If one thinks deeply enough about the subjective value they place on their connection to other individuals, would they discover clearly distinct rankings of value?
(This is an extended comment, not a properly sourced answer)
I have a feeling that you are looking for an explanation where it is shown that loving/treating two or more people equally results in some sort of contradiction or fallacy. That is not the case. Based on logic alone, there's no apriori reason that an agent can't assign the exact same value/ranking to two distinct entities (or more).
There might be empirical evidence suggesting that it is impossible to value two other people equally, but that would be a question for psychologists, not philosophers.
There is a case to be made that "loving" or "valuing" a person looses its meaning if it is applied to too broad a category. I was part of a large social circle that included over a 100 people, and another member of the group told us once that she loved each and every one us and that we were all her special friends. I remember thinking to myself that her statement doesn't really make sense: By definition, a friend is someone you single out for special treatment compared to other people. if everyone in the group was her special friend, then there was nothing special about the friendship. Another way of looking at it is: If everyone is a VIP (Very Important Person), then no one is a VIP - VIP by definition should apply to a small number of people compared to the overall group.
So although there is no contradiction in valuing more than one person, there is some sort limit on how many people you can value, before the term looses it's meaning.
In the case of your earlier post about polyamory - which this seems to be a follow up on - there is no inherent contradiction in the idea of polyamory itself. It is possible to say however, that beyond a certain number of partners, the person is no longer polyamorous, they are simply promiscuous.
I think one thing that would help your line of questioning a bit is that you can restrict your question to this: can you love two people maximally and equally.
It seems obvious and intuitive that I can love/value people equally. For instance, there's a category of people who I do not know. For such people, I value them as human beings and from this ascribe to them moral value. As far as I can tell all such people are people I value equally.
There's also a lot of open questions as demonstrated by the comments whether valuing/loving people can be reduced to a single composite value (or perhaps whether even if there are numeric (or more generally ordinal) values for valuing people).
For instance, I may have friends that I love playing board games with, and other friends that I like to talk about heavy matters with, but I might "love them equally" under some valuation.
It seems the area where this might pose an issue is something like this:
Can I have two number ones in my life?
Here, I think there's more of an open question than "can 2000 people be tied for #1000" in terms of my valuing people. The less high up on the hierarchy there more obvious it is that there can / could be ties.
But then it's hard to think of what specific philosophical resources one can use to look at this question.
Here's some suggestions for possibly sympathetic views:
- Aristotle's Nicomachean Ethics BK I -- on the good we pursue in life, the concept of eudaimonia and BK VIII - on friendship and its different forms. (See for instance his critique of Plato's Republic and the idea of common children and his ideas about the nature of family).
- Kierkegaard's Works of Love. A helpful secondary source is M. Jamie Ferreira who works through different sections. I don't know what would be the best section for help with your question (or line of questions).
- Kierkegaard's Fear and Trembling. On it simplest level, it asks does loving God mean hating Isaac? For the contra, Levinas' Totality and Infinity. And all of the secondary literature on this are basically about the question of whether and how having different loves relates.
- The Confucian Analects -- though you would definitely need a guide to interpret it. And Mencius.
- Interestingly, Hegel, especially in the Philosophy of Right.
For literature that would tend to disagree with you:
- I feel like Sartre and de Beauvoir both wrote things about love that would strongly disagree with what you're suggesting.
- Michel Foucault, History of Sexuality
- Many contemporary interpreters of Kant somehow get a polyamory or something like that out of him (even though his own views are greatly opposed to it).
Certainly, but the logic would likely be fuzzy (T/F for any given aspect of affinity can be a value between 0 and 1). Certainly relationships can have a utility function.
In terms of valuing two other people equally, there is no mathematical or philosophical reason one cannot, unless the sorting algorithm requires a clear hierarchy with no ties...
Your question has a common language issue: what is "value two other persons equally"? So, the answer is yes and no.
Yes, because all our interactions end up in one final and binary outcome: attraction or rejection. So, if you feel attracted to your father and mother, you value two other persons equally.
No, because for the outcome above, we assess hundreds of features of each person. Your father can have a funny conversation, your mother not so much, but she's patient and he isn't at all. While you feel attracted to both of them, you have a completely different assessment of each one. In such case, you do NOT value two other persons equally.
The 'two causes' (or the persons) of one's birth are equally important. So people give equal importance to their parents.
In the case of identical twins also most of us value them equally until we know closely.
Good mothers value their children equally.
Sanyasins, when they are in a higher level, value everybody equally.