**Adam V** has already mentioned the four founders wanting to have a way to select students who were eponymous with each founder's desired traits and skills in their students. If I'm to take your question *literally*, though -- why is the object used to sort the Hogwarts students  a hat, instead of, say, a magical ruff, a pair of shoes, or a cravat? -- then I can offer this information from J.K. Rowling:

>**J.K. Rowling:** The Sorting Hat does not appear in my earliest plans for Hogwarts. I debated several different methods for sorting students (because I knew from early on that there would be four houses, all with very different qualities). The first was an elaborate, Heath Robinson-ish machine that did all kinds of magical things before reaching a decision, but I did not like it: it felt at once too complicated, and too easy. Next I placed four statues of the four founders in the Entrance Hall, which came alive and selected students from the throng in front of them while the school watched. This was better, but still not quite right. Finally, I wrote a list of the ways in which people can be chosen: eeny meeny miny mo, short straws, chosen by team captains, names out of a hat - names out of a talking hat - putting on a hat - the Sorting Hat. [POTTERMORE LINK - THE SORTING HAT - BOOK 1, CHAPTER 7][1] or [SCREENSHOT][2].

Also, according to J.K. Rowling, the Sorting Hat is a [Legilimens][3] (screenshot); however, it does not possess human emotions per se. Were a human to be the one to sort the students, he/she might harbor subconscious prejudices that could lead to an incorrect sorting. The Sorting Hat is not human; it does not necessarily think like a human. It is the closest, I think, Hogwarts can get to a truly neutral party for sorting.

The exception to the "no emotions" rule, I think, can be found in *Order of the Phoenix*:

>Have the houses been united<br>
As they once were meant to be.<br>
And now the Sorting Hat is here<br>
And you all know the score:<br>
I sort you into houses<br>
Because that is what I’m for,<br>
But this year I’ll go further,<br>
Listen closely to my song:<br>
Though condemned I am to split you<br>
Still I worry that it’s wrong,<br>
Though I must fulfil my duty<br>
And must quarter every year<br>
Still I wonder whether Sorting<br>
May not bring the end I fear.<br>
Oh, know the perils, read the signs,<br>
The warning history shows,<br>
For our Hogwarts is in danger<br>
From external, deadly foes<br>
And we must unite inside her<br>
Or we’ll crumble from within<br>
I have told you, I have warned you ...<br>
Let the Sorting now begin.<br><br>
>*Order of the Phoenix* - pages 186-187 - Bloomsbury - chapter 11, *The Sorting Hat's New Song*


  [1]: https://www.pottermore.com/writing-by-jk-rowling/the-sorting-hat
  [2]: https://i.sstatic.net/9S1Ox.jpg
  [3]: https://i.sstatic.net/ndJ5Q.jpg