I understand some of bechira but this has always puzzled me: If we are equally inclined to do good or evil, what is it that makes the final choice?
Not so much an answer as much as why I think it's impossible to give you one:
Free Will lives in a region between algorithm and randomness. (See Metahalakhah, by R/Dr Moshe Koppel, ch. 2-3, for an actual information theory treatment of this topic.) If our decisions were an algorithm, then we'd be robots, with a given history of inputs causing our decisions inevitably. No freedom. If we were random, our "decisions" would be mere rolls of the dice, and not really caused by anything within us either. No will. Nor would we be morally accountable for anything we did in either case -- the algorithm can't be blamed for following its programming, and the die cannot be blamed for which way it falls.
But what this means is that Free Will is also ineffable. If we could pin what we're doing down into words, it would mean that Free Will is an algorithm. If we would claim there is nothing needing description, we would be reducing decision-making to randomness -- the decision has no cause.
I think this is what led @Loewian and @user3714808 to their rather terse answers. We all know what Free Will is, we just can't describe it. All we can say is, "Your free will is the factor that determines the final outcome."
We are what make the final choice.
It's like Loewian said, but let me explain and deepen this out a little:
Maybe the answer to your question lies within the fact one has free will to begin with.
Let me explain; what exactly is free will? We have been giving a free will in order to make choices or decisions on our OWN and with our OWN responsibility, INDEPENDENT of other influences. I wrote some words in capital because it's the essence of free will: It makes us able to act from the I - act on our own - it gives us a sense that we're existing on our own, individual beings, it makes us focused on the self, feeling independent.. While it's our task to be an Eved (Servant of) HaShem and it's a fact that we're basically in everything depend upon G-d, there lies within us a part which makes the I-part within us bigger and stronger, and when we have a choice it's the I-part which often draws us to one side or the other. It's important to have this, because without is one wouldn't have free will to begin with.
The question that remains is if one's following his own will - or if one makes his will the Will of HaShem, and the Will of HaShem his own.
But the path we chose is our own.
this question was asked in shaarei kedusha by Rabbi Chaim Vital (part 3 ch.2)
If both inclinations are equal in strength, then where does the power of free will come in to tip the scale this way or that way? And if the free will is stronger then the inclinations, then what is the point of the inclinations? .....
We have also clarified the matter of the good and evil inclinations in a man. They are two forms added to a man besides his soul. And they are light from the angels (good inclination) and light from the klipos (evil inclinations), outside of the good inclination and external to it. But being that the soul itself is innermost than all of them, and being that it is the essence of a man, therefore it is in his power to tilt the free will to the place that he wants - because he (the soul) is greater than them. Now, his primary desire is towards the good inclination, because it is holy like him and also near to him. But for the body, it's primary desire is to the evil inclination, because both are from the side of evil (physicality), and also they are closer to each other. It is because of this that there is a battle between the physicality and the soul. Because since the soul cannot do the mitzvot except through the body, which tends towards the evil inclination, because of this there is a great difficulty to subjugate it (the evil inclination).