live with your automatic update to constantly install broken versions of Composer, just create a cronjob that runs once a month or more.
If you think this is too much, then update manually and see if everything works.
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