The quasi-legislative role of a person allows him the right o make rules and regulations having the force of law (Merriam-Webster). According to his own knowledge and observation, one can create a rule which would further the organization. On the other hand, the quasi-judicial role of a person gives him the authority to decide on disputes and impose penalties on the person and the organization (Wikimedia Foundations, Inc.).
One post man was sick for one week so he was not able to deliver the mails. While the other knows it, he deliberately did not finish he tasks of the other post man, leaving some mails undelivered.
Upon the return of the sick postman, he discovered that not all mails were delivered and some of them are urgent. It has caused the conflict between the two postmen so that the Postmaster had to intervene.
As a judicial authority, the Postmaster has pushed for a truce between the two postmen, giving a proper sanction to the one who failed to deliver the mail such as asking him to deliver the remaining mails, while helping the sick post man to deliver the recent mails. The Postmaster has also created a rule that the postman at the adjacent county should be responsible for all the letters left by a sick postman-partner so that he is liable for any loss or delay.