Editing Condorcet method (section)

==Example==
{{Tenn voting example}}

To find the Condorcet winner every candidate must be matched against every other candidate in a series of imaginary one-on-one contests. In each pairing the winner is the candidate preferred by a majority of voters. When results for every possible pairing have been found they are as follows:

{| class="wikitable"
|-
! Pair !! Winner
|-
| Memphis (42%) vs. Nashville (58%)|| Nashville
|-
| Memphis (42%) vs. Chattanooga (58%)|| Chattanooga
|-
| Memphis (42%) vs. Knoxville (58%)|| Knoxville
|-
| Nashville (68%) vs. Chattanooga (32%)|| Nashville
|-
| Nashville (68%) vs. Knoxville (32%)||Nashville
|-
| Chattanooga (83%) vs. Knoxville (17%)|| Chattanooga
|}

The results can also be shown in the form of a matrix:

{| class="wikitable"
|-
!1st
! colspan="4" style="background: #ccffcc" | Nashville [N]
|3 Wins ↓
|-
!2nd
! colspan="3" style="background: #ddddff" | Chattanooga [C]
| {{diagonal split header|↓ 2 Wins|→ 1 Loss}}
| style="white-space:nowrap;" | [N] 68%<br/>[C] 32%
|-
!3rd
! colspan="2" style="background: #ffeedd" | Knoxville [K]
| {{diagonal split header|↓ 1 Win|→ 2 Losses}}
| style="white-space:nowrap;" | [C] 83% <br />[K] 17%
| style="white-space:nowrap;" | [N] 68% <br />[K] 32%
|-
!4th
! style="background: #ffdddd" | Memphis [M]
|3 Losses →
| style="white-space:nowrap;" | [K] 58% <br />[M] 42%
| style="white-space:nowrap;" | [C] 58% <br />[M] 42%
| style="white-space:nowrap;" | [N] 58% <br />[M] 42%
|}

As can be seen from both of the tables above, Nashville beats every other candidate. This means that Nashville is the Condorcet winner. Nashville will thus win an election held under any possible Condorcet method.

While any Condorcet method will elect Nashville as the winner, if instead an election based on the same votes were held using [[first-past-the-post]] or [[instant-runoff voting]], these systems would select Memphis<ref group="footnotes">The largest bloc ([[Plurality (voting)|plurality]]) of first place votes is 42% for Memphis; no other rankings are considered. So even though 58%—a true majority—would be inconvenienced by having the capital at the most remote location, Memphis wins.</ref> and Knoxville<ref group="footnotes">Chattanooga (15%) is eliminated in the first round; votes transfer to Knoxville. Nashville (26%) eliminated in the second around; votes transfer to Knoxville. Knoxville wins with 58%.</ref> respectively. This would occur despite the fact that most people would have preferred Nashville to either of those "winners". Condorcet methods make these preferences obvious rather than ignoring or discarding them.

On the other hand, in this example Chattanooga also defeats Knoxville and Memphis when paired against those cities. If we changed the basis for defining preference and determined that Memphis voters preferred Chattanooga as a second choice rather than as a third choice, Chattanooga would be the Condorcet winner even though finishing in last place in a first-past-the-post election.

An alternative way of thinking about this example if a [[Smith set|Smith-efficient]] Condorcet method that passes [[Independence of Smith-dominated alternatives|ISDA]] is used to determine the winner is that 58% of the voters, a [[Mutual majority criterion|mutual majority]], ranked Memphis last (making Memphis the [[majority loser criterion|majority loser]]) and Nashville, Chattanooga, and Knoxville above Memphis, ruling Memphis out. At that point, the voters who preferred Memphis as their 1st choice could only help to choose a winner among Nashville, Chattanooga, and Knoxville, and because they all preferred Nashville as their 1st choice among those three, Nashville would have had a 68% majority of 1st choices among the remaining candidates and won as the majority's 1st choice.