[EM] Weak FBC and equal-ranking-allowed IRV

Chris Benham chrisbenham at bigpond.com
Mon Dec 1 17:42:28 PST 2003

A while back you were having a discussion with  Kevin Venzke (and 
 Donald) about how, if allowed,
equal-ranking  in IRV should be handled. Your most recent contribution:
On Mon.Oct.20, 2003  I  posted something pointing out that  whole-votes 
 equal-ranking-allowed IRV
doesn't really comply with weak FBC, but I finished with the sentence:

"I agree that the whole votes version is better because it does greatly
ameliorate the "favourite betrayal" problem."

I have changed my mind, and now agree with you that the split-votes version
is better. I think that it is absurd that half an even number of voters voting
AB and the other half BA should have a different effect from all of them voting
A=B, and also that it is unfair that a faction of voters who  support candidates
A and B by all voting either AB or BA, should be in any way disadvantaged compared
to a faction who support candidates C and D by all voting C=D.
Off-list, someone told me:
"Incidentally, Woodall calls "Symmetric-Completion" the ability to treat equal
equal rankings (or at least truncation) as equivalent to an equal mixture of every
possible strict ordering.  He speaks of methods passing or failing this standard..."
I like it.
 Whole-votes equal-ranking-allowed IRV is far too Approval-like,and I suggest that
it be called "Preferential Approval". It is not even clear to me that there is a 
better strategy in it than just giving out first preferences to all the candidates
you would approve under Approval.
Inspired by Kevin Venzke's high-resolution ratings ballot "Gradual Information Approval"
idea, I posted plain ranked-ballot "Gradual Information Runoff":
In it I mentioned "equal preferences ok" and "no split votes". I have changed my mind 
about that and now think that if equal preferences (besides truncation) is allowed then
the vote should be split, so that each voter contributes no more than one vote in total
to candidates not marked "not viable". I could live with equal prefernces (except for
truncation) simply not being allowed. Compared to IRV, GIR trades in a little bit of
later-no-harm for a little bit of Condorcet compliance. With 3 candidates, it is 
equivalent to IRV.
I found this in the archives:
In it is erroneously claimed that the split-votes version of equal-ranking IRV 
(and also,in effect, the normal equal-ranking not allowed version) fails "GITC"
(Generalised Independence from Twins Criterion), and has a "rich party" problem.
Elsewhere this fellow says that a "twin" is the same thing as a "clone", and gives 
this definition:

A set of alternatives, X[1], X[2], .. X[m] is a clone set provided that for

every alternative Z, where Z is not one of X[1], .. X[m], the following is

Every ballot that ranks Z higher than one of X[1] .. X[m] ranks Z higher than
all of them.  Every ballot that ranks Z lower than one of them, ranks Z lower
than all of them.  No ballot ranks Z equal to any of them. 

As well, there must be at least one alternative outside the set of clones,
and at least two alternatives in the set of clones."

So therefore GTIC must be the same as Clone Independence, or as he puts it, this:

"Name:  Independence of Clones Criterion: ICC 


  If there are alternatives X1, X2 ... Xn that are a 
 clone set <http://condorcet.org/emr/defn.shtml#clones>, and if one of these clones is 
 eliminated <http://condorcet.org/emr/defn.shtml#eliminate> from every ballot, then, if the winner for the old ballots 
was in the clone set, the winner for the new ballots must also be in the clone
set.  If an alternative outside the clone set won for the old ballots, the
same alternative must win for the new ballots."

Part of his post goes:
"2.  Give each of the alternatives an equal fraction of the vote.
So, for example, once A=B=C reaches the top of the ballot (through
elimination), each of A, B, and C will get 1/3 of a vote.  Once one
of them is eliminated, the each get 1/2.  And finally when two are
eliminated, 1.

This doesn't appear to have the problem I mentioned above, but it does
fail GITC.
Candidates are A and B, which are not twins, X and Y, which are. 

42 A B X Y
30 B X Y A
27 X=Y=B A
32 X Y B A
31 Y X B A"

X wins, but if Y is not there B wins. And so he concludes:
"So, having a twin caused X to win.  This is called the rich party problem 
because it means that parties that can afford to run more candidates will 
have an unfair advantage."

The big flaw in this argument is that the clone set is BXY.

 He continues:
"3. Just don't allow equal rankings, except by leaving candidates unranked.
This is the most obvious solution.  It is possible that the electorate
wouldn't understand, and use, equal rankings anyway.  And it passes

Unfortunately, it passes GITC for the same kind of technical reasons
that make plurality pass GITC.  That is, because voters are forced
to distinguish between candidates randomly, even if they have no
preference, they will break up what based on their true preferences,
are twins.  However, the rich party problem remains."

Here I think that he is improperly classifying Plurality as not a ranked-ballot

Chris Benham 


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