Final answer:
Special liberty in a military context is usually authorized by a service member's commanding officer as a form of leave that is not counted against vacation days, to reward performance or for other reasons deemed appropriate by command.
Step-by-step explanation:
The individual who has the authority to authorize a four-day special liberty may vary depending on the specific context and organization. However, within the military structure, special liberty (which can be thought of as leave or time-off that is not counted against vacation days) is typically granted at the discretion of a service member's commanding officer. The commander balances the need for operational readiness with the morale and welfare of the troops.
For example, in the United States Navy, a commanding officer may grant special liberty to reward performance, celebrate holidays, or compensate for extraordinary work schedules. Different branches and units may have their own protocols, and the authorization may not always come from the same rank or position, but ultimately it is a leadership decision at the command level.