Consider the example of 21 voters, which are split in three groups depending on their preferences over these candidates: Number of voters
(6) (7) (8)
First Choice
b
c
a
Second Choice
c b b
Third Choice
a a c

a) Suppose voters are asked to cast a vote for their top candidate only. Who is the winner? Is the result the 'best' choice from a social point of view? That is, does the winner best capture the voters' preferences? Provide an argumentation of your answer.
b) Which candidate will be selected by majority voting? Justify your answer.
c) What is the outcome under the Borda voting system? What is wrong with the Borda rule? Justify your answer.
d) Suppose that the group of the 7 voters after some deliberation change their minds about how to order their two least favourite candidates. So instead of preferring b to a, they now prefer a to b. So we have the following preferences over the candidates a, b, c (consider the table below). Find the new winner with plurality scoring, majority and Borda systems. Comment the results.

Number of voters
(6) (7) (8)
First Choice
b
c
a
Second Choice
c a b
Third Choice
a b c