Is it possible for some people to be conscious of their own free will, while others are not conscious of theirs?

In my experience, people with a strong conscience, or with strong moral principles, who are socially empathetic, and willing to help others even when this might come with a relatively high price to themselves, are clearer about what (according to them) needs to be done, clearer about which possible options to try to realize, and this makes them less likely to believe that it's up to them, or that they are free to do either this or that. When someone does something morally praise-worthy, they quite often say they had no choice, they only did what someone or anyone needed to do, and since they were present, that someone was them. I believe we need to take that kind of talk at face value.

The options we imagine we have are only imagined options. We are never completely free in arbitrarily realizing either this or that option. Anyone who has ever struggled with any form of mental compulsion or addiction knows this.

I believe that there are differences in sensitivity and perspicuity. Some people may have a clearer sense of moral direction (which may not necessarily be a good thing, btw). But this doesn't mean being more sensitive to or having a clearer sense of their "free will". We do not have any experiences of "free will". That is, we can have various experiences of being more or less in control (or not being in control) of our own behavior, our actions, our physical reactions -- and those could be called "experiences of free will" (or the lack thereof), but we never directly "see" that free will. What we perceive and feel, are just imaginings and feelings (hope, fear, smooth flow or inner conflict, dreams and daydreams).

A statement like "Cynthia perceived that it was possible ..." also seems a bit an abuse of language. We don't perceive facts. We assert facts and theories. I perceive a grey cat. But I do not perceive the fact that the cat is grey.

In regards to the value of "seeing clearly", there is a beautiful autobiographical short story by Isaac Babel about the merely relative value of clear, sharp lines, Line and Color. When the narrator tells Kerensky that he needs a pair of glasses to see reality as it is, in sharp lines, Kerensky counters with

You can keep that line of yours with its repulsive reality. You are living the sordid life of a trigonometry teacher, while I am enveloped by wonders’ even in a hole like Klyazma!

The whole anecdote, especially with its ominous end, commenting on Trotzky taking the stage after Kerensky, at a mass rally half a year later, has more philosophical depth than most philosophical musings. And since it's merely literature, it also has the advantage that it seems to leave everyone free to make up their own mind.

The question posed is interesting since it is situated in a fuzzy borderland between philosophy and psychology. It probes if differences in how agents subjectively experience possibility might be relevant for the free will debate. It seems to suggest that (or ask whether) disagreements about the so-called problem of free will might be partially due to people projecting their own particular mode of experience of having multiple alternatives onto reality.

Now, it's clear there are psychological differences in this regard. There are psychological studies about this, trying to correlate a subject's sense of agency - the feeling of being in control, being the author of one's actions - with the number of available options, with locus of control (whether one sees the outcome as dependent on or caused by one's action), with explicit beliefs in having free will, and also with feelings of being free, unconstrained. Some somewhat alarming experimental studies show that is is relatively easy to trick people into feeling/believing that something that they see happening is controlled by them even though what actually is happening is demonstrably outside of their control and may even be random. See: illusion of control.

The question then is: Does this have any bearing on the philosophical problem of free will? Answer: Yes, it does, though it may not quite settle all metaphysical issues (if one believes there are any left).

First of all, I think, it shows that the belief that one "could have done otherwise" (looking back) or the belief that any of a set of alternative options is "available (up to me to realize)" is not some uniform given that has the same content or valence for all individuals. In this regard it's also important to see that "seeing more alternatives" can be correlated both with a stronger feeling of agency (and responsibility) (for some people) and with a weaker one (for others). An extreme case is described in Musil's _Der Mann ohne Eigenschaften_ (The man without qualities) in which the protagonist, Ulrich, sees himself as a Möglichkeitsmensch, someone with an overwhelming sense of counter-factual possibilities, a sense which does not make practical life (and relations with other people) easier, but rather paralyzes him.

Both decisiveness and paralysis can result from a richer, stronger modal awareness. This at least somewhat undermines phenomenological based arguments for a hard, libertarian free will. But the problem here shifts from "do we have free will" or "is free will real" to "what matters for (healthy, normal) agency". We want to be able to see multiple options (but not always), we need imagination, but we cannot deal with too many, since that can also make decisive, "free" action just as impossible as having no options at all.^A

(A) The same pyschological minefield is the subject of Barry Schwartz, The Paradox of Choice - Why More is Less, 2004.

Musil's Man Without Qualities contains a lot of explicit philosophical musings. The classic problem of free will is the subject of the chapters about a murderer, Moosbrugger.

