Recently, I was explaining to my high school class what the Borda Count was. We had taken a class survey on something and everyone ranked their choices in order of preference. I calculated the Borda Count scores and showed the class the official class ranking of their choices. One student asked "That seemed a bit complicated...couldn't you have just taken the average ranking of each option?"
I went back and did her suggestion, and just looked at each choice's average ranking, and it turned out to lead to the same outcome as just doing the Borda Count. So now I don't know if this is equivalent to the Borda Count, or is there some obscure situation where these different methods lead to different societal ranking. Are they equivalent or is there some counter example? I feel like if they were just equivalent, then this would be the standard definition of the Borda Count process, right?