Aries is correct, except that you must also mention that the sternocleomastoid muscles lie over the transverse processes of the crevical vertebra, and so you have to hit from a little forward, or hit very hard to get past the padding of the muscles. Also there are nerve plexi at each intervertebral space, and hitting those hurts and can knock a guy out.
There are actually four carotid arteries in the neck, they arise from two just above the collarbones, and the vasculature of the skull is arranged so that any two could be shut off, and you would be fine. A good choke not only impedes blood to the head, but also cuts off the jugular veins which prevent blood from leaving. Since arteries are under much higher pressure than veins, the intercranial pressure increases and that is one of the primary reasons for black-out.