Consider a variation of the Borda count method in which a fi

Consider a variation of the Borda count method in which a first-place vote in an election with N candidates is worth F points (where F > N) and all other places in the ballot are the same as in the ordinary Borda count: N-1 points of second place, N-2 point 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.

Solution

If there are 2 candidates then the candidate who wins the vote would get F points

and according to the condition F > N

so the last place candidate would get N-1 point

now for two candidates N = 2

so the first place candidate would get F >2 points

or the minimum points that the first place candidate would get is F = N+1

considering that the points are positive integer values.