Question

1 1 The results of a hypothetical election for the best professor at MCC are shown below. In this table, there are 100 voters, representing 100%. Professor Rankings (1 is the highest) А 2 4 3 B 3 2 2 с 2 3 4 D 4 4 % of Vote 25 22 24 29 (a) If we consider only the first- and second-place votes as approval votes, which professor is in first-place? Second-place? فيه 1 (b) Using the Borda method with low points, professor A has 252 points, professor B has 203 points, and professor C has 304 points. Find the low point total for D. Who wins? (c) One of the professors has a majority of the first-place votes. Who is that? (d) Did the Borda method violate the majority criteria of fairness? (Yes or No)

Answer 1

HIS solution Professor Ranking А 1 2 3 B 3 1 4 2 3 2 С. 2 3 ។ D 4 4 1 1 % vote 25 22 24 29 (9) For First and second-place votes A. 1+2 1.5 2 В Э 3+1 2 = 2.0 C → 2+3 = 2.5 2 4+4 D こ 4 2 so First Rank - A Second Ronk - B (B) A Low point (1425) +(2X22) + (1x24) + ( 3X29) 5) 252 B-Low point → (3X25) +(1X22)+(2X24)+ (2x29) =) 203

2 C-Low point + (2x25)+(3X22)+(372417 (4429) = 304 D-Low point = (4x25)+(4X22) + (1x24)+(1829) 241 winning Rank I B D A С a B I Ranker D Borda method not violate the majority criteria of fairness. Its Best method for Finding winner.