Final answer:
Under strong ethical egoism, it would not be morally permissible to act or advise others to act against their self-interest. Ethical egoism conflicts with the idea of regulating ethical conflicts in a way that sometimes requires conduct contrary to one's self-interest. The Categorical Imperative and other ethical theories oppose such self-centered approaches.
Step-by-step explanation:
If ethical egoism is true, it suggests that it is morally permissible to act in one's own self-interest. Therefore, under strong ethical egoism, which states that it is always right to aim at one's own greatest good, it would never be morally permissible for someone to suggest or obligate others to act against their self-interest.
This would contrast with the view that individuals should act to maximize their own benefits, even if this means acting at the expense of others’ interests.
However, an objection to ethical egoism is its incompatibility with ethical conflict-regulation which suggests that moral guidelines should regulate interpersonal conflicts of interest. Ethical egoism rejects the notion that conduct contrary to one's interest is sometimes morally required, and this is the crux of the dilemma when evaluating actions like harming others for personal gain.
In the hypothetical case of someone killing their grandfather for an inheritance, ethical egoism may justify such an act due to the benefit gained, even though commonly accepted moral standards would condemn such an act.
The debate around ethical egoism is further complicated by objections against it, such as the impossibility of expecting the entire world's population to act in a way that benefits one individual, and the fundamental conflict of interest that arises if everyone were to be an egoist.
The Categorical Imperative and other ethical theories propose that one should never use a person merely as a means to an end, emphasizing the value of individuals beyond their utility to others.