The New Yorker has apparently updated its rules recently. I found a blog posting from mid-2015, which analyzed the winner captions and included the fine print:
https://webcache.googleusercontent.c...&ct=clnk&gl=us
Each week, we provide a cartoon in need of a caption. You, the reader, submit your caption below, we choose three finalists, and you vote for your favorite… Any resident of the United States, Canada (except Quebec), Australia, the United Kingdom, or the Republic of Ireland age eighteen or older can enter or vote.
Edit: The current rules do not mention any geographic restrictions at all. Anyone over 13 who is not an employee/family member/etc. can participate.