The most probable answer and the most likely one among the options presented in this problem would be C. Neither beauty nor popularity was considered in the contest.
It is considered that when you use either, you partner it with or, and when you use neither, you partner it with nor. Having this partnership would not confuse the reader or listener to what is actually being explained or what the sentence is trying to present. Interchanging their partners would result to a contradiction in the idea between them. To add, it also sounds wrong.
