Excellent article, Merlin!
Most of the confusion arises from the definition of altruism, but also about the difference between actions and moral principles.
Does a moral philosophy require sacrifice under some circumstances for us to call it altruism? There could be very moderate forms of altruism proposed where the individual is "permitted" to pursue their own happiness, but will at some point treat a conflict between the individual's well-being and and that of others with a call to sacrifice. Or it could be a harsh form altruism that treats any form of happiness or personal gain as a terrible sin that calls for more sacrifice. But they are only differences in degree and both agree that, at some point, others are to be valued over self.
Your venn diagram about interactions between people doesn't show some pertinent complications - motivation/psychology. We derive some set of values and ethics (whether it was absorbed unthinkingly from the surroundings or thought out and chosen). And, to a degree, aspects of our psychology follow. A dedicated and observant Christian will make sacrifices and would feel guilt if he didn't. But he may also have formed powerful defenses against low self-esteem that lead him to 'sin' with 'selfish' actions. People can, and do, have mixed premises, and mixed motivations, and differing levels of awareness.
Philosophy, psychology, and the resultant set of actions are like three different horizontal layers of venn diagrams that relate to interactions with others that attempt to deliniate the understanding of altruism/egoism in action.
I completely agree with having non-overlapping circles when talking about the philosophy of egoism and the philosophy of altruism. Those who try to find a middle ground are simply muddled, and probably altruists who want to find a way to make it seem less harsh, or egoist who are trying to appease altruists with a hope for middle ground. But the concept is clear. In a conflict there must be a choice, and if the choice is that others must be treated as the primary beneficiary - for moral reasons - then it is altruism and can never intersect with egoism.
I think that part of Rand's genius was to see that one has to choose a principle of who should be the primary beneficiary - even in the most benevolent of cultures where no one is calling for extreme, or even mild sacrifices. Otherwise, this choice - which is an abstraction - this definition of what is the primary value, when it isn't clear means that the mechanism for logically parsing all subsequent value priorities is left muddled.
The structure of knowledge is such that we must goes from a base of what should the primary value be, to the issue of moral sovereignty and the issue of the rightness in acting towards one's own happiness under all circumstances. Without a clear choice in who should be the primary value, there is no individual sovereignty, and there can be no clear cut political principles to define the boundaries for actions. We often jump right to individual rights (their having arisen from our metaphysical nature) but when we look through any lense where we are viewing the primary difference between altruism and egoism we see - from that differing perspective - the logical necessity of egoism for being able to defend having free association, legal protections for individual rights, free trade, etc.
Said another way it is, "You can do anything you want. But to do so with moral certainty, you must recognize that this is not for you alone, but for all who are human." And, to make that work, you have to find a universal set of boundaries of actions - individual rights. What you can do by right, versus what you have to have permission to do.
“Do you ask if it's ever proper to help another man? No—if he claims it as right or as a moral duty that you owe him. Yes—if such is your own desire based on your own selfish pleasure in the value of his person and his struggle” (AS975).
This strikes me as an odd use of “selfish” when the primary beneficiary of such action is somebody else.
She says, "...your own selfish pleasure..." and rejects any moral duty. That describes something identical to a voluntary trade in that the help given provided more to the giver in that case than what was given. If you see a struggling artist and like their work, and you make a donation and do so knowing that you don't have to and the amount you donate does not cause you any financial stress, then you have done so because your pleasure in furthering the art, and the artist that you admire is greater then the loss of a small sum of money. It is selfish and like the side you are on in a trade, you are the primary beneficiary from your perspective. In trade, each person is the primary beneficiary of their action. That is important because it is a source of conflation in many arguments in this area.
Who you hold as the primary value in the event where a choice is required, and who might be measured, in some transaction, as having benefited more, are not the same things.
A parent can be helping their children in the same fashion - they are not sacrificing because of the value of the children to them. The artist is different only in degree. And as Ayn Rand pointed out, it would be a sacrifice if a parent had to support other people's children at the expense of their own.
Despite Ayn Rand’s many polemics against altruism as a moral ideal, it is not the case that she totally rejected altruism in the practical, concrete sense.
Here is where we disagree. If you define altruism as the philosophy where the primary value is others, then she did reject it totally and that is clear where she states, "...if he claims it as right or moral duty..." She is saying that when you must, as a moral principle engage in sacrifice, put the value of others above your own, then it is altruism and it is totally rejected.
And this takes us to the venn diagram on actions. To make an objective determination on whether an action has a primary beneficiary of 'other' or 'self' is not the same as to say that an action is morally required because it benefits other over self or visa versa. People hold mixed or muddled principles and they act with varying motivations and levels of awareness due to the nature of our psychology.
Actions are complex end states in the sense that we can abstract and isolate moral perspectives as a kind of way to view that aspect of an action. But we can also attempt to grasp the motivation behind a given action, and because of the complex state of the psychology of the actor at the time this can be difficult. Because of our nature, and the requirments of the reality we live in, we must have a moral code, and we need to define a primary value, and all of our subsequent values will vary accordingly. And our psychology will vary to a degree based upon the entire structure of values we have at a time.
Further, I'd say that even though an action can be examined, and an underlying moral principle might be identified, and in addition, it might be possible to identify the psychological aspects behind the action, there is an epistemological problem with going on to say that it is possible to objectively identify who the primary beneficiary is. I say that because it presupposes that one is working from a given moral philosophy to start with.
There is a kind of fallacy to pointing at X and saying it is of "practical" value to this or that person. Putting the word "practical" in front of "value" doesn't take away the question of "by what standard?" As an Objectivist, there may or may not be a primary beneficiary in a given interaction and the way an Objectivist judges the outcome of an interaction is in terms of each individual's benefits based upon the pursuit of their happiness and well-being.
Take a look at the various arguments by those who make use of "primary beneficiary" or "practical value" to see if there is ambiguation there.