Is the Ability to Choose, Freedom?

No.

To choose just means that there are choices, at least two.

Immediately it can be discerned that your 'freedom' is already curtailed by these choices, ie you cannot make a choice other than these choices.

And then even if you can choose, ie select one of the choices, it does not mean that you are choosing freely.

For you may be already predisposed or conditioned in one way or another, internally or externally, rational or otherwise, physically, physiologically or psychologically, to prefer one over another.

Even without the overt threat of physical harm or denial to access to resources such as food or money, you can be tempted by the promised outcomes, perceived or real, of your choices, valued in terms valuable to you, be it money, prestige, power, principles, or whatever that matters to you.

To choose freely means you can be completely indifferent to the choices and any arbitrary choice is just as good, or as bad, as the other. (Or is it?)

So the real source of freedom and of power is that which is able to influence and condition your decision about choices.

It could be a belief, for example a belief in rationality and the maximisation of benefits accrued to oneself.

If so then choosing means accessing knowledge and data to compute the outcomes of your choices and ranking these outcomes according to some value. And not to be free then means either not having the knowledge and data, or the inability to compute the outcome and make the evaluations correctly.

Or it could be a belief that the outcome must be 'good', not only to you but to all; or it is a belief that the outcome must be one that pleases God, or god or gods, or just someone or something else.

But then you are truly not free at all. For these beliefs hold you captive, in that you cannot abandon them, and you apply them consistently, consciously or not, and even that you cannot choose if you have none of them.

And then also no one really have complete knowledge to compute outcomes or to evaluate them. There will always be unknowns and unknowables that will make all such forecasts uncertain, if not even meaningless, ie you may have done just as 'well' making a random choice.

To take a political example, merely being democratic does not mean you are free. It only mean you can choose. And your choice is entirely influenced and manipulated by the promises of the politicians. They will make promises valued in terms that are valuable to you. For example the Republicans in the US promised 'Christian values' to tempt the 'Christians' to vote them. And the 'Christians' fell for it.

In effect what really happened at the polls is that you are taken captive by the democratic illusion that you are free if you can vote. The reality is that you are just giving legitimacy to one with the majority vote to possess and exercise power over all the land.

So what then in true freedom?

That is another question altogether, and may have nothing to do with choosing altogether.