 The only difference between the two election scenarios is that the third voter changed the ranking of the bottom three candidates.  In election scenario 1, the third  voter has candidate \(A\) ranked first, then \(C\) ranked second, \(B\) ranked third  and \(D\) ranked last.   In election scenario 2, this voter still has \(A\) ranked first, but ranks \(B\) second, \(D\) third and \(C\) last. In  election scenario 1, candidate \(C\) is the Borda Count winner (the Borda scores are \(\BS(A)=9, \BS(B)=5, \BS(C)=10\), and \(\BS(D)=6\)).   In the  election scenario 2, candidate \(A\) is  the Borda Count winner (the Borda scores are \(\BS(A)=9, \BS(B)=6, \BS(C)=8\), and \(\BS(D)=7\)).    According to her ranking in election scenario 1, this voter prefers the outcome in election scenario 2 (candidate \(A\), the Borda winner in election scenario 2, is ranked above candidate \(C\), the Borda winner in election scenario 1).    So, if we assume that election scenario 1 represents the “true” preferences of the electorate, it is in the interest of the third voter  to misrepresent her preferences as in election scenario 2.  This is an instance of a general result known as the Gibbard-Satterthwaite Theorem (Gibbard 1973; Satterthwaite 1975): Under natural assumptions, there is no voting method that guarantees that voters will choose their ballots sincerely (for a precise statement of this theorem  see Theorem 3.1.2 from Taylor 2005 or Section 3.3 of List 2013). 