Question

Assume the following preference order for four goods, w, x, y, and z, of a total of 26 people:

# of people 9 6 2 4 5
W X Y Y Z
Z Y X Z X
X Z Z X Y
Y W W W W

You want to extract the will of the group and employ different rules. What is the group's preference order when you employ:
A) Plurality Vote
B) Condorcet Vote
C) Borda Count
D) "Vote for Three"

E) elimination vote (stepwise, eliminate the respective plurality loser); say who will be eliminated at each step.

Answer 1

Answer (A): Going by Plurality vote (i.e. the candidate who gets more than 50% of the total votes wins), we can see that none of the candidates have the plurality majority. All the candidates have secured 5 votes each.

Answer (B): Going by Condorcet vote (i.e. the candidate who gets a majority in all the voting systems wins), we can see that none of the candidates have the Condorcet majority. All the candidates have a majority in all the four voting patterns.

Answer (C): Going by Borda Count (i.e. the candidate who gets a majority of points as per the points given in corresponding to the votes he secures in all the voting systems wins), we can again see that none of the candidates have the Borda count majority, as the candidates have a an equal number of votes.

Answer (D): Going by Vote for Three Count (i.e. voting for only three candidates and not more), we can again see that none of the candidates have the Vote for three count majority, as the candidates have a an equal number of votes. Even if there were three candidates, we would have not see any one with the majority.

Answer (E): Going by Elimination Count (i.e. eliminating the weakest candidate from the voting system), we can see that from the first voting system Y will stay and the rest will be eliminated as Y has the more votes than others, from the Second voting system X and Z will stay and the rest will be eliminated as X and Z have equal and more votes than others, from the Third voting system again X and Z will stay and the rest will be eliminated as X and Z have equal and more votes than others, from the Fourth voting system only W will stay and the rest will be eliminated as W has more votes than others.

                                     Now, here, X has been winner two times, Y winner once, Z winner twice and W winner once. Therefore, only X and Z will stay and other will get eliminated. Out of X and Z, we wil again have no majority.