What does the president consider to be the most important criterion when making political appointments to the bureaucracy?

loyalty to the President

Explanation:

The President of the United States makes all the important political appointment of the bureaucracy to the Government offices. He does that appointing his favorite officials to the offices of the United States different federal agencies. One of the most important criteria that the President considers while appointing the bureaucracy officials is "loyalty to the President."

The President seeks those people who are loyal to him and follows every orders and advices of the President. The President keeps in mind that no one disobeys him and follows his order without any hesitations.

Thus the answer is "loyalty to the President."

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