Uncovered set: Difference between revisions

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!x
!x
!y
!y
!z
!v
!v
!z
!Copeland score
!Copeland score
|-
|-
|x
|x
| ---
| ---
|Win
|Win
|Win
|Lose
|Lose
|Win
|(2-1)=1
|(2-1)=1
|-
|-
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|v
|v
|Win
|Win
|Lose
|Lose
|Lose
| ---
| ---
|Lose
|(1-2)=-1
|(1-2)=-1
|-
|-
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|Lose
|Lose
|Lose
|Lose
| ---
|Win
|Win
| ---
|(1-2)=-1
|(1-2)=-1
|}
|}
Notice that the Smith set includes all candidates (this can be seen by observing that there is a [[beatpath]] of x>y>z>v>x). But the uncovered set is all candidates except z; this is because y>z and all candidates who beat y (just x) also beat z. <ref>https://economics.stackexchange.com/a/27691</ref> (Notice that the Copeland set is even smaller; it is just v and x).
Notice that the Smith set includes all candidates (this can be seen by observing that there is a [[beatpath]] of x>y>z>v>x, or alternatively by observing that no matter how many candidates you look at from top to bottom, there is still some candidate outside of the group being looked at that one of the candidates in the group lose or tie to). But the uncovered set is all candidates except z; this is because y>z and all candidates who beat y (just x) also beat z. <ref>https://economics.stackexchange.com/a/27691</ref> (Notice that the Copeland set is even smaller; it is just v and x).


== Notes ==
== Notes ==