.....under the same circumstances, there would be different outcomes.....
To me, that sounds like randomness. To have everything in one particular state - memories, preferences, weather, environment, thought pattern to that point, temperature, hunger.....- and have there be more than one possible "next thing"......that's random.
If everything up to that point does not determine what you do next, how is that anything other than random?
Depends on how you define random. If you are talking about predictability, then yes, it is random. But if you are talking about purpose, then it is not necessarily random. Hypothetically, a scenario could exist where free will would allow for different, but still directed
, outcomes from the same circumstances.
If this were the case, however, then the obvious next question would be, "how would this be possible?". The answer could depend on the nature of conciousness. Clearly awareness does effect our decisions, I don't think there is any doubt about that. But, some people have some strange views about consciousness (most of which have little to no evidence behind them), which could allow for such a scenario. Most of them involve the supernatural, and so are illogical by definition.
So I guess, in reality, it is random in both senses of the word, but for the sake of argument, the hypothetical free will could account for different outcomes from the same circumstances that do have a purpose.
Let us get back to the first meaning of randomness I proposed: predictability. This, I believe, is another factor that influences the view that there is something called free will and that it is special. I think that every instance where you have the same circumstances and yet get a different result, is only because the circumstances are perceived to be the same, but actually aren't. Human (and other animal) decisions are a perfect example for this, because external factors can seemingly be very very similar, in some cases it could possibly be justified to say that the factors are pretty much exactly the same. The only difference in those circumstances lies in our brain chemistry and wiring. But again this relies on previous events, as they rely on the events preceding them and so on..
The real proof IMO, is the fact that we make the same decisions all the time, and that apparent "randomness" is not very common. People react similarly to the same things, and certain circumstances tend to breed the same type of people. There is so much evidence, thousands of years of human history in fact, that show us we aren't as special and unique as we like to think.