[Election-Methods] How to use rankings below approval cut-off

[Stéphane Rouillon]

The method described below Kevin's comment does something with the 
additional information.

S. Rouillon

Kevin Venzke a écrit :
> Juho,
>
> --- Juho <juho4880 at yahoo.co.uk> a écrit :
>   
>> I don't fully agree that "the whole purpose of specifying NOTB is to  
>> allow us to ignore those rankings". It think in this case it is good  
>> to allow a voter to say "I don't support A and B but in the case that  
>> one of them will be elected I prefer A to B".
>>     
>
> "In this case"? Doesn't it matter what you do with the information? I'm not
> a fan of letting voters provide more data if the method won't do anything
> with it.
>
> Kevin Venzke
>   

> 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.
> 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,
> Am I right in gathering that the approval cutoffs don't actually have
> any effect on who wins??!
>
> Chris Benham
---------------------------
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
-----------------

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





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