The rules for winning matters

[BMAD]

As the title states, the rules for winning matters. There are three popular methods outside of the majority rule:

(1) Plurality: The topic with the most first-choice votes ("preferneces") wins.

(2) Instant Runoff: Eliminate the third-place topic (in number of preferences), and add the 2nd-choice votes of

that topic to preferences of the first two.

(3) Point system: Two points for each 1st choice, one for each 2nd choice.

Create a scenario where we have fifteen votes for three candidates and depending on the rules for winning there is a completely different winner each time.

[phil1882]

candidate 1: 6 first choice 1 second choice

candidate 2: 5 first choice 5 second choice

candidate 3: 4 first choice 9 second choice

rule 1: candidate 1 wins.

rule 2: candidate 2 wins? im not sure how instant run off works.

rule 3: candidate 3 wins. 13 points for c1, 15 for c2, 17 for c3.

[BMAD]

candidate 1: 6 first choice 1 second choice

candidate 2: 5 first choice 5 second choice

candidate 3: 4 first choice 9 second choice

rule 1: candidate 1 wins.

rule 2: candidate 2 wins? im not sure how instant run off works.

rule 3: candidate 3 wins. 13 points for c1, 15 for c2, 17 for c3.

run off works when the third placed person votes are eliminated and the voter's that picked that candidate now must pick their second choice. Then the one with the most between the two remaining is the winner, So to show this answer your solution needs to be reformatted.

[bonanova]

This is Phil's solution parsed out among fifteen ballots.

Indicating preferred and alternate choices:

-----
1 3
1 3
1 3
1 3
1 3
1 3
-----
2 3
2 3
2 3
2 3
2 3
-----
3 2
3 2
3 2
3 2

1 wins plurality
2 wins instant runoff
3 wins points

[BMAD]

This is Phil's solution parsed out among fifteen ballots.

Indicating preferred and alternate choices:

-----

1 3

1 3

1 3

1 3

1 3

1 3

-----

2 3

2 3

2 3

2 3

2 3

-----

3 2

3 2

3 2

3 2

1 wins plurality

2 wins instant runoff

3 wins points

i agree. I just wanted to see the parsing.