Chapter 1, Problem 75E

Consider a modified Borda count where a first-place vote is worth $F$ points ( $F>N$ where $\text{N}$ denotes the number of candidates) and all other places in the ballot are the same as in the ordinary Borda count: $N-1$ points for second place, $N-2$ points for third place, ..., 1 point for last place. By choosing $F$ large enough, we can make this variation of the Borda count method satisfy the majority criterion. Find the smallest value of $F$ (expressed in terms of $N$) for which this happens.