4,208
edits
Copeland's method: Difference between revisions
Removed merge request
(Categorize criterion compliances and failures, add independence of covered alternatives failure) |
(Removed merge request) |
||
| (8 intermediate revisions by 2 users not shown) | |||
Line 1:
{{Wikipedia}}
'''Copeland's method''' is a [[Smith criterion|Smith-efficient]]<ref>http://dss.in.tum.de/files/brandt-research/choicesets.pdf "The Copeland set C is given
by [...] i.e., the set of alternatives with maximal Copeland score." "Theorem 1. The Copeland set [...] [is] contained
Line 48 ⟶ 47:
==Criterion failures==
=== Schwartz ===
In the election
{{ballots|
1: A > B3 > B1 > B2 > C
1: B3 > B1 > B2 > C > A
2: C > A > B2 > B1 > B3
}}
the Schwartz winner is C, but Copeland elects A.
=== Independence of clones ===
Copeland's method is vulnerable to crowding. This example is [[w:Independence_of_clones_criterion#Copeland|due to Wikipedia]].
First consider the election
{{ballots|
1: A>B>C
1: B>C>A
2: C>A>B}}
C is the Condorcet winner and thus also the Copeland winner. Now clone B into B1, B2, and B3:
{{ballots|
1: A > B3 > B1 > B2 > C
1: B3 > B1 > B2 > C > A
2: C > A > B2 > B1 > B3
}}
The Copeland winner changes to A.
Since the Copeland winner is unique in both cases, every method that elects from the Copeland set must also fail clone independence.
=== Independence of covered alternatives ===
Line 68 ⟶ 102:
where every candidate is in the Copeland set. Thus eliminating a covered alternative changed the Copeland set.
=== Dominant mutual third burial resistance ===
Copeland fails dominant mutual third burial resistance.<ref>{{cite web|url=http://lists.electorama.com/pipermail/election-methods-electorama.com/2022-June/003987.html|title=Copeland DMTBR (DMTCBR) failure|website=Election-methods mailing list archives|date=2022-06-26|last=Munsterhjelm|first=K.}}</ref>
==Generalizations==
Line 86 ⟶ 124:
[[Category:Condorcet-related concepts]]
[[Category:Ranked voting methods]]
[[Category:Condorcet methods]]
[[Category:Monotonic electoral systems]]
{{fromwikipedia}}
| |||