What traits are you identifying here?
Focusing on what you have bolded, I feel like I’m detecting (in order of appearance) apathy, independence, being discerning/discriminatory, being respectful & loyal. Overall, an attitude of conditional social strength with past experience in leadership, subsequently rejected.
Would you say these are the traits of an alpha male? Is there anything you’d add/take away?
When I was in school there were no leaders like that, just a guy who bullied people and molested me, I pretended not to like it but I did, the guy wasn’t an adult but my age. The closest thing to a leader like you describe was this mongrel troll who, would go around making up fake and ludicrous stories all the time, usually stories about being a eunuch or getting a sex-change, eventually found out it was fake news though, but most popular guy in school actually.
Those are traits… and what leads to them is valuing them enough to pursue them and it’s always comparative, so if you lost the genetic lottery you may well just be screwed.
The one problem I have with my list is that it’s not very precise… It’s too broad and I wish I could narrow it down more precisely but when I try I run into trouble.
For example, shield was pointing out a show of independence and selectiveness… traditionally characteristics of someone with power.
So maybe “independence” is more precise than power…
But then I think if you’re “independent” and selective out of necessity or fear, due to being a social reject or easily defeated by people’s expectations of you… that just makes you sad and pathetic, not an alpha.
It always seems to default back to power…
…and is it this incident that you have formed the basis of your whole entirety on? if so, is that a helpful thought to hold onto for all these years?
What would you say the main traits that you exhibit are?
When I say traits, I mean in the psychological sense of dispositions. These can lead to power, wisdom and charm, for sure. You might even be able to say that someone has a wise or charming disposition, but even these seem to be a result of more fundamental “ways of being that you tend to demonstrate” i.e. traits. Power certainly isn’t a disposition, but to clarify whether or not you consider the terminology debatable, I want to consider the kinds of more precise things that you mentioned you were running into trouble with - that’s what makes it an interesting subject in my opinion: that it’s troublesome.
Surely the reason it always seems to default back to power is that “alpha” is basically a rank of power by definition - it’s a little tautological of an observation, but I guess not without value altogether.
This is more like what I was after, but it seems strange to me to associate the kind of social dominance that defines an alpha with a trait that appears to counteract that. I see where it comes from: being able to dominate but not needing it or seeking it out. It results in a demonstration of lack of social weakness, which is essential to being dominant and is linked to what I identified as apathy. If independence is meant in this way, then sure - although like apathy it can also be indicative of social statuses that are very much not alpha-like - as you pointed out. That’s not to say it can’t be added to a list though.
Silhouette wrote:
The alpha male would exhibit a keen awareness of his surroundings and the people in it. He would be an observer rather than a charismatic charming male seducing every female. He has no concerns or necessity to prove anything, he may be a loner. The female who catches his attention is the one who stands apart, waiting for him to approach, he may feign disinterest in her, because he is the one in charge of the chase. He is a man of many thoughts, few words initially, he has a quiet personality, physical strength, but not necessarily in the conventional ideal, he may even be rather unattractive, but his intellectual prowess is strong, interesting. He is a man you are drawn to and the discerning female instinctively knows this man has much more to give and only a few are allowed through the portals of intimacy with this man.
Which reminds me of quote from Pride and Prejudice
“no one can be really esteemed accomplished who does not greatly surpass what is usually met with. A woman must have a thorough knowledge of music, singing, drawing, dancing, and the modern languages, to deserve the word; and besides all this, she must possess a certain something in her air and manner of walking, the tone of her voice, her address and expressions, or the word will be but half deserved.” says Caroline Bingley
“All this she must possess,” added Darcy, “and to all this she must yet add something more substantial, in the improvement of her mind by extensive reading.” Mr. Darcy
“I am no longer surprised at your knowing only six accomplished women. I rather wonder now at your knowing any.” Elizabeth Bennet
Alpha males are just as rare. 
Have you just described your ideal man or the typical alpha male?
Or perhaps your description is indicative of an alpha by virtue of you being attracted to what you just described, and probably not being alone with your tastes, regardless of whether you were being objective or if there was a tainting element of subjectivity at play.
I’m somewhat reminded of the behaviour of a bull in a field of cows: the bull is an observing loner, needing to prove nothing, until he chooses a female who is standing apart and the deed happens.
A concern I have is that your description also matches that of a stalker or someone who has no social dominance and is thereby forced to be a loner. How much more common is it for the female to be repulsed by the “male gaze” of an observer than excited? Clearly it’s not always “intellectual prowess” that clinches this reaction from a distance, and the ability to mimic intellectual prowess would be just as effective at first appearance.
Perhaps you are requiring first a social situation where a true show of intellect is able to be drawn out - but that won’t happen if the person is a loner speaking few words due to his quiet personality even in a social situation.
In short it seems, at least from only a few readings through your words and without further elaboration from yourself, that you’re describing an ideal that runs into problems when it comes to real situations, such as those I’ve just been hinting at.
