Psychological egoism claims that each person has but one ultimate aim: her own welfare. This allows for action that fails to maximize perceived self-interest, but rules out the sort of behavior psychological egoists like to target — such as altruistic behavior or motivation by thoughts of duty alone. It allows for weakness of will, since in weakness of will cases I am still aiming at my own welfare; I am weak in that I do not act as I aim. And it allows for aiming at things other than one’s welfare, such as helping others, where these things are a means to one’s welfare.

Egoism (Stanford Encyclopedia of Philosophy). (2019, January 15). Stanford Encyclopedia of Philosophy.