Pairwise counting: Difference between revisions
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Here is an example of a pairwise victory table for the [https://en.wikipedia.org/wiki/2009_Burlington_mayoral_election Burlington 2009] election:
{| class="wikitable"
| colspan="3" rowspan="2" |
|
| style="background-color: {{Green Party (United States)/meta/color }};" |
| style="background-color: {{Independent politician/meta/color }};" |
| style="background-color: {{Vermont Republican Party/meta/color}};" |
| style="background-color: {{Vermont Progressive Party/meta/color}};" |
| style="background-color: {{Vermont Democratic Party/meta/color}};" |
|-
!wi
!JS
!DS
!KW
!BK
! AM
|-
! style="background-color: {{Vermont Democratic Party/meta/color}}; width: 2px;" |
!AM
| colspan="6" |Andy
Montroll (5–0)
|5 Wins ↓
|-
! style="background-color: {{Vermont Progressive Party/meta/color}}; width: 2px;" |
!BK
| colspan="5" |Bob
Kiss (4–1)
|1 Loss →
↓ 4 Wins
|4067 (AM) –
3477 (BK)
|-
! style="background-color: {{Vermont Republican Party/meta/color}}; width: 2px;" |
!KW
| colspan="4" | Kurt
Wright (3–2)
| 2 Losses →
3 Wins ↓
| 4314 (BK) –
4064 (KW)
|4597 (AM) –
3668 (KW)
|-
! style="background-color: {{Independent politician/meta/color }}; width: 2px;" |
!DS
| colspan="3" |Dan
Smith (2–3)
|3 Losses →
2 Wins ↓
|3975 (KW) –
3793 (DS)
|3946 (BK) –
3577 (DS)
|4573 (AM) –
2998 (DS)
|-
! style="background-color: {{Green Party (United States)/meta/color }}; width: 2px;" |
!JS
| colspan="2" | James
Simpson (1–4)
|4 Losses →
1 Win ↓
|5573 (DS) –
721 (JS)
| 5274 (KW) –
1309 (JS)
|5517 (BK) –
845 (JS)
|6267 (AM) –
591 (JS)
|-
| style="width: 2px;" |
!wi
|Write-in (0–5)
|5 Losses →
|3338 (JS) –
165 (wi)
|6057 (DS) –
117 (wi)
|6063 (KW) –
163 (wi)
|6149 (BK) –
116 (wi)
|6658 (AM) –
104 (wi)
|}
== Terminology ==
The following terms are often used when discussing pairwise counting:
'''Pairwise win/beat''' and '''pairwise lose''': When one candidate receives more votes in a pairwise matchup against another candidate, they "pairwise beat" that candidate, with the other candidate in the matchup pairwise losing.
'''Pairwise winner''' and '''pairwise loser''': the candidate who pairwise wins is the pairwise winner, with the other candidate being the pairwise loser.
'''Pairwise tie''': When two candidates receive the same number of votes in their pairwise matchup.
'''Pairwise order/ranking''': Also known as a [[Condorcet ranking]], it is a ranking of candidates such that each candidate is ranked above all candidates they pairwise beat. One does not always exist due to the [[Condorcet paradox]], though there is always a [[Smith set ranking|Smith ranking]] which more generally holds instead for groups of candidates.
==Notes==
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