What if the alpha type isn’t your type?
It seems like the person who the most people want to be around is the one with the most stories, humour and comfort in his surroundings - they appear to be the ones who demonstrate being enjoyable to be around and command attention simply by expressing what they want to express. The loner doesn’t prove any ability to be a good team-mate in a successful relationship in his silence, or directly any excitement or fun for something less long term. At least they can be more mysterious, proving a discerning taste that hints that they are much less likely to stray from somebody they finally find to be worthy - thus the indirect prospect of learning about them in itself can become exciting. But they aren’t the ones who social situations revolve around. Group movements revolve around conversation, and people instinctively look to the person at the centre of that for decisions - presumably at least in part through the subconscious acceptance that everyone else is looking in that direction too. It’s not so common for everyone to subsequently look to the loner for a final nod of approval or to offer an overriding, more appealing alternative like a mastermind. It’s more likely for the mystique of someone of the type you describe to allow the female imagination to run riot and cause the adreneline to flow at the possibility of it all coming true, only to be broken if you actually engage with him. Sure it’s possible for them to live up to your hopes, maybe to even surpass them, but that seems like the makings of an exciting romantic encounter more than contact with the alpha.
Clearly the term “Power” isn’t very good at getting the concept across… I’d be tempted to say the term “competence” is perhaps a safer way to express it, but not really…
You can be really competent at utterly useless things, which does nothing for you…
I think the most precise way I could get the concept across is to say the power earned or deserved through competence is the only power that counts.
That would mean being powerful because of who your daddy is should not be of any use when it comes to being an alpha… which I think holds true.
As for it being a tautology…
power does not automatically makes you an alpha… nor is being an alpha the only means of attaining power…
Hence the list and the disqualifier…
I ultimately don’t think “independence” is a very good term for anything to do with humans… we’re pack animals, we don’t do “independence” very well.
It seems to me that we, unlike some animals, neither physically nor mentally “dominate” each other to attain Alpha status.
Our status comes from instilling others with confidence in our power/competence, wisdom, charm and lack of antisocial behavior… and when we face rivals we dominate in groups.
i.e. If I have the biggest gang win.
But we don’t attain the biggest gang by being a domineering bully… we can afford to be a bully once we have the biggest gang… but that’s not how we get the gang.
The various cultures have different rules about how you ought to conduct yourself…
The exact methods by which you can demonstrate power, wisdom, etc tends to be very different… hence why it’s very difficult to nail it down to anything more specific.
“Alpha males are jerks, I can’t stand how attracted to them I am”. 
Ah, so you meant power in that sense. I actually prefer using it in the way you intended, particularly in order to make the most sense of “Will to Power” but it’s far more commonly used in the sense of “being in power” - having and using influence over people. So I assumed that, my bad.
I have no objections to competence as an indicator of alpha male status. As is a theme so far, all these things we can associate with an alpha can occur in others who are not alphas when there is a lack of other indicators as well. Perhaps this is inevitable. Also, as before, I don’t really regard competence as a trait as it says nothing about the kind of behaviour that results in it, and that was what I was getting at in the OP.
I agree that while inherited power can put you in a position of social dominance, it is not sufficient to generate genuine respect by itself. Undeserved competence can though - whilst it may not show, breed or necessitate adaptable competence, it may engender sufficient respect at least in the short term.
True, indicating that alpha refers to specific types of power rather than power in general. Point conceded.
Agreed, not personally but generally speaking.
We don’t dominate each other physically - there can be a physicality in play fighting, but this is much more important to other species than us, at least in our adult stages.
Mental domination is far more appropriate, but again, neither necessary nor applicable in all ways or to all extents. As you say, various cultures have different rules, and an adaptability and tempered use of mental domination to a sufficient degree of competence sees the most success in attaining alpha status.
But even more than this, I judge experiential dominance and dominance in humour (the ability to engage the imagination and to alleviate stress respectively) to be the primary arena of dominance - which we certainly do indulge in even as humans. Intellectual dominance serves as a reliable accompaniment to bolster this, and even a little physicality can accentuate it. Our social quarrels, both individual and in groups rarely come to blows except in less civilised parts of society. Humour, experience, enhanced by intellect and supported by physicality is what wins.
Again, as you say, there are cultural variations, but I think the above pattern has the widest applicability. I would add in a sense of socially consensual justice and we have the charming, social, wise and powerful/competent alpha male.
Returning to my original trait list though, I think a good measure of alpha status is the degree to which you can get away with exhibiting those traits. Strength is best communicated through excess and challenging ideals such as we have laid out. The ideals cover merely the indicators, but not so much the specific behavioural traits that are seen in practice.
Being a leader is actually opposite of that which is stated. Look at wolf packs as the best example.
Sounds more like a lion in a pride than an alpha which is associated with wolves.
“The lion and tiger may be more powerful, but the wolf does not participate in the circus.”
