** Please show scratch work!!! For the following sets of individual preference o

Question

** Please show scratch work!!!

For the following sets of individual preference orderings, answer these two questions: Which option is the Condorcet winner (put NONE if no Condorcet winner exists)? Which option would be chosen using the Borda count method (with point totals of 4,3,2,1)? 2.1 Annie: A> D> B>C Brian: A> B> D>C Carol: C> D> B> A David: D>A> C B Edith: D> C> B> A 2.2 Fiona: A> B>C>D Grant: B>C> D> A Heidi: B> D>C>A Isaac: C> A> D>B Jesse D> A> B>C

Explanation / Answer

2.1

A vs B

A has highest preference than B, 3 times. So, A > B

A vs C

A has highest preference than C, 3 times. So, A > C

A vs D

D has highest preference than A, 3 times. So, D > A

Let us compare D now with B and C

B vs D

D has highest preference than B, 4 times. So, D > B

C vs D

D has highest preference than C, 4 times. So, D > C

So, Condorcet winner is D.

Option A - 4+ 4 + 1 + 3 + 1 = 13 points

Option B - 2+3+2+1+2 = 10 points

Option C - 1+1+4+2+3 = 11 points

Option D - 3+2+3+4+4 = 16 points

So, option D is chosen by Borda count method.

2.2

A vs B

A has highest preference than B, 3 times. So, A > B

A vs C

C has highest preference than A, 3 times. So, C > A

A vs D

D has highest preference than A, 3 times. So, D > A

Let us compare D now with C (As, C and D has highest preference than A)

C vs D

C has highest preference than D, 3 times. So, C > D

B vs C

B has highest preference than C, 4 times. So, B > C

So, C > A and C > D but B > C and A > B. Therefore there is no Condorcet winner. The answer is NONE.

Option A - 4+ 1 + 1 + 3 + 3 = 12 points

Option B - 3+4+4+1+2 = 14 points

Option C - 2+3+2+4+1 = 12 points

Option D - 1+2+3+2+4 = 12 points

So, option B is chosen by Borda count method.

Voting preference Voters Annie Brian Carol David Edith 1st preference A A C D D 2nd preference D B D A C 3rd preference B D B C B 4th preference C C A B A

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