Final answer:
Alexander Hamilton theorizes that frequent appointment processes for judges would endanger the independence of the judiciary. Lifetime appointments for judges ensure their independence and protect them from political influence.
Step-by-step explanation:
Alexander Hamilton, in his writings in Federalist No. 78, theorized that if judges were not given lifetime appointments and instead went through a frequent appointment process, it would endanger the independence of the judiciary. According to Hamilton, an independent judiciary is crucial for protecting the people from unjust laws. By providing judges with lifetime appointments, they are free from undue political influence and pressure to decide cases according to the desires of the President or Congress. The framers of the Constitution chose lifetime terms for judges to ensure the long-term stability and independence of the judiciary.