[EM] Schulze and Margins was: Reversal Software output 6/9/1999

[Blake Cretney]

Markus Schulze wrote:

> Dear Blake,
> 
> you wrote (10 Jun 1999):
> > > "Marg" is the Condorcet(Margins) variation.
> >
> > Calling this method Condorcet seems to be an error started on this
> > list.  I'm going to refer to Minmax to refer to the same method since
> > this term is used in academic journals.  I use Minmax(Margins) to
> > refer to the Marginal variant.
> 
> I agree with you. There are lots of different interpretations of
> Condorcet's wordings. And that interpretation that is used in this
> list doesn't seem to be a justifiable one.

You once emailed me a quote on Condorcet's musings on extending his
method to more than three candidates.  You might post that to EM, as I
consider it decisive on this matter.

> 
> You wrote (10 Jun 1999):
> > 1.  Why is it useful to have truncation resistance, if anyone who
> > would leave candidates unranked can avoid the punishment by simply
> > randomly ranking those candidates?  This seems like something intended
> > to trap the gullible.
> 
> This would have been an argument against votes-against only if it had
> been true that a voter could avoid the punishment by simply randomly
> ranking the otherwise unranked candidates.

That is precisely what I contend.  If everyone who would have not
participated in a particular pair-wise contest instead votes randomly,
then the effect on average will be to give each side 1/2 the number of
abstaining votes.  The method of assigning half points for pair-wise
abstentions has been shown to be equivalent to margins.  I therefore
conclude that voters who leave candidates unranked, whether sincerely
or not, have the ability to cause their votes to be counted as in
margins.  So, if there is punishment, it is avoidable.  Your next
statement, of course, argues that there is no punishment.

> It has already been discussed that randomly ranking the otherwise
> unranked candidates is a useful strategy only if the winner of the
> elections is always that candidate whose highest number of votes
> against in any pairwise comparison (= win or defeat) is the smallest.

what I call Minmax.

> But for every other election method that uses votes-against instead of
> margins this is not a useful strategy.

It has been discussed, but we obviously came away from that
discussion with different conclusions.  This is unfortunate, since
this should be a provable point.  Perhaps a computer model would be
useful.

In fact, I think a strong argument can be made without the computer. 
Tell me if any of the following statements are incorrect.

1.  In Minmax, this is a useful strategy for elections involving 3
candidates. (or more in fact)
2.  Schulze is equivalent to Minmax for 3 or fewer candidates.
3.  My statement holds true for Schulze elections involving 3
candidates.  Obviously incomplete rankings have no effect for two or
one candidates.

Now, as more candidates are added, more situations arise where
random-filling can backfire.  I believe that what you are alluding to
is the possibility that with a long chain

A>B>C>D>E

in this case, a group of voters whose true preference is
E A
and who choose to randomly rank B C D, may hurt E by unintentionally
strengthening a path that works against it.  Unless I have
misunderstood you, it is your argument that this possibility makes it
impossible to say that random-filling is a useful strategy (unless of
course information is known to avoid this scenario).

However, the problem is that there is no more reason to believe that
the effect on extended paths will help than hurt.  That is, for the
middle of extended paths the effect is on average neutral.

However, we know from the three candidate examples that the effect on
short paths is not neutral, it is in favour of random-filling. 
Putting these two together, I conclude that even in Schulze,
random-filling is the best strategy in the absence of other
information.

Of course, one could argue that a strategy is only good if it always
works, not merely works on average.  If that is your view, consider
the following method.

Confused Plurality-  Each voter votes for one candidate.  99% of
ballots are chosen to be reverse-ballots, the remaining are
forward-ballots.  Each candidate is given a score equal to the number
of forward-ballots naming it, minus the number of reverse-ballots
naming it.  The winner is the candidate with the highest score.

It is obvious that the best strategy in absence of information is to
cast a vote for the candidate you most dislike.  Would it be
meaningful to define "sincere" strategy as otherwise?  If we define
sincere voting as voting for one's favourite, should we expect people
to vote sincerely because there is a 1% chance of an insincere vote
back-firing?

> You wrote (10 Jun 1999):
> > 2.  Why would anyone use truncation as a defensive strategy if it
> > tends to hurt their chances of winning, and the defensive strategy of
> > voting a reverser last is available?
> 
> Voters don't tend to use order-reversal. But they tend to truncate
> if they have to fear that an additional ranking could hurt their
> already ranked candidates.

Are you saying that voters will truncate if an additional ranking
merely "could" hurt, or will they truncate only if it on average does
hurt.

> The aim of the use of votes-against instead of margins is to
> minimize the probability that a voter could be punished for making
> an additional ranking.

It certainly does reduce that possibility, but goes to the extreme
that leaving candidates unranked on average hurts your favourite. 
Your statement above suggests that you do not believe this to be the
case with Schulze.  If you were convinced otherwise, might this alter
your stand on this issue?

> 
> You wrote (10 Jun 1999):
> > VA seems like a very strange method to me, an attempt by Mike
> > Ossipoff to combine Approval and Concorcet.  In other methods, a
> > sincere vote is the best (or at least equal to the best) vote when no
> > strategic information is known, and then as knowledge is picked up,
> > strategic possibilities result.  The winning-votes-only methods are
> > unique in that a sincere vote isn't always the best vote even when NO
> > information is known.
> 
> It is not true that Ossipoff's VA is the unique election method
> for which a sincere vote isn't always the best vote even when no
> information is known. The problem is that other people don't
> discuss the problem of equal rankings.
> 
> Example 1: If IRO is used then it is a useful strategy to give
> different rankings to your most favorite candidates even if you
> like them equally.
> 
> Example 2: If "first past the post" is used then it is a useful
> strategy to vote for only one candidate even if you don't have
> a unique favorite candidate.

I guess another example would be the version of IRV used in
Australia, where you would want to rank all candidates to avoid having
your ballot considered spoiled.  I assume this issue of avoiding a
spoiled ballot is what you're getting at with the two examples above.

I see a few important differences between these examples and VA.  One
is that these methods are open and explicit about the rules.  It is
obvious to everyone participating in a plurality election that you are
expected to choose a single candidate, and that your vote will be
thrown out otherwise.  VA allows people to make votes which I contend
are obviously unjustifiable, but does not give the warning that an
outright ban does.

More importantly, perhaps, is how the analysis of these methods
progresses.  When analyzing the Australian method, one would assume
that voters will complete their ballots regardless of whether they
sincerely have a complete ranking.  I think it is perfectly reasonable
to call any of these rankings "sincere" in the sense that it is as
sincere as the method allows.  In VA, however, it is often assumed
that people will vote partial rankings, and these partial rankings are
labeled as being sincere.

I guess I might have to amend my statement to say that the
winning-votes-only methods are unique in that a vote which is sincere,
and not actually a spoiled ballot, is not the best strategic vote,
even with no information.  This "uniqueness" is a pretty esoteric
point though, and not really central to my argument.

---
Blake Cretney
See the EM Resource:  http://www.fortunecity.com/meltingpot/harrow/124
My Path voting Site:  http://www.fortunecity.com/meltingpot/harrow/124/path