This question has been asked hundreds of times before, but I did not see any relevant answer so I will repost. Sorry if there is any helpful answer, please don't vote down but please link to the question(s) with such answers.

The problem can be reproduced as follows:

1. When I remove the password of an administrator account, "Log In without Password", I cannot use that account to authenticate.
2. When I do something that requires authentication, I cannot use an admin without a password to authenticate. If I leave the password box blank without a password while choosing a non-password admin, authentication fails (in terminal or in GUI).

How to fix this problem?