How does the President influence the judiciary?

The President's influence on the judiciary primarily comes through the power to appoint federal judges, which is a critical aspect of the checks and balances inherent in the U.S. government. When a vacancy arises in the federal judiciary, the President can nominate a candidate for a judgeship, which reflects the President's ideological preferences and policies. However, these nominations require confirmation by the Senate, which adds a layer of oversight and means that the process is a collaborative one between the executive and legislative branches. This opportunity to shape the judiciary allows the President to leave a lasting impact on legal interpretations and the direction of judicial precedent, especially through Supreme Court nominations.

The other choices do not accurately portray the President's role in influencing the judiciary. The President does not write decisions on federal cases, as judicial decisions are made by judges in federal courts. Establishing court procedures falls under the purview of legislative authority and judicial rules, not the executive branch. Lastly, the President is not directly involved in court cases, as the judiciary operates independently and separate from the executive branch to maintain impartiality and avoid conflicts of interest.