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

[Stephane Rouillon]

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
>
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