General Synonyms:
* Order
* Command
* Directive
* Instruction
* Requirement
* Authorization
* Permission
* Authority
* Power
* Charge
* Duty
* Responsibility
Synonyms emphasizing authority:
* Decree
* Edict
* Proclamation
* Enactment
* Regulation
* Law
Synonyms emphasizing obligation:
* Requirement
* Obligation
* Duty
* Responsibility
* Necessity
Synonyms emphasizing purpose:
* Mission
* Purpose
* Goal
* Objective
* Aim
Synonyms for "to mandate":
* To order
* To command
* To require
* To decree
* To authorize
* To empower
* To delegate
* To impose
The best synonym for "mandate" will depend on the specific context and the nuance you want to convey.