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: |
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{| class="wikitable" |
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| colspan="3" rowspan="2" | |
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| |
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| style="background-color: {{Green Party (United States)/meta/color }};" | |
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| style="background-color: {{Independent politician/meta/color }};" | |
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| style="background-color: {{Vermont Republican Party/meta/color}};" | |
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| style="background-color: {{Vermont Progressive Party/meta/color}};" | |
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| style="background-color: {{Vermont Democratic Party/meta/color}};" | |
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|- |
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!wi |
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!JS |
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!DS |
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!KW |
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!BK |
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! AM |
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|- |
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! style="background-color: {{Vermont Democratic Party/meta/color}}; width: 2px;" | |
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!AM |
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| colspan="6" |Andy |
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Montroll (5–0) |
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|5 Wins ↓ |
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|- |
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! style="background-color: {{Vermont Progressive Party/meta/color}}; width: 2px;" | |
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!BK |
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| colspan="5" |Bob |
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Kiss (4–1) |
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|1 Loss → |
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↓ 4 Wins |
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|4067 (AM) – |
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3477 (BK) |
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|- |
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! style="background-color: {{Vermont Republican Party/meta/color}}; width: 2px;" | |
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!KW |
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| colspan="4" | Kurt |
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Wright (3–2) |
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| 2 Losses → |
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3 Wins ↓ |
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| 4314 (BK) – |
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4064 (KW) |
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|4597 (AM) – |
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3668 (KW) |
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|- |
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! style="background-color: {{Independent politician/meta/color }}; width: 2px;" | |
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!DS |
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| colspan="3" |Dan |
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Smith (2–3) |
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|3 Losses → |
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2 Wins ↓ |
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|3975 (KW) – |
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3793 (DS) |
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|3946 (BK) – |
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3577 (DS) |
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|4573 (AM) – |
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2998 (DS) |
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|- |
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! style="background-color: {{Green Party (United States)/meta/color }}; width: 2px;" | |
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!JS |
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| colspan="2" | James |
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Simpson (1–4) |
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|4 Losses → |
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1 Win ↓ |
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|5573 (DS) – |
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721 (JS) |
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| 5274 (KW) – |
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1309 (JS) |
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|5517 (BK) – |
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845 (JS) |
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|6267 (AM) – |
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591 (JS) |
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|- |
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| style="width: 2px;" | |
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!wi |
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|Write-in (0–5) |
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|5 Losses → |
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|3338 (JS) – |
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165 (wi) |
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|6057 (DS) – |
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117 (wi) |
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|6063 (KW) – |
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163 (wi) |
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|6149 (BK) – |
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116 (wi) |
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|6658 (AM) – |
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104 (wi) |
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|} |
|} |
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== Terminology == |
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The following terms are often used when discussing pairwise counting: |
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'''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. |
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'''Pairwise winner''' and '''pairwise loser''': the candidate who pairwise wins is the pairwise winner, with the other candidate being the pairwise loser. |
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'''Pairwise tie''': When two candidates receive the same number of votes in their pairwise matchup. |
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'''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. |
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==Notes== |
==Notes== |