Condorcet winner criterion: Difference between revisions
no edit summary
No edit summary |
|||
Line 1:
{{Wikipedia}}<!-- {{cleanup|date=February 2020}} -->{{Image frame|width=450|content=Suppose the voters had been polled on their preferences among the candidates, and the following preferences in head-to-head matchups are produced between French Fries (FF), Hamburger (H), and Cookies (C) (FF>C shows the number of voters who prefer FF over C, for example):
FF>H:51, FF>C:60
The '''Condorcet candidate''', '''Pairwise Champion''' (PC), '''beats-all winner''', or '''Condorcet winner''' (CW) of an [[election]] is the candidate who is preferred by more voters than any other candidate in [[Pairwise counting|pairwise matchups]]. This is determined by observing whether more voters rank or score the Condorcet winner higher than each of the other candidates than the other way around. ▼
H>FF:49, H>C:70
C>FF:40, C>H:20
If for each pair of candidates, we subtract the number of votes preferring the second candidate over the first from the number of votes preferring the first to the second, then we'll know which one won the head-to-head matchup.
(Margins)
<p style="border: 5px dotted green;">FF>H:2 (Win), FF>C:20 (Win)</p>
H>FF:-2, H>C:20 (Win)
C>FF:-20, C>H:-50
The Condorcet winner (if one exists) will be the candidate who got a majority of votes (as indicated by the positive margin) in all of their head-to-head matchups.
FF (French Fries) is the CW here.
▲|caption=Example of finding the Condorcet winner|border=|max-width=}}The '''Condorcet candidate''', '''Pairwise Champion''' (PC), '''beats-all winner''', or '''Condorcet winner''' (CW) of an [[election]] is the candidate who is preferred by more voters than any other candidate in [[Pairwise counting|pairwise matchups]]. This is determined by observing whether more voters rank or score the Condorcet winner higher than each of the other candidates than the other way around.
The '''Condorcet criterion''' for a [[voting system]] is that it chooses the beats-all winner when one exists. Any method conforming to the Condorcet criterion is known as a [[Condorcet method]].
| |||