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

Markus Schulze schulze at sol.physik.tu-berlin.de
Sun Jun 20 09:47:33 PDT 1999

Dear Blake,

you wrote (13 Jun 1999):
> Markus Schulze wrote:
> > Blake 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.

Condorcet writes (on page LXVIII of the preface of his "Essai sur
l'application de l'analyse a la probabilite des decisions rendues a la
pluralite des voix"): "From the considerations, we have just made, we
get the general rule, that in all those situations, in which we have to
choose, we have to take successively all those propositions that have
a plurality, beginning with those that have the largest, & to pronounce
the result, that is created by those first propositions, as soon as they
create one, without considering the following less probable propositions."

On page 126 of the Essai, he writes: "Create an opinion of those n*(n-1)/2
propositions, which win most of the votes. If this opinion is one of the
n*(n-1)*...*2 possible, then consider as elected that subject, with which
this opinion agrees with its preference. If this opinion is one of the
(2^(n*(n-1)/2))-n*(n-1)*...*2 impossible opinions, then eliminate of this
impossible opinion successively those propositions, that have a smaller
plurality, & accept the resulting opinion of the remaining propositions."

You wrote (13 Jun 1999):
> Markus Schulze wrote:
> > Blake 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.

Your argumentation is strange. It seems to me that you assume that
if a given voter has absolutely no informations about the opinions and
the voting behaviour of the other voters this voter will (to calculate
his optimal strategy) assume that the opinions of the other voters
are distributed randomly and that the other voters don't use any

You wrote (13 Jun 1999):
> 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?

I don't understand what you mean. As Schulze meets the Condorcet
Criterion, you know the answer to your above question.

You wrote (13 Jun 1999):
> > 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?

Isn't this strategical problem of MinMax(VA)
caused by its violation of Reversal Symmetry?

You wrote (13 Jun 1999):
> > 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 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.

I don't agree with you. You are actually saying that it is allowed
to declare all those ballots that don't rank all candidates invalid
but it is not allowed to try to encourage rather than to deter the
voters from ranking the candidates.

On the one side, you write: "I think it is perfectly reasonable to call
any of these rankings 'sincere' in the sense that it is as sincere as the
method (=IRO, FPTP,...) allows." On the other side, you don't say:
"I think it is perfectly reasonable to call a voter who uses
random-filling 'sincere' in the sense that he is as sincere as the
method (=VA) encourages."

Markus Schulze

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