Pairwise preference: Difference between revisions
→Presentation
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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. Sometimes such a ranking does not exist due to the [[Condorcet paradox]]. As a related concept, there is always a [[Smith set ranking|Smith ranking]] that applies to groups of candidates, and which reduces to the Condorcet ranking when one exists.
== Presenting pairwise preferences ==
This section covers how to demonstrate pairwise preferences.
Sometimes only the "dominance relation" (wins, losses, and ties) is shown, rather than the exact numbers. So for example, if A beat B in their pairwise matchup, it'd be possible to write "Win" (or a green checkmark) in the A>B cell and "Loss" (or a red X) in the B>A cell.
=== Vertical versus horizontal ===
A pairwise table may be demonstrated either vertically or horizontally; that is, for the following horizontal table:
{| class="wikitable"
|+Horizontal table;
Wins are bolded
!
!A
!B
!C
|-
|A
| ---
|'''35'''
|'''40'''
|-
|B
|27
| ---
|37
|-
|C
|31
|'''42'''
| ---
|}
it could also be written vertically as
{| class="wikitable"
|+Vertical table
!
!A
!B
!C
|-
|A
| ---
|27
|31
|-
|B
|'''35'''
| ---
|'''42'''
|-
|C
|'''40'''
|37
| ---
|}
This article mostly uses the horizontal table.
=== Percentages ===
| |||