It can exist in a universe in which magical, intangible devices exist in people's brains that allow them to defy the laws of physics and make choices unconstrained. Or in a universe in which we all exist with aseity, as it turns out, which is unlikely in the extreme.

How can an exactly identical situation have multiple possible outcomes? — Cidat

Seriously, though, compatibilism is the obvious answer, and that seems to be what you are looking for.

You could always say that it was plausible that you could have chosen otherwise in a given situation, that there could be a universe in which you chose otherwise - you just didn't. This doesn't require a situation to have multiple possible outcomes and is compatible with determinism or the idea that your actions have traceable causes. This is not libertarian free-will, but it is the closest we will probably get in this universe.

There are varying degrees of capitulation to esotericism that characterize philosophers' attempts to defend the idea of free-will, but your question is pretty simply answered: yes, there is a universe in which libertarian free will could exist.

There could be a universe in which every antecedent cause is dependent upon a future state of the universe, even, and that makes even less sense to me than the existence of libertarian free will.

It is possible until the determinist can find anything else in the universe that controls a persons actions. They have utterly failed in that regard.

A tip for the determinist wanting to rise to @NOS4A2's challenge is to read... literally anything about human physiology.

Are you not your physiology?

Can libertarian free will (the idea that it's possible to have done something else in the past) exist in any universe whatsoever? My gut answer is no because it seems illogical to justify its existence. How can an exactly identical situation have multiple possible outcomes? If you try to explain what would make an agent choose one action over another, you seem to be reinforcing the idea that actions have a cause. — Cidat

My position on determinism is that, if we can't, in any feasible way, use current knowledge about the world to predict future human behavior, then a claim that there is no free will is meaningless. So, some human behavior is predictable to a certain extent. People who grow up in Japan will almost certainly learn Japanese. People who were abused as children are more likely to abuse others. People's behavior might be predictable to some degree from the results of Myers-Briggs or other similar testing. But those predictions of human behavior will work in only a very general and probabilistic way.

So, we have free will by default.

Can libertarian free will (the idea that it's possible to have done something else in the past) exist in any universe whatsoever? My gut answer is no because it seems illogical to justify its existence. How can an exactly identical situation have multiple possible outcomes? If you try to explain what would make an agent choose one action over another, you seem to be reinforcing the idea that actions have a cause. — Cidat

In one set up of libertarian free will actions have a cause but that cause is not necessity. It's freedom. It's an entirely different causal structure which does not follow the form "if A then necessarily B", or however one wants to bring necessity into the linguistic structure. The reason these things don't conflict is because causal structures which follow the necessary form are inventions by us rather than ontological realities: just because we've found some things which always follow a rule, and those things compose us, that doesn't mean we follow those rules. That's the fallacy of composition. So while we can be composed of things which sometimes follow necessary rules, we ourselves don't have to follow those rules: we follow a different causality, the causality of freedom, in which an agent causes things rather than a prior state of affairs.

I mean if one takes into account modern physics, we cannot say the universe is deterministic, it is probabilistic, so strict determinism cannot arise, unless one argues for it in an academic matter.

But, let's entertain the supposition that QM was not discovered, and that we lived in a Newtonian or even a pre-Newtonian universe, what happens?

You get arguments both for and against determinism. I am unclear if any of the classical figures argued for libertarianism, they were mostly compatibilists.

Having said all this, it's kind of irrelevant to the argument of freedom. We are speaking about extremely small portions of matter studied in isolation from overwhelming complexity.

Once you get to the level of human beings, talking about freedom in relation to physics is a massive distortion of the scope of physics.

So is libertarianism plausible? Sure, as is almost any view on this matter, given that by our levels of sophistication, physics and human choices are vastly different domains of life and enquiry.

Well, is determinism theoretically possible? If we want to be fair, we should not assume either is the established Truth. But this answer to the question “Is libertarian free will theoretically possible?” seems to assume or accept determinism to be the Truth in which free will must be analyzed to fit in this world view.

But this can be easily flipped, and one can assume or accept free will to be the Truth and that determinism must be analyzed to fit in with this world view.

If you say, of course determinism is the Truth, we see it at work everyday of our lives(billiard balls chemical reactions), etc, it is actual and thus theoretical possible. Sure, alternatively, we can say free will is the Truth, we see it at work everyday of lives(who will I love, will I commit that crime, etc), it is actual and thus theoretically possible.

there needs not be a reason for every thing we do. also, we can have multiple equally compelling reasons to do different things.