Ranked Robin: Difference between revisions
→Example of a ballot set that requires all 4 tie-breaking degrees: I missed that Deegan also had 3 matchups wins when I originally posted this. I had to add 4 ballots to make Fabio beat Deegan.
(→Example election: Forgot to change some “>”s to “=“s when I originally transferred over the ballot set.) |
(→Example of a ballot set that requires all 4 tie-breaking degrees: I missed that Deegan also had 3 matchups wins when I originally posted this. I had to add 4 ballots to make Fabio beat Deegan.) |
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Line 117:
4: Ava>Bianca=Fabio
4: Ava=Bianca>Fabio
2: Bianca=Fabio>Ava=Eli}}Here's the preference matrix:
Line 136 ⟶ 138:
|'''39'''
|'''42'''
|'''
|'''
|-
|'''Bianca over'''
Line 145 ⟶ 147:
|''31''
|'''46'''
|'''
|'''
|-
|'''Cedric over'''
Line 163 ⟶ 165:
|—
|'''30'''
|
|'''175'''
|-
Line 178 ⟶ 180:
|''16''
|''24''
|''
|''
|''
|—
|'''
|-
|''Column total (votes against)''
|''149''
|''149''
|''
|''
|''
|''
|'''
|}
'''Ranked Robin:''' Ava and Bianca tie for pairwise beating the greatest number of other candidates, '''3'''.
Line 197 ⟶ 199:
'''1<sup>st</sup> Degree:''' Ava and Bianca tie for the greatest total difference in votes for and against other tied finalists (both <math>29-29=0</math>).
'''2<sup>nd</sup> Degree:''' Ava and Bianca tie for the greatest total difference in votes for and against all other candidates (both <math>
'''3<sup>rd</sup> Degree:''' Ava and Bianca tie for the least ''losing'' (and '''winning''') votes between them, ''149'' (and '''
'''4<sup>th</sup> Degree:''' The shortest beatpath from Ava to Bianca is Ava→Deegan→Bianca and the shortest beatpath from Bianca to Ava is Bianca→Cedric→Ava. The difference between the number of votes preferring Ava over Deegan and the number of votes preferring Deegan over Ava is <math>39-38=1</math>. From Deegan to Bianca, the difference is <math>37-31=6</math>. The sum of the differences in the beatpath from Ava to Bianca (the total beatpath strength) is <math>1+6=7</math>. From Bianca to Cedric, the difference is <math>35-28=7</math>. From Cedric to Ava, the difference is <math>33-26=7</math>. The total beatpath strength from Bianca to Ava is <math>7+7=14</math>. Bianca has the greatest (sum of) total beatpath strength(s) among tied candidates, so Bianca is elected.
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