A note on Condorcet's other paradox

Abstract : We report in this note some results on the theoretical likelihood of Condorcet's Other Paradox in three alternative elections. This paradox occurs when we have a voting situation such that no Wheighted Scoring Rule (WSR) will select the Pairwise Majority Rule Winner as the WSR winner. We conclude from our study that actual observances of Condorcet's Other Paradox should be very rare events.