Construct an example in which Dominic is the winner under the Borda count method (using the standard point system), but Barclay is the Majority candidate.
Hint: Start by adding one voter to the column where Barclay is first (to help Barclay be the majority candidate) AND Dominic is not far behind (to make it easier to use another column to give Dominic points for the Borda count method). Now Barclay is the majority candidate (with all of the first-place votes), but is beating Dominic in the Borda count 3 to 2. Now add a voter to the column where Dominic is in first AND Barclay is far behind so that Dominic gets a lot more points than Barclay. Now Dominic is beating Barclay in the Borda count method. Unfortunately, Barclay is no longer the majority candidate.
In general, you add one voter to a column to help Barclay be the majority candidate, then add a voter to another column to help Dominic catch up on Borda points.
There are two columns where Eddie is in first. Do you want to put any voters in these columns? Be aware you can put zeros in columns to represent no one voting in that order.
There are two columns where Barclay is first. These help Barclay gain the majority of first place votes.
Watch out - one of them also gives Barclay way more Borda points than Dominic per vote. Do you want to use that one?
There are two columns that will give Dominic the most Borda points per vote. Which one should you use? Which one really helps Dominic overtake Barclay in the number of points gained?
Dominic Dominic Barclay Barclay Eddie Eddie
Barclay Eddie Dominic Eddie Dominic Barclay
Eddie Barclay Eddie Dominic Barclay Dominic