What allows to make a choice For example, the body has the choice to walk on path A or B. Before the body starts walking, there must be thoughts of path A and B. There must also be a (mental?) decision/choice made to walk on one path or the other. 

What is it that allows to make choices?

I have always been at loss to understand what that untouchable phenomenon is. What is it that let's me choose at all?
I have trouble phrasing the question. So I will give another example. When someone offers me a marijuana joint, there are the options to accept or decline. Both feel just as far, just as easy to make. Sometimes I accept, sometimes reject. What phenomenon chooses? I've never been able to 'touch' that phenomenon directly.

This question about changing habits is the same question as this one.

EDIT:
In another attempt to convey what is being asked (my apologies), there is now another question (this one with a bounty) What is volition?
When a person has a choice between Path A or B, on what basis would that person make that decision, for it to be the right one? For that one has to have a very good knowledge of the True Dhamma. How can one differentiate between what is the Truth and what is not. Even if there is only one path, there is a lower level and a higher level to it. How would a person know such a thing?  Take for example Generosity. Giving (dana) is one of the integral parts of the practice of Dhamma. When practiced in itself, it is a basis of merit or wholesome kamma, but only when combined with morality, concentration and insight, will it lead to liberation from samsara, the cycle of repeated existence. So it is of the recollection of one's own generosity. This is Chaganussati (meditation about generosity).

That is why I would say that you and I are living in very unfortunate times. It is very rare that you and I get to find someone who will teach us the correct path, the True Dhamma, and how to meditate the proper way. Once we learn how to, we will be able to practice these while we are walking, while standing, sitting or when lying down in bed. Then there is no such thing as ‘Choice’. We have found our guide in whom we will place our complete trust. Then we will have unflinching faith in the Path that was shown to us. Then what is important is to practice the little Dhamma that you have learnt. Today almost all the people only read about dhamma. Next moment all this is forgotten. Then there are others who only talk about Dhamma that they think that they’ve understood. They are only fooling themselves to think that they have understood, and put many others too in the wrong path, thereby creating a lot of ‘Akusala Kamma”.  

The path to enlightenment is not so easy. It is a path that goes against the stream. Buddha called this "Patisothagami " or going against the stream. It is just like when almost all the fish in the water are swimming with the flow while only one fish is trying hard to swim against the flow. It's not swimming against the resistance of the flow of water but also the resistance of the other fish that may impede its path.