Final answer:
The prescription of a placebo in the scenario described violates the principle of veracity, which mandates honesty in the patient-physician relationship. It does not directly violate the principles of nonmaleficence, beneficence, justice, or autonomy as the placebo is not intrinsically harmful or unjust.
Step-by-step explanation:
A doctor prescribing a placebo to a patient complaining of non-existent pain is primarily a violation of the principle of veracity. The principle of veracity requires health care providers to tell the truth and be honest with their patients. In this case, giving a placebo without the patient's knowledge involves deception, undermining the trust essential to the patient-physician relationship. It contrasts with the Act Utilitarian approach, which may justify lying to prevent harm or discomfort, and the Rule Utilitarian approach, which values truth to maintain trust long-term in the medical profession.
The principle of nonmaleficence could also be considered, but it generally pertains to not causing unnecessary harm through interventions or treatment. The principles of beneficence, justice, and autonomy are not directly violated in this scenario since the placebo itself is not causing harm and does not involve inequitable treatment or impede self-determination.