Setting the record straight: A note on sophisticated voting under Borda's method

The purpose of this note is to correct some inaccuracies in the literature regarding sophisticated voting under Borda's method. It is shown that if a single candidate must be elected and voters vote sophisticatedly under Borda's method, then: (1) Contrary to both Black's (1976) and Ludwin's (1978) claims, a voter's undominated voting strategy may require him not to give top ranking to his most preferred candidate; (2) Contrary to Black's (1976) claim, an undominated strategy may be such that ail candidates except the most preferred one are ranked last; (3) Whereas a candidate who constitutes the true bottom preference of an absolute majority of the voters will never be elected if voters vote sincerely, this candidate may be elected if voters vote strategically; (4) The election of a candidate who constitutes the true top preference of an absolute majority of the voters is not systematic: ceteris paribus this candidate may be definitely elected when voters vote sincerely but not when they vote strategically, as well as vice versa.