Sunday Times Teaser 3116 – Poll Positions
by Nick MacKinnon
Published Sunday June 12 2022 (link)
In an election for golf-club president, voters ranked all four candidates, with no voters agreeing on the rankings. Three election methods were considered.
Under First-past-the-post, since the first-preferences order was A, B, C, D, the president would have been A.
Under Alternative Vote, since A had no majority of first preferences, D was eliminated, with his 2nd and 3rd preferences becoming 1st or 2nd preferences for others. There was still no majority of 1st preferences, and B was eliminated, with his 2nd preferences becoming 1st preferences for others. C now had a majority of 1st preferences, and would have been president.
Under a Borda points system, candidates were given 4, 3, 2, or 1 points for each 1st, 2nd, 3rd or 4th preference respectively. D and C were equal on points, followed by B then A.
How many Borda points did each candidate receive?