Emphasizing Lack of Justification:
* Dictum
* Edict
* Fiat
* Command
* Order
* Pronouncement
* Mandate
* Ukase (formal, often used for Russian decrees)
* Whimsical decision
* Unjustified ruling
* Capricious judgment
Emphasizing Power and Authority:
* Imperial decree
* Royal proclamation
* Dictatorial order
* Authoritarian decision
* Tyrannical edict
* Unilateral declaration
Emphasizing Unfairness:
* Unjust decree
* Unreasonable rule
* Oppressive law
* Arbitrary ruling
* Injustice
The best synonym for "arbitrary decree" depends on the specific context and the emphasis you want to place on the lack of justification, power, or unfairness.