I was thinking last night about Peter Pettigrew and why he would have been sorted into Gryffindor. According to Pottermore, he was a hatstall, with the hat deliberating over whether to put him in Gryffindor or Slytherin for over five minutes: “The Sorting Hat, which is infamously stubborn, still refuses to accept that its decision in the case of [Pettigrew] may have been erroneous, citing the manner in which Pettigrew died as (dubious) evidence” (link). Dubious evidence indeed, since his “heroic” death was faked after he betrayed the Potters!
Pettigrew is far from brave. In fact, almost all of his actions are motivated by one thing: fear. No one is constantly fearless, but giving in to fear in the way that he does hardly seems like a Gryffindor trait. So why would he have been a Gryffindor?
On the other hand, why would he be a Slytherin? He’s not particularly ambitious or cunning. When he does play a part in complicated schemes, he’s usually following Voldemort’s orders rather than coming up with the plan on his own. There are Slytherin characters, like Crabbe and Goyle, who have a lot in common with Pettigrew, but they hardly seem to belong there any more than he does in Gryffindor.
In a way, he’s the opposite of characters like Harry and Hermione, who would do well in more than one house. Pettigrew doesn’t have the strengths of any house. So I think he must have preferred Gryffindor and wanted to be brave. He was certainly drawn toward Gryffindors as friends, and probably admired their courage even if he didn’t have much himself. Likewise, Crabbe and Goyle – who lack the Slytherin characteristics of ambition or cunning, but show none of the other houses’ traits either – come from families that are usually in Slytherin and share the founder’s prejudice against muggle-borns. They would undoubtedly have preferred Slytherin, and that must be enough to skew the process.
There are very rare cases where the hat shouts out a house the moment it touches a child’s head, but most are not a perfect fit for the house where they end up. Hermione was likely placed in Gryffindor rather than Ravenclaw because, despite being both courageous and intelligent, she had read about the houses and knew she wanted Gryffindor. Harry certainly ended up there because he asked not to be a Slytherin. For characters who have the traits of two houses, the hat takes their preferences into account. It makes sense that the same would hold true of characters who don’t have the qualities of any house. It would then be based entirely on what they value or admire, rather than the qualities they possess.