When looking at votes-as-cast, it's easy to show how Borda can elect a unanimously despised candidate:
Voter rating <---preferred despised---> ---------------------------------------- 40 A C D E 60 B C D E In other words, C, D, and E are all despised candidates. Even though B has a 60% majority, C wins the Borda count with 200 points compared to B with 180.