Chapter 1, Problem 63E

Reverse Borda count. Another commonly used variation of the conventional Borda count method is the following: A first place is worth 1 point, second place is worth 2 points, ..., last place is worth $N$ points (where $N$ is the number of candidates). The candidate with the fewest points is the winner, second fewest points is second, and so on. Explain why this variation is equivalent to the original Borda count described in this chapter (i.e., it produces exactly the same winner and the same ranking of the candidates).