Final answer:
Alexander Hamilton believed that judges should have life appointments in order to ensure their independence from political influence.
Step-by-step explanation:
Alexander Hamilton believed that judges should have life appointments because it would ensure their independence from political influence. In Federalist No. 78, Hamilton argued that the judiciary was the least dangerous branch of government because it had neither the power of the sword nor the purse, but only the power of judgment. By giving judges life tenure, they would be free from the pressures of political winds and could focus on interpreting and applying the law impartially.