Final answer:
A court order compelling a public official to perform an official duty without discretion is called a writ of mandamus. The concept of judicial review allows courts to require officials to fulfill their obligations, enforcing the rule of law with no personal discretion involved.
Step-by-step explanation:
A court order requiring a public official to perform an official duty over which he or she has no discretion is known as a writ of mandamus. This legal order mandates a state or public official to carry out a prescribed action. The historic conflict in Marbury vs. Madison (1803), citing Blackstone's definition, led to the establishment of the concept of judicial review, which empowers the courts to overturn laws based on their constitutionality. Judicial review ensures that public officials are bound to perform their duties as defined by law, and have no discretion to refuse when ordered by the court through a writ of mandamus.
For instance, President Dwight D. Eisenhower's enforcement of the Supreme Court's integration order during the 1957 Little Rock, Arkansas school desegregation is a vivid example of executive power backing judicial decisions to ensure compliance when regular state channels fail to act appropriately. Similarly, a police officer has the authority to enforce the law, like issuing a speeding ticket, but does not have the discretion to command services outside their official duties.