Here's why:
* Past is a preposition meaning "beyond" or "by." It's used to describe movement or location relative to something.
* Passed is the past tense of the verb "to pass," meaning to move by or beyond something.
In the sentence, "Are you going to run that past him?", we're talking about moving something (the information) "beyond" or "by" him for his consideration. Therefore, "past" is the correct word.