Final answer:
The ethical principle that treats everyone the same and shows no favoritism or discrimination is known as the principle of justice, which aligns with strict egalitarianism in moral philosophy.
Step-by-step explanation:
The principle that the ethical choice treats everyone the same and shows no favoritism or discrimination is most closely associated with the principle of justice approach to dealing with moral issues.
This principle insists on an equitable distribution and practice in fields such as health care, where it is crucial that patients are treated fairly and similarly in relevant circumstances. It also extends to other areas of social life, such as in clinical trials where it dictates fair treatment and the impartiality of participant involvement.
In a broader sense, this principle aligns with strict egalitarianism, which seeks to ensure every person has the same level of material goods and services, upholding a strict sense of equality that values equal respect for each person. The ethical standpoint here seeks to eliminate favoritism and discrimination, thereby maintaining fairness and equality.