The projection of syntactic information from the righthand element onto the output word is known as feature percolation.
The righthand head rule is considered a broadly general and universal principle of morphology.
In derivational morphology (i.e. the creation of new words), the head is that morpheme that provides the part of speech (PoS) information.
The same applies to the noun 'personality', which is also derived from 'personal', this time by adding the nominal suffix '-ity' to the right of the input word.
In relation to inflectional morphology, the righthand head rule holds that the rightmost element of a word provides the most essential additional semantic information.
This suffix provides the past tense feature which is also the main additional semantic content of the output word 'played'.