A group of fun-loving people have decided to play a practical joke on one of their friends, but they can't decide which friend, Alice (A), Betty (B), or Connie (C). Their preferences are: Who wins using the Borda count method? Does this violate the Condorcet criterion?

A) Betty, No
B) Connie, No
C) Alice, Yes
D) Betty, Yes
E) Alice, No

Question

A group of fun-loving people have decided to play a practical joke on one of their friends, but they can't decide which friend, Alice (A), Betty (B), or Connie (C). Their preferences are:  ​ Who wins using the Borda count method? Does this violate the Condorcet criterion?
​
A) Betty, No 
B) Connie, No 
C) Alice, Yes 
D) Betty, Yes 
E) Alice, No

Quizplus · Accepted Answer

According to the Borda count method, each preference is assigned a certain number of points. For this group, the highest preference (A) is assigned 3 points, the second-highest preference (B) is assigned 2 points, and the lowest preference (C) is assigned 1 point.

Using this method, the points for each friend are as follows:
- Alice: 3 + 1 + 1 = 5
- Betty: 2 + 2 + 3 = 7
- Connie: 1 + 3 + 2 = 6

Therefore, Betty wins using the Borda count method.

This result does violate the Condorcet criterion, which states that if there is a candidate who would win against every other candidate in a head-to-head matchup, they should be the overall winner. In this case, Alice beats both Betty and Connie in head-to-head matchups (A vs B: 2-1, A vs C: 2-1), but she does not win under the Borda count method.

A Group of Fun-Loving People Have Decided to Play a Practical