Condorcet ranking: Difference between revisions
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Methods that produce Condorcet rankings include [[Kemeny-Young]] and [[Ranked Pairs]]; methods that produce Smith rankings include [[Pairwise Sorted Methods]].
Smith or Condorcet rankings can be visualized in the following form:
{| class="wikitable"
| colspan="3" rowspan="2" |
|
|
|
|
|
|
|-
!wi
!JS
!DS
!KW
!BK
!AM
|-
!
!AM
| colspan="6" |Andy
Montroll (5–0)
|5 Wins ↓
|-
!
!BK
| colspan="5" |Bob
Kiss (4–1)
|1 Loss →
↓ 4 Wins
|4067 (AM) –
3477 (BK)
|-
!
!KW
| colspan="4" |Kurt
Wright (3–2)
|2 Losses →
3 Wins ↓
|4314 (BK) –
4064 (KW)
|4597 (AM) –
3668 (KW)
|-
!
!DS
| colspan="3" |Dan
Smith (2–3)
|3 Losses →
2 Wins ↓
|3975 (KW) –
3793 (DS)
|3946 (BK) –
3577 (DS)
|4573 (AM) –
2998 (DS)
|-
!
!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)
|-
|
!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)
|}
With generalized Smith rankings in particular, some rows would have to be groups of candidates, rather than solely individual candidates. Hypothetical example:
{| class="wikitable"
| colspan="3" rowspan="2" |
|
|
|
|
|
|
|-
!wi
!JS
!DS
!KW
!BK
!AM
|-
!
!AM
| colspan="6" |Andy
Montroll (5–0)
|5 Wins ↓
|-
!
!BK
| colspan="5" |Bob
Kiss (4–1)
|1 Loss →
↓ 4 Wins
|4067 (AM) –
3477 (BK)
|-
!
!KW
| colspan="4" |Kurt
Wright (3–2)
|2 Losses →
3 Wins ↓
|4314 (BK) –
4064 (KW)
|4597 (AM) –
3668 (KW)
|-
!
!DS
| colspan="3" |Dan
Smith (2–3)
|3 Losses →
2 Wins ↓
|3975 (KW) –
3793 (DS)
|3946 (BK) –
3577 (DS)
|4573 (AM) –
2998 (DS)
|-
!
!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)
|-
|
!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)
|}
#
#
# Wright – defeats all candidates below, including Smith (3,975 to 3,793)
# Smith – defeats Simpson (5,573 to 721) and the write-in candidates
# Simpson – defeats only the write-in candidates (3,338 to 165 for all write-in candidates combined)
Montroll was therefore preferred over Kiss by 54% of voters
=== Hypothetical results under various voting systems ===
The winner under other voting methods can be deduced, assuming the electorate did not employ [[tactical voting]] in any case:
* Wright would have won under [[Plurality voting|plurality]].
* Kiss won under [[Instant-runoff voting|IRV]], and would have won under a [[two-round system]] vs Wright
This makes it more ambiguous as to how to record the exact margins of each pairwise matchup, as even if all candidates in a group of candidates pairwise beat all candidates not in the group, they may each do so with different margins.<br />
[[Category:Voting theory]]
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