Question

Consider the following preferences and election problem. Let us assume that a president has to be elected. 4 candidates want to become a president, who are representing different political ideologies: A is a left-wing candidate, B is a social-democrat, C is a right-liberal candidate and D is a right-wing candidate. 20% of the voters (group left) preference A≻B≻C≻D, 30% of the voters (group social democrats) have the preference B≻A≻C≻D, 10% of the voters (group right-liberal) preference C≻B≻A≻D, 40% of the voters (group right) have preference D≻C≻B≻A. Please note the sign “ ≻ “ means “preferred to.”. In total we have 100 voters.

A What is the election outcome if a pure plurality voting system is applied? How many votes does the winner receives?

B Who will be elected if the Instant Runoff voting system is applied? Who will be the first and second ranked candidate in the first election round? How much votes will the winner get in the second round?

C. Who will win if the system of unanimity is applied?

D. Who will win, if the point-count voting is applied? Please note, the voters have to rank their preferences for the first 3 candidates like, the most preferred candidate get 3 points, the second ranked candidate gets 2 points and the third ranked candidate gets 1 point. The fourth preferred candidate get zero points. How many points will be distributed in total and how much points will the winner receive?

Answer 1

(A) Plurality system of voting means the candidate is getting maximum vote in respect to the other contestants but not getting absolute majority i.e. more than 50% of the votes cast. If the plurality system is applied D is the winner. D receives 40 votes.

(B) Instant-runoff voting (IRV) is a form of ranked preferential voting system which is used with more than two candidates in single-seat elections. Instead of stating support for only one candidate, voters will rank the candidates in order of preference in IRV elections. At first, ballots are counted for the top preference of each elector.

First and second ranked candiadates in the first election round is D receiving 40 votes and B is receiving 30 votes. In the second round B receiving 30 votes and D receiving zero votes. Taking both the rounds into consideration B is the winner under this voting system..

(C) If some voter abstains the system of unanimity is applied then  D is the winner because the total count of the voters will also decrease so the percentage for D still remains the highest.

(D)

Pattern	Percentage	A	B	C	D
A>B>C>D	20%	20*3=60	20*2=40	20*1=20	0
B>A>C>D	30%	30*2=60	30*3=90	30*1=30	0
C>B>A>D	10%	10*1=10	10*2=20	10*3=30	0
D>C>B>A	40%	40*0=0	40*1=40	40*2=80	40*3=120
Total votes		130	190	160	120

Total votes is (130+190+160+120)=600 votes assuming score 3 for first rank candidate, score 2 for second rank candiadate and score 1 for third rank candidate.

The winner obtained 190 votes. the winning candiadate is B