Suppose I am deciding whether or not to buy ice cream. Suppose also that all things being equal, a past-omniscient agent would predict a 50/50 chance of my buying ice cream. How does my final decision get made? Is there a reason for it?
Before I go any further, I want to note that I'm not talking about probabilities that result from a lack of knowledge on our part. If I flip a coin, I typically estimate the odds of tails at 50%, but that's really due to my ignorance about the behavior of a coin when I flip it. However, an observer who is omniscient about the past will be able to predict the outcome of my coin flip by computing what the laws of physics have to say about forces on the coin. In other words, when I speak of probabilities below, I'm talking about probabilities as they appear to an observer who is omniscient about the past.
According to libertarians, I somehow choose to buy or not buy the ice cream without my decision being (1) fully determined by the past, (2) random, or (3) some combination of determined and random.
Let's suppose that the world is not fully deterministic. How can the outcome of an event be partially determined?
Well, in quantum mechanics, as an example, the probability distribution for the event outcomes is determined, but the actual outcome is the result of a random selection according to the distribution.
For example, suppose a quantum theory predicts a 67% chance of an experiment finding an electron spin-up versus a 33% chance of finding the electron spin down. The theory says that nature acts as if the experiment is equivalent to placing 67 red balls and 33 green balls in a barrel, and randomly drawing a ball from the barrel. If the ball comes up red, then the electron is spin up, otherwise it is spin down. The past-omniscient observer only knows how many of each type of ball there are in the barrel.
This way of looking at events is quite general. It's not general because the world is physical, material or made up of quantum elements. It's general in the theoretical sense. If the past is determining something, then the past is altering the probability that an outcome will occur. A fully deterministic world is one in which the probabilities of outcomes are either 0% or 100%.
When pushed, even libertarians will agree that the past makes certain outcomes more probable than others. Will I choose to step in front of a moving bus this afternoon? Being a happy, stable person who lives a charmed life, probably not. Indeed, very probably not. Even if the libertarian believes I have the "free choice" to step in front of a moving bus, they can still admit that that choice is highly improbably due to factors in my past.
However, when we factor out the probability, what is left for a decision to be based upon?
It's very frustrating trying to pin down incompatibilists on this issue. As far as I can tell, the incompatibilist's belief in libertarian free will is generated by moral considerations, and comes without any technical accounting. For most libertarians, there is not only no mechanism for free will, but there's no way of distinguishing free will from randomness.
To make my argument more airtight, I'm going to suppose there's a detailed accounting for deterministic factors. What we'll see is that there's no basis for an agent to make a choice except via fundamental randomness.
Suppose I enumerate all the reasons I have to buy ice cream, and all the reasons not to buy ice cream. Suppose there turn out to be 5 reasons to buy (B1, B2, ..., B5), and 5 reasons not to buy (N1, N2, ..., N5).
For example, perhaps
N2 = "Ice cream will make me fat, and I want to be slim."
B4 = "Ice cream is one of the great pleasures of life, and I don't want to miss out on life's pleasures."
Each reason has an associated importance or weight. Being vain, I assign 10 points to N2, and 5 points to B4.
Since my vanity is is a part of my character, and my character is part of the past state of things, it is predictable. That is, the weight assigned to each reason is mostly determined by the past.
Suppose that these reasons and their weights translate into a 50/50 chance that I will buy the ice cream. That is, we are assuming that, all things being equal, the weight I assign to the reasons is such that they happen to cancel each other out.
At this stage of the thought experiment, the libertarian would say that I choose to buy or not to buy using my free will. What does this mean?
Well, something has to change the weighting of the reasons. It must be that, as I make my decision, I reassign weights to my reasons, and this causes me to come down on one side of the decision or the other.
But on what basis can I reassign weights to my reasons?
Presumably, the libertarian does not mean I am whimsical in reassigning the weights. Whimsy is random. There's no reason for it. It is arbitrary. To see this, imagine that my brain incorporates a random number generator which randomly shifts the weights of all the reasons. If the random number generator happens to throw the balance to buying the ice cream, I can't rationalize the decision by saying that my decision occurred because of B1-B5.
Could I have an actual reason to change my weights?
No. If I did have a reason to change weights such that I buy the ice cream, this reason would constitute B6, and should have been accounted for in my set. That is, the existence of such a reason contradicts the premise that I already had a complete set of reasons in sets B and N.
Is it possible that I discovered a new reason at the moment of my decision?
No. Nothing in the analysis above is phrased in terms of my own perspective. Rather, it's phrased in the perspective of a past-omniscient observer. It doesn't matter whether I was aware of B5. If I was unaware of it, the past-omniscient agent would have assigned it a low weight.
Is my attention to a particular reason the missing factor?
Well, attention or memory or prominence to consciousness may be a factor, but it doesn't help. Either there is a reason for the reason to have prominence to my consciousness or not. If there is a reason, it is already accounted for. If there isn't a reason, it is random.
At this stage, we are forced to conclude that whatever is not determined to the past-omniscient observer is fundamentally random. That is, there can be no possible reason or cause for the selection from the determined probabilities.
I would not be surprised to see some libertarians try to escape this conclusion by trying to redefine the word random. However, there's really nothing special to my definition. Just because an event occurs in the mind of an agent doesn't make any difference to my definition. There remains no reason for the decision, whether you call it random or not. Any attempt to make such a distinction is like saying that when a random event occurs in the mind of an agent, it's called whimsy. What value such nomenclature might have is beyond me.