Independence of clone alternatives: Difference between revisions

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m (Changed clone set ambiguity example slightly to emphasize the point.)
m (Moved STAR voting example to the example section)
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By adding clones, the Condorcet winner B<sub>1</sub> becomes defeated. All three clones beat each other in clear defeats.
By adding clones, the Condorcet winner B<sub>1</sub> becomes defeated. All three clones beat each other in clear defeats.
A benefits from that. So, by adding two clones of B, B changed from winner to loser. Thus, the minimax method is vulnerable against spoilers and fails the independence of clones criterion.
A benefits from that. So, by adding two clones of B, B changed from winner to loser. Thus, the minimax method is vulnerable against spoilers and fails the independence of clones criterion.

=== STAR voting===

STAR voting consists of an automatic runoff between the two candidates with the highest rated scores. Suppose we use the rated definition of cloning, where a candidate's clones have scores nearly identical to the candidate who was cloned. If the winner in STAR voting differs from the [[Range voting]] winner, then cloning the latter will make him or her win. Therefore, STAR voting has a teaming incentive.

==== Clones not nominated ====

'''Test case 1'''
* Test case 1 https://github.com/larryhastings/starvote/blob/master/test_elections/test_election_demonstrate_cloneproofness_1.starvote
*Test case1 - expected results: https://github.com/larryhastings/starvote/blob/master/test_elections/test_election_demonstrate_cloneproofness_1.txt

{| class="wikitable"
|-
! !! colspan=3|Scores
|-
! # of voters !! Amy !! Brian !! Clancy
|-
| 2 || 5 || 2 || 1
|-
| 4 || 4 || 2 || 1
|-
| 11 || 0 || 1 || 1
|}

The finalists are Amy and Brian, and Brian beats Amy pairwise and thus wins.

==== Clones nominated ====

'''Test case 2'''
* Test case2 https://github.com/larryhastings/starvote/blob/master/test_elections/test_election_demonstrate_cloneproofness_2.starvote
*Test case2 - expected results: https://github.com/larryhastings/starvote/blob/master/test_elections/test_election_demonstrate_cloneproofness_2.txt

{| class="wikitable"
|-
! !! colspan=4|Scores
|-
! # of voters !! Amy !! Amy's clone !! Brian !! Clancy
|-
| 2 || 5 || 5 || 2 || 1
|-
| 2 || 4 || 3 || 2 || 1
|-
| 2 || 4 || 5 || 2 || 1
|-
| 11 || 0 || 0 || 1 || 1
|}

The finalists are Amy and her clone, and Amy's clone wins.


== Notes ==
== Notes ==
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There is no longer a [[Condorcet winner]]. However, there is still a [[Smith set]] which only consists of the B clones. So in order to be cloneproof, a [[Condorcet method]] has to be [[Smith-efficient]] in this example.
There is no longer a [[Condorcet winner]]. However, there is still a [[Smith set]] which only consists of the B clones. So in order to be cloneproof, a [[Condorcet method]] has to be [[Smith-efficient]] in this example.

== STAR voting==

STAR voting consists of an automatic runoff between the two candidates with the highest rated scores. Suppose we use the rated definition of cloning, where a candidate's clones have scores nearly identical to the candidate who was cloned. If the winner in STAR voting differs from the [[Range voting]] winner, then cloning the latter will make him or her win. Therefore, STAR voting has a teaming incentive.

===Example===

==== Clones not nominated ====

'''Test case 1'''
* Test case 1 https://github.com/larryhastings/starvote/blob/master/test_elections/test_election_demonstrate_cloneproofness_1.starvote
*Test case1 - expected results: https://github.com/larryhastings/starvote/blob/master/test_elections/test_election_demonstrate_cloneproofness_1.txt

{| class="wikitable"
|-
! !! colspan=3|Scores
|-
! # of voters !! Amy !! Brian !! Clancy
|-
| 2 || 5 || 2 || 1
|-
| 4 || 4 || 2 || 1
|-
| 11 || 0 || 1 || 1
|}

The finalists are Amy and Brian, and Brian beats Amy pairwise and thus wins.

==== Clones nominated ====

'''Test case 2'''
* Test case2 https://github.com/larryhastings/starvote/blob/master/test_elections/test_election_demonstrate_cloneproofness_2.starvote
*Test case2 - expected results: https://github.com/larryhastings/starvote/blob/master/test_elections/test_election_demonstrate_cloneproofness_2.txt

{| class="wikitable"
|-
! !! colspan=4|Scores
|-
! # of voters !! Amy !! Amy's clone !! Brian !! Clancy
|-
| 2 || 5 || 5 || 2 || 1
|-
| 2 || 4 || 3 || 2 || 1
|-
| 2 || 4 || 5 || 2 || 1
|-
| 11 || 0 || 0 || 1 || 1
|}

The finalists are Amy and her clone, and Amy's clone wins.


==See also==
==See also==