How does the sorting hat choose your house?

          In class last Wednesday we briefly discussed how Harry has a "slytherin side" that the sorting hat recognized. It is arguable that it was sensing Voldemort's horcrux, but I believe that Harry has slytherin potential outside of his horcrux just as Hermione (aka the brightest witch of her age) would be right at home in ravenclaw, and Neville Longbottom could happily spend his days in Hufflepuff.  Whether it is ambition, loyalty, intelligence, or courage, I think the sorting hat sees which characteristic you need most and places you accordingly. Who would need bravery more than Harry, Hermione, and Ron? Gilderoy Lockhart definitely needed to wisen up and Peter Pettigrew needed courage more than anything. Sirius Black also was sorted into gryffindor despite his family's (incuding Bellatrix lestrange) legacy of slytherin. It could also be said that Draco Malfoy needed to gain ambition of his own instead of being an extention of his father's will. OBviously we can never know for sure how each wizard is sorted in his or her house, but this theory seems to be the most workable to me. This issue however, also brings up the question: how much the sorting hat can "see" and what power is has to say without a doubt which house you belong in? I don't know the answer but it is certainly an interesting concept to consider.