It might be that basing morality on pain and pleasure is too simplistic for you. Or maybe you’re dissatisfied with the idea that everyone counts the same for utilitarians. Maybe you think you should be allowed to care more about your family and friends—or yourself for that matter—than random strangers. Egoism, the moral theory that what is morally good or bad depends on what’s in your best interest, solves those problems.
Interests are whatever you care about. If you like chocolate, then it is in your interest to eat devil’s food cake, rather than angel’s food cake. Your life will be better in some way when your interests are satisfied, whatever they are. If it is in your interest to graduate form college and get a job, then achieving those things would improve your life. An egoist would say that whatever is in your interest is morally permissible (and maybe obligatory), and whatever is against your interest is morally impermissible.
The Russian-American philosopher Ayn Rand is the most widely-known defender of egoism. She calls the theory ‘objectivism’, but it’s the same thing.
An ultimate value is that final goal or end to which all lesser goals are the means—and it sets the standard by which all lesser goals are evaluated. An organism's life is its standard of value, that which furthers its life is the good, that which threatens it is the evil. …
The Objectivist ethics holds man’s life as the standard of value—and his own life as the ethical purpose of every individual man. …
Man must choose his actions, values and goals by the standard of that which is proper to man—in order to achieve, maintain, fulfill and enjoy that ultimate value, that end in itself, which is his own life.
Rand says that everyone’s first priority as a living thing is to survive, but since people are conscious (as opposed to animals, which Rand thought were not conscious), they have a special definition of survival, we need to be fulfilled, not just avoid death. And according to Rand, the way to be fulfilled is to work toward (and eventually achieve) our rational desires, or interests. She thinks that it must be morally permissible to pursue one’s own survival above all else, so it must be permissible to pursue one’s own interests above all else.
It might seem at first like egoism is just the moral theory of selfish people, and since selfishness is something we usually think of as immoral, egoists need to explain why their view makes sense as a moral theory. What they are likely to say is that you know your interests better than anyone else, your interests are more complicated the gratification of your immediate desires, and it’s unfair and unreasonable to expect people to worry about the needs of others.
Let’s look at those claims in more detail. First, consider the claim that you know your interests better than anyone else. It’s hard to argue with this. You probably know what you want and what will make your life better than anyone else. You can probably think of cases where someone tried to do what they thought was in your best interest and got it completely wrong. I don’t know what your interests are, and I don’t know exactly what will make your life better. Egoists would say that I should just stay out of your business and worry about my own problems.
Second, consider the claim that your interests are more complicated than just immediate gratification of desires. This is where egoism really distinguishes itself form simple selfishness. You have lots of interests, and the most important ones are probably more long-term. Suppose it is in your interest to be healthy. That’s sort of a long-term, ongoing interest. It’s more complicated than interests like your interest in eating some delicious devil’s food cake. Certainly both of those things will make your like better, but in importantly different ways. If you eat the cake, you’ll enjoy the experience, and then it will be over. If you are healthy, you’ll enjoy lots of benefits and for your whole life (as long as you stay healthy). And eating cake all the time, while it would satisfy your short-term interest in eating cake, would not make you healthy. So It’s not really in your interest to do whatever you feel like doing all the time. While it might be in your interest to have a lot of money, and robbing a bank might be the easiest way to satisfy that interest, you probably have a lot of other interests—like staying out of prison—that conflict with it. So egoism has to be about carefully judging which things are really in your overall interest in the long term. Acting selfishly is usually not going to help you achieve your broader, long-term interests.
Third, consider the claim that it is unfair and unreasonable to expect people to worry about the needs of others. Egoists say that the best situation for everyone is where we all look out for our own interests, and when there is a conflict between you interests and mine, we simply negotiate and compromise to get as close as we can to what we want. Egoists say that the fairest world is one in which each person pursues her or his own interests. That way everyone gets the same opportunity and no one is left out.
But egoism, as you probably expected, has its problems too. Those three claims each have a flaw, and there is another problem with egoism as a moral theory in general. Egoists say that you know best what is good for you—what is in your interest. That sounds right, but psychologists will tell you that it’s just not true. People are notoriously bad at knowing what will make them happy. People make bad decisions about their own lives all the time. And this gets into the next claim about having complex interests that are not the same as just being selfish. People pursue immediate interests over long-term ones all the time, not because they are bad or foolish, but because it’s really hard to figure out when a short-term interest will conflict with a long-term one. Even when it’s obvious, like in the cake example, it’s really hard to resist, because the cake will satisfy your interest right now, whereas “being healthy” only pays off over a long time, and it doesn’t seem to make that much difference right now, while you’re staring down that delicious cake. Again, psychologists have done a lot of well-documented work on this phenomenon, and it’s clear that people are really bad at weighing long-term, complex interests against simple, immediate ones. The third claim of egoism, that its best when everyone looks out for themselves has a really obvious problem. Not everyone can look out for themselves, and not everyone is in an equal position to pursue their interests. Children, the disabled, the mentally impaired, and probably even cultural minorities, the poor, and the elderly are all at a serious disadvantage when it comes to negotiating for their interests. If a rich, powerful, well-educated person’s interests come into conflict with an old, poor, mentally impaired minority member, and each one cares only about his own interests, who do you suppose will come out ahead in that negotiation? It’s not a fair fight, and to assume that if everyone looks out for his own interests then everyone will get a fair chance is to assume that the world is a level playing field, when it’s really not.
Finally, there is one last problem that egoists have, and it’s about what it means to be a moral theory. The thing about egoism is that it’s in your best interest if you are and egoist, and everyone else is not. That is, if you only care about yourself, but other people care about you, then things are going to go much better for you than if everyone else was looking out for themselves just like you are. If you’re an egoist, it’s in your interest to be the only egoist. That way you can take advantage of everyone else but they won’t take advantage of you. So egoism is not recommendable—egoism would demand that you try to convince other people not to be egoists. In fact, you’d want to keep it a secret that you are an egoist, so no one thinks you are trying to take advantage of them (even though if it were in your interest, you would be morally obligated to). If you can’t recommend a moral theory to other people, and you have to keep it a secret yourself, we may wonder if it is a moral theory at all, and not just a smart-sounding justification for being selfish.
 Rand, Ayn, The Virtue of Selfishness, Signet, 1964. Chapter 1.