[Election-Methods] Mixing Condorcet and Approval...

[Chris Benham]

Stephane Rouillon wrote:

>I would suggest a Condorcet method usind residual approbation weights
>with an approval cut-off (noted "|" ).
>It's a mix of Condorcet, IRV and approval.
>
>The idea is:
>1) to rank candidates using a Condorcet (ranked pairs, winning votes
>for example) method;
>2) eliminate last candidate like in IRV and give him the weight
>according to the number of voters
>having that candidate as last approved;
>3) repeat 1) and 2) until winner selection.
>
>Stephane,
>Am I right in gathering that the approval cutoffs don't actually have
>any effect on who wins??!
>
>Chris Benham
>
>33: A > B | C
>31: B > C | A
>33: C | A > B
>3:   B | A > C
>
>C is eliminated with 33 votes as support.
>B is eliminated with 34 votes as support.
>A is last eliminated but receives no rallying voters and finishes with 33
>votes as support.
>
>B wins.
>

Stephane,

I think I now get it, but to say that an  "eliminated" candidate wins is 
very strange because in the election
method context "eliminate" normally means "disqualify from winning, drop 
from the ballots and henceforth ignore".
 From your original description it seemed that the approvals served only 
to give all the candidates each a final "approbation"
score (just for decoration).

As I now understand it, this method just looks like a very complicated 
way of nearly always electing the Approval winner.

49: A | > C
48: B | > C
03: C | > B

C>B 52-48,  C>A 52-48,  B>A 51-49.  RP(wv) order C>B>A. 

By my calculation your method elects the Approval winner A, violating 
Majority Loser, Majority for Solid Coalitions and
the Condorcet criterion.

Is that right?

Chris Benham



>Yes. Sorry my wife's name comes up when I remote login...
>I think your statement is wrong. Let's try a counter-example:
>
>3 candidates A, B, C and 100 voters.
>Ballots:
>35: A > B > C
>33: B > C > A
>32: C > A > B
>
>Repetitive Condorcet (Ranked Pairs(winning votes)  ) elimination would produce
>
>at round 1:
>68: B > C
>67: A > B
>Thus ranking A > B > C
>C is eliminated.
>
>at round 2:
>67: A > B is the ranking
>B is eliminated
>
>at round 3:
>A wins.
>
>Now in which kind of ballot could an approval cut-off remove some support from
>A
>and give it to another candidate? Any ballot with A not in first position nor
>in last.
>Thus concentrating on the C > A > B voters to vote C | A > B instead of C > A
>| B
>removes final support from A and gives it to C. Not enough A still wins.
>
>Can we obtain an equivalent pairwise succession while raising the number of
>adjustable ballots (the ones with A in second position)?
>Let's add some B > A > C and try to adapt the others:
>33: A > B > C
>31: B > C > A
>33: C > A > B
>3:   B > A > C
>
>Pairwise comparison would produce the same 3 round process (values are
>different).
>66: A > B
>67: B > C
>64: C > A
>
>Let's put the cut-offs to disadvantage A:
>33: A > B | C
>31: B > C | A
>33: C | A > B
>3:   B | A > C
>
>C is eliminated with 33 votes as support.
>B is eliminated with 34 votes as support.
>A is last eliminated but receives no rallying voters and finishes with 33
>votes as support.
>
>B wins.
>
>This method is proposed within SPPA.
>
>Stéphane Rouillon
>
>Chris Benham a écrit :
>
>  
>
>>Elisabeth Varin wrote:
>>
>>    
>>
>>>I read several ways to mix Condorcet and Approval on recent mails.
>>>This is my favourite, using the latest proposed ballot example.
>>>
>>>I would suggest a Condorcet method usind residual approbation weights
>>>with an approval cut-off (noted "|" ).
>>>It's a mix of Condorcet, IRV and approval.
>>>
>>>The idea is:
>>>1) to rank candidates using a Condorcet (ranked pairs, winning votes
>>>for example) method;
>>>2) eliminate last candidate like in IRV and give him the weight
>>>according to the number of voters
>>>having that candidate as last approved;
>>>3) repeat 1) and 2) until winner selection.
>>>      
>>>
>>Stephane (?),
>>Am I right in gathering that the approval cutoffs don't actually have
>>any effect on who wins??!
>>
>>Chris Benham
>>
>>----
>>Election-Methods mailing list - see http://electorama.com/em for list info
>>    
>>
>
>
>
>  
>
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