Question

5 candidates- a,b,c,d, and e with 20 voters. using the borda count method, what is the maximum number of points a candidate can receive? minimum number of points? howmany given out by one ballot? total number of points given out to all 5 candidates?

Answer 1

each voter ranks the candidates in order of his preference,

giving 5 points to 1st, 4 points to 2nd, 3 points to 3rd, 2 points to 4th and 1 point to the last preference.

therefore number of points a candidate can recieve :

N = 5n₁+ 4n₂+ 3n₃+ 2n₄ + 1n₅

(where n₁= no of voters who ranked the candidate 1st,

n₂= no of voters who ranked the candidate 2nd,

n₃= no of voters who ranked the candidate 3rd,

n₄= no of voters who ranked the candidate 4th,

n₅= no of voters who ranked the candidate last.)

N will be maximum if all voters give the candidate 1st preference.

therefore, N_max= 5*20

or, N_max = 100 points ;

N will be minimum if all voters give the candidate last preference.

therefore, N_min = 1*20

or, N_min=20 points ;

one ballot is casted by one voter.he ranks all the candidates and gives them the points.

therefore, number of points given by 1 voter = 5+4+3+2+1 = 15 points ;

total number of points given to all candidates = (points given by 1 voter)x(total number of voters)

or,total number of points given to all candidates = 15x20 = 300 ;