Condorcet loser criterion: Difference between revisions
no edit summary
No edit summary |
No edit summary |
||
Line 1:
{{Wikipedia}}{{Image frame|width=500|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
In single-winner [[voting system]] theory, the '''Condorcet loser criterion''' is a measure for differentiating voting systems. It implies the [[majority loser criterion]].▼
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)
FF>H:2, FF>C:20
H>FF:-2 (Loss), H>C:20
<p style="border: 5px dotted red;">C>FF:-20 (Loss), C>H:-50 (Loss) </p>
The Condorcet loser (if one exists) will be the candidate who got a minority of votes (as indicated by the negative margin) in all of their head-to-head matchups.
C (Cookies) is the CL here.
▲|caption=Example of finding the Condorcet loser|border=|max-width=}}In single-winner [[voting system]] theory, the '''Condorcet loser criterion''' is a measure for differentiating voting systems. It implies the [[majority loser criterion]].
A [[voting system]] complying with the Condorcet loser criterion will never allow a ''Condorcet loser'' to win. A Condorcet loser is a candidate who can be defeated in a [[Condorcet method|head-to-head competition]] against each other candidate. (Not all elections will have a Condorcet loser since it is possible for three or more candidates to be mutually defeatable in different head-to-head competitions. However, there is always a [[Smith loser set]], which is the smallest group of candidates such that any of them can be defeated by any candidate not in the group.)
| |||