Here are 7 voters\' preferences for 5 options. The most preferred option is to t

Question

Here are 7 voters' preferences for 5 options. The most preferred option is to the left and the least preferred is to the right. Assume they vote according to their real preferences - they don't strategize. VOTER 1: A D B E C VOTER 2: A D B E C VOTER 3: C B D E A VOTER 4: C D B A E VOTER 5: B C D A E VOTER 6: E C D B A VOTER 7: A B C D E Which would win by plurality voting? Which option would win by approval voting if 1 and 2 voted for their top two choices, and the rest voted for their top three choices? Which would win by the Borda count method? Which would win by preferential voting (single transferable vote, the one used in the Oscars)? (If, at a certain stage before the end, two options are tied for lowest votes, eliminate them both.)

Explanation / Answer

A) A will win by plurality voting;

B) By approval voting D will win as all voters except 7 approve of D;

C) By borda count method;

(1*4+2*3+

3*2+1*1+0)/7=2.428

(2*4+2*3+

1*2+0*1+2*0)/7=2.285

(0*4+3*3+

3*2+1*1+0)/7=2.285

(1*4+0*3+

0*2+3*1+3*0)/7=1

Clearly B is the winner with 2.428 points;

Candidate First Rank Second Rank Third Rank Fourth Rank Fifth Rank Borda Count A 3/7 0/7 0/7 2/7 2/7 (3*4+2*1+2*0)/7=2 B 1/7 2/7 3/7 1/7 0/7

(1*4+2*3+

3*2+1*1+0)/7=2.428

C 2/7 2/7 1/7 0/7 2/7

(2*4+2*3+

1*2+0*1+2*0)/7=2.285

D 0/7 3/7 3/7 1/7 0/7

(0*4+3*3+

3*2+1*1+0)/7=2.285

E 1/7 0/7 0/7 3/7 3/7

(1*4+0*3+

0*2+3*1+3*0)/7=1

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