Final answer:
An ethical egoist would assert that everyone should act in their own self-interest (claim number 3), aligning with the ideas of ethical egoism which states that seeking one's personal good is both rational and moral. Other claims either misunderstand egoism or describe psychological egoism, which is distinct from ethical egoism.
Step-by-step explanation:
The claim of an ethical egoist would most closely align with claim number 3) everyone ought to do what will serve his or her own interests. This is based on the principle that it is always right to aim at one's own greatest good as described in both strong and weak forms of ethical egoism. This form of egoism also suggests that acting in one's self-interest is a moral requirement if we accept rational egoism and ethical rationalism, indicating that self-interest is not only pragmatic but ethically necessary.
The alternative claims either relate to psychological egoism, which states that all human actions are motivated by self-interest even if they appear altruistic, or to egoism as a tool for the common good, which posits that by each individual serving their self-interest, the greater good is inadvertently served. These concepts, while related to ethical egoism, do not encapsulate the idea that individual self-interest is an ethical imperative. The first claim is not egoistic at all, as it lacks an opinion on what others should do; the second claim is a misunderstanding of egoism, as true egoists are not concerned with everyone being better off; the fourth claim describes psychological egoism, not ethical egoism.