[EM] Query for one and all, Clones

[Kevin Venzke]

John,

Permit me to offer some answers:

 --- "John B. Hodges" <jbhodges at usit.net> a écrit : 
> >From: "James Gilmour" <jgilmour at globalnet.co.uk>
> >Subject: RE: [EM] Query for one and all
> >JBH asked:
> >>  My question, for one and all: Is there any desirable quality, that
> >>  any single-winner method has, that this method does not have?
> >
> 
> (JBH) These are exactly the sort of replies I was hoping to get. But 
> I must ask for further explanation.

> >Two problems.
> >1. Your second and subsequent preferences count against your first preference.
> >2. If more than first preferences have to be counted, the value of 
> >the votes of different voters may
> >be different if the voters truncate after different numbers of preferences.
> >James

> James: (1) would seem to be true of all methods that allow voting for 
> more than one candidate. But with MCA, as with IRV/STV, your 
> later-choices do not come into play unless your first-choice has 
> failed to win.  So, (1) is much less true of MCA than it is of plain 
> Approval.

(1) is not true of IRV, or Condorcet when there are no cycles.

You say "unless your first-choice has failed to win," but note that your
first choice is still capable of winning, which is different from the IRV
situation.

You're correct that GB (I will call it that to avoid confusing it with
the MCA that I understand) is better than Approval here.  The bigger problem
is (2).

> (2) is true of any method that allows truncation; since it 
> is at the voter's discretion, I see no grounds for complaint.

Suppose one voter only sincerely approves and ranks 1 candidate, and another 
voter does 5 candidates.  Unless the method goes down to the fifth rankings,
the second voter is not able to make all the compromises he might've been
willing to.  A voter should not use more ranks than will be seen (also true in 
the original MCA: if you know the winner will win by being majority favorite, 
the middle rank is useless).  To protect uninformed voters, this suggests to me 
that the number of MCA/GB ranks be few and fixed in number.

> >Condorcet, Condorcet Loser, Consistency, Independence of Clones,
> >Reversal Symmetry, Smith, later-no-harm, Participation.
> >
> >Markus Schulze
 
> Consistency: is there any 
> method that passes this, other than Plurality? 

Approval does, at least...

> How does MCA NOT pass that? 

This is actually pretty similar to the Participation failure.  Imagine:
One electorate has two majority favorites, with A narrowly beating B.
Second electorate has no majority favorite, but say B is a lot of people's
favorite and A is no one's.  A has higher 1st+2nd approval, though, and wins.
Combined: B is majority favorite and wins.

> Please remind me what "Reversal Symmetry" and "later-no-harm" 
> mean, why they are desirable, and why MCA does not pass them. Much 
> Thanks-

"Reversal symmetry" doesn't seem too important, but it should be pretty
clear that you can't flip GB or MCA ballots around and get a consistent result,
because the rankings are evaluated from the top down.

"Later-no-harm" is James Gilmour's problem (1), the fact that you can cause
second-favorite to beat favorite.  (Imagine that favorite could win at a later
stage, if you had not helped second-favorite get a majority at an earlier stage.)

>(JBH) Good, simple demonstration. But, remember that in MCA ties are allowed; so, 
>shouldn't the voters rank C1, C2, C3 equally? 
>2 A > B > (C2, C1, C3) 
>3 B > (C3, C2, C1) > A 
>4 (C1, C2, C3) > A > B 
>The winner is a tie between C1, C2, C3; use tie-breaking 
>method to pick one. If the voters do not rank them equally when the option is allowed, 
>doesn't that show they are not true clones? 

This is a good idea, but "clone" just means all the voters stick those candidates
next to each other, not necessarily equally.

Also, there are strategic reasons not to rank them equally.  The non-C voters hurt
the C clones by ranking them separately.  The C voters might want to rank them
separately if they think other voters will compromise on C1, which can't happen if 
the C voters compromise on A first.


Having said that, it occurs to me that the original, three-rank MCA is not 
clone-proof if you interpret the MCA ballot as an ordinary ranked ballot.  But with 
that interpretation, I don't think Approval is clone-proof, either, because Approval
would have to survive the introduction of new candidates, with a group of voters
that insist on bullet-voting for their favorite.

In other words, original MCA is not clone-proof if you require that it produce
the same winner, regardless of how the voters (sincerely) react to an additional,
non-winning candidate.

So I agree with Markus' listed criteria failures, provided that Approval is also
failed on Clone Independence, along with all limited-rank methods.

Reminds me of the Approval, IIA issue.


Kevin Venzke
stepjak at yahoo.fr


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