Perception theory is diverse/scattered, and this applies directly to how philosophers would answer this question. Under introspective versions of perception theory, see https://iep.utm.edu/introspe/ there could be a perception of the feeling of willing and of the multiple real choices that constitute strong free will.

However, as that discussion makes clear, there are examples that lead to objections to introspection theories, as well as examples leading to objections to each of its rivals.

The SEP on the Problem of Perception reveals one of the drivers behind the disputes between philosophers over perception theory. Basically, most philosophers have rejected the highly intuitive sense datum theory because it implies a Cartesian theater, and most philosophers reject this ideologically. See https://plato.stanford.edu/entries/perception-problem/#ObjSenDatThe

The latest in consciousness research supports a fusion of several of these theories. Per the decision theory studies of Thinking Fast and Slow, our unconscious System 1 mind does most of our mental processing, with our conscious System 2 acting as a backstop to avoid gross mistakes from system 1’s neural net processing. Per Incognito, our system 1 communicates with system 2 by populating an illusory Cartesian Theater with Qualia and logic conceptions. This IS a sense datum model, but one where the sense datum are manufactured by a theory based set of predispositions by system 1. So our sense datum are far from infallible, and they have some degree of non cognitive Theory-theory embedded in them. Requests from system 2 for more resolution GETS more qualia and conceptual details from system 1, so introspection provides more insight. But as system 1 in unconscious, irrational, and non-cognitive there are limits to introspection.

What does this model say about free will? Well, the primary evolutionary purpose of system 2, our conscious minds, is to overrule decisions by system 1. AND system 2 has to WORK to do this, and this initiative is limited. So decision choices, and acts of will being difficult, which are features of libertarian free will, are intrinsic in this model. It is reasonable for most people therefore to believe they have free will.

Note that concepts as well as sensory perception are passed from system 1 to 2. So experiencing free will is also very possible in this model. Concepts are easier for system 1 to create (many trees over here) than detailed qualia, so it is reasonable to expect voice and willing to be among the concepts we experience.

However, the system 1/2 model includes both flawed introspection and the ability for system 2 to retrain system 1. Therefore either free will experiences or free will deniers may be MISTAKEN in what they claim to experience. AND under ideological motivation, a hard determinist may retrain her system 1 to no longer pass the experiences of choice or willing.

In my reading experience about half of hard determinist philosophers admit they find they need to live as if they have free will, which suggests there are some hard limits in how well their system 1s can be retrained to override evolutionary predispositions. But the other half may actually be able to reprogram their innate cognitive processes. Or they may have only convinced themselves in a step of self delusion.

Relative to your question, yes this model accepts that a small number of people could intrinsically not experience free will while most of us do. AND that an additional number of people could train themselves out of feeling their free will. It is also compatible with everyone actually experiencing free will, while some minority fallaciously report they do not.

Free will and imperfect knowledge (e.g. a lack of "seeing") are - in my opinion - orthogonal, with the exception that if you don't believe there is a choice at all then you would not be able to exercise free will.

Take the game of chess, where the "choices" are pretty cut and dried as the turns each player takes making a move.

Just because I don't know every possible outcome of every move I might make doesn't mean I can't exercise free will among the possible moves I see and the various consequences I intuit based on my prior knowledge and experience.

If we were to say that "a chess player cannot exercise free will unless they can 'see' all possible outcomes for the whole game and choose the one they want", then we can conclude that there can be no free will in chess given the limits of human ability.

Certainly, you could choose to define free will to include the idea of perfect knowledge (of the possible choices and their outcomes), but it seems to me that it would have limited analytical and explanatory value versus keeping the two separate.

You ask:

Is it possible for some people to be conscious of their own free will, while others are not conscious of theirs?

Absolutely, and it follows naturally from the fact that some people reject the existence of free will as we do not perceive what we believe does not exist. This is tied up in the debates about where perception and conception should be circumscribed, with radical positions like McDowell's being suggestive that perception itself is in a way, below the threshold of self-consciousness. To believe you have free will is by necessity to conceptualize it in some fashion, particularly as it is not an empirical experience so much as one derived from reason and language. If one genuinely believes they have no choice, and that their actions are not fundamentally a choice, how would even be possible to perceive or somehow register action as choice? In my estimation, it only remains a question of whether or not one's beliefs about free will are contradicted by one's intuitions as it seems rather peculiar to believe that most people don't have intuitions that their choices are indeed theirs to make. In this sense, most people are very blind to determinism in the sense its difficult to conceptualize how one's phenomenal experience doesn't vindicate that naive intuition about one's relation to the world, that one is free to choose.

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