Question

2. Consider a hypothetical beauty contest, where there are five finalists (i.e., final candidates) and seven reviewers (i.e., voters) who jointly decide Miss KU. The five finalists are Aram,

Bora, Chanhui, Dahye, and Eunmi. The seven reviewers have the following order of preferences over the five finalists.

Adam: Aram-Bora-Chanhui-Dahye-Eunmi

Ben: Aram-Dahye-Bora-Eunmi-Chanhui

Chris: Aram-Dahye-Bora- Eunmi -Chanhui

David: Chanhui-Bora-Dahye- Eunmi -Aram

Eileen: Chanhui-Dahye-Bora-Aram- Eunmi

Fred: Bora-Chanhui-Dahye-Aram- Eunmi

Gale: Eunmi -Chanhui-Dahye-Boram-Aram

Because different reviewers have different orders of preferences over the five finalists, they agreed to choose the winner(s) democratically, but they could not agree on a voting procedure.

(1) If the plurality rule is used, who is selected as Miss KU? Among the seven reviewers, who has an incentive to defend the plurality rule as the voting procedure?

(2) If the Borda count is used, who is going to be Miss KU? Who has an incentive to defend the Borda count as the voting procedure?

(3) If the STV rule is used, who will be Miss KU? Who has an incentive to defend the STV rule as the voting procedure?

(4) If Gale is the dictator who has the ultimate power in the decision making, who will be selected as Miss KU?

Answer 1

1) Plurality system, the electoral process in which the candidate who polls more votes than any other candidate is elected. It is distinguished from the majority system, in which, to win, a candidate must receive more votes than all other candidates combined.

Aram has is preferred by 3 reviewers, Chanhui by 2, Bora, and Enumi both have 1 reviewer that prefers them over others. Hence by the rule of plurality Aram is selected as Miss KU. Adam, Ben, and Chris have the incentive to defend the plurality system as their preferred candidate will win by that system of voting.

2) The Borda Count Method is a simple tool that is used in elections and decision-making in various contemporary situations. Each candidate is given a number of points, and once all votes have been counted, the option with the most points is considered the best, and therefore the winner. The Borda Count Method is intended to be able to choose different options and candidates, rather than the option that is preferred by the majority. For this reason, it is also described as a consensus-based voting system. The opposite of this is a majority system.

In the Borda Count Method, points are given to each choice based on ranking. For example, the lowest rank gets 1 point, and each consecutive spot on the list gets an extra point. If there are five options, the top rank is therefore awarded 5 points. Mathematically, the first rank gets N points, the second N-1, the third N-2, and the fourth N-3, etc. Total Score for each of the candidate based on the above system is as follows:

Candidate	Score
Aram	(5*3+1*2+2*2)=21
Bora	(2*2+3*3+5+2)=20
Chanhui	(3+2*2+5*2+1*2)=19
Dahye	(3*3+4*3+2)=23
Eunmi	(1*3+2*3+5)=14

As we can clearly see using Borda count, Dheya scores the highest and hence he wins. Eileen seems to have an incentive to defend Borda as Dahye is her second choice and he gets to win.

4)If Gale is the dictator who has the ultimate power in decision making, Eunmi will be selected as Miss KU as she is the one who is most preferred by Gale.