A resume should not be written in the first person. A resume is a marketing piece and business correspondence. No recruiter or future employer wants to read a resume full of "I did this and I did that..." Furthermore, writing a resume in the first person often leads to it becoming too verbose.
Writing a resume in the third person was also slated a major "pet peeve" among many recruiters. There is no absolutely no reason for such. Once again, a resume is simply a quick marketing piece about the job seeker's background and how it matches the requirements of the position. It is not a biography for a book jacket cover. For example: "Mr. Smith is an excellent recruiter, who has placed many Architects..." Recruiter Trey Cameron of the Cameron Craig Group shared the following comment, "At least make it sound like you actually wrote the resume yourself. I don't care how experienced or senior level you are."