Tideman vs. Schulze

[Norman Petry]

On 29 Jul 1998 Mike Ossipoff wrote:

>
>As for Tideman's method, as I understand it, it doesn't offer
>anything that Schulze's method doesn't offer. Its rule is
>probably more difficult to explain or describe. Tideman may
>meet Independence from Clones, but it seems to me that it
>, in a different (& more likely) subcycle situation, causes
>a worse violation than the one that it avoids. That's why
>I haven't mentioned it when listing EM's better methods.
>I personally don't count it among those.
>

First of all, I want to emphasise that I've no doubt that Schulze's
beat-path method is technically superior to Tideman.  Markus has provided
examples in which Tideman's method fails to produce consistent results and
violates the "No-Show" criterion.  Tideman himself recognised certain
problems with his method (which involved a lack of complete independence
from clones in rare cases) that he patched using a fairly complex tiebreaker
rule (see "Complete Independence of Clones in the Ranked Pairs Rule", Social
Choice and Welfare (1989) 6: 167-173)).

I've applied Schulze's method to Tideman's own examples which demonstrated
that his original method (see "Independence of Clones as a Criterion for
Voting Rules", Social Choice and Welfare (1987) 4: 185-206)) had problems,
and found that the beat-path method appears to be completely independent of
clones without a complex tiebreaker.  The problem Tideman himself observed
was that when ties occur between candidates, the order in which the various
propositions (A>C, for example) are locked or skipped can affect the final
ordering, with the result that independence of clones is sometimes violated.
Because Markus' method is not dependent on ordering, it neatly avoids this
problem.

So given these problems, and the fact that we have a technically superior
method, why did I mention Tideman?

What I _like_ about Tideman is that his algorithmic definition is quite
simple to apply in a hand count, and seems to make intuitive sense.  Tideman
says that to determine the final ordering of candidates, just begin by
looking at the propositions backed by the most evidence (i.e.: the candidate
pairs having the strongest majorities), and work your way down to the weaker
propositions until you have a final ordering.  Since we want to avoid any
contradictions (cycles), just skip any propositions that would produce such
a result.  Although this is not the easiest possible way of determining a
pairwise winner, I think I could explain it to the average voter and have
them accept it as a valid approach.  Furthermore, I don't know to what
extent "name recognition" matters, but it seems to me that Tideman's method
_is_ Condorcet's method (or at least one very valid interpretation of it),
and could be "sold" to voters as such.  In 1785, Condorcet wrote:

"...The preceding reflections suggest this general rule: that whenever it is
essential to make the election, it is necessary to take successively all the
propositions that have a majority, beginning with those possessing the
largest.  As soon as these first propositions produce a result, it should be
taken as the decision, without regard for the less probable decisions that
follow." -- Condorcet, Essay on the Application of Mathematics to the Theory
of Decision-Making

To me, this sounds like Tideman's method!  Despite the fact that Tideman
doesn't offer everything Schulze provides, it does satisfy many important
criteria, including: Clone Independence("almost always", without the fancy
tiebreaker), Condorcet Winner, Pareto, MIIAC, and probably most others
mentioned on this list (I must admit that I haven't studied this in detail).
If a Tideman variant were proposed using absolute number of votes rather
than margins (to meet GMC), would it be inferior in _any_ respect to
Smith//Condorcet[EM]?  If not, that's why I suggested it could be considered
as another reasonable option between Smith//Condorcet[EM] and Schulze.

***

Now, getting back to Schulze's method:

I like this method as well.  It's mathematically elegant, and seems to meet
important criteria more successfully than any other single-winner method
that's been proposed.  Aside from failing Markus' "Positive Participation"
criterion (which I don't think any method has been proven to satisfy), it's
probably as close to a perfect method as can be achieved using single-ballot
voting.

_I_ accept the validity of this method on the grounds that it can be proven
to meet important criteria.  If the method were in widespread use, I would
probably also just accept it on the grounds that it produces good results
(just as STV is accepted even though it fails some academic criteria, such
as house-monotonicity).  Learning how to calculate the Schulze winner is not
_too_ difficult, and using a computer, this is certainly a practical method,
since it depends only on the pairwise comparison matrix for producing its
result (some methods require information from individual ballots, which make
them less practical in large-scale elections).

Here's the problem:

How would we go about explaining the workings of this method to voters?
Perhaps I'm missing something obvious, but I don't understand intuitively
why "beat-paths" should matter in determining winners.  Since the beat-path
scores are not determined by head-to-head comparisons between the pair of
candidates affected, but rather on intermediate majorities between different
(but overlapping) sets of voters in different pairwise contests, why should
that information be relevant as to who should win?  Is there a way of
explaining this which does satisfy "common-sense"?  If so, could someone
_please_ explain it to me, since I'd like to be able to promote this method.
If not, this seems like a practical (although not theoretical!) disadvantage
of Schulze's method.  The average voter would initially be quite suspicious
of adopting a method which they can't understand, no matter how many proofs
of criteria-compliance they're provided with.

***

Finally, you wrote:

>probably more difficult to explain or describe. Tideman may
>meet Independence from Clones, but it seems to me that it
>, in a different (& more likely) subcycle situation, causes
>a worse violation than the one that it avoids. That's why

Could you please clarify (preferably with an example) of what you mean by
this?  I'm very interested!


Norm Petry


-----Original Message-----
From: Mike Ositoff <ntk at netcom.com>
To: election-methods-list at eskimo.com <election-methods-list at eskimo.com>
Cc: election-methods-list at eskimo.com <election-methods-list at eskimo.com>;
chbeun at worldonline.nl <chbeun at worldonline.nl>
Date: July 29, 1998 9:09 PM
Subject: Re: Bottoms Up for Herman Beun


>Absolutely--Unless perfectionism is important to the party-members
>to whom the method would have to be advocated, then Rank STV(MO)
>is likely to be unnecessarily complex, for the amount of improvement
>of results.
>
>I was following the principle of trying to maximize the likelihood
>that the STV result used would be the right one, by giving precedence
>to the STV result whose N is more likely to match the number of
>seats that the party wins. So it's about probabilistic perfection.
>My rules would give precedence to the N that is closer to the number
>of seats won in the previous election, on the assumption that that
>number of seats is the most likely again.
>
>True enough: House nonmonoticity is probably rare, and then, even
>when house nonmonoticity occurs in the procedure's results, it
>probably won't be right at or next to the N that equals the
>number of seats that the party wins. Of course if the party
>wins a few seats more or less than last time, then my procedure
>would sometimes be giving precedence to the wrong count anyway.
>
>So sure--for simplicity & brevity of rules, it's probably better
>not to use 2 different precedence rules. That hadn't occurred to
>me about the previous fractie-size being a problematic added input,
>but maybe, especially when weighed against the need.
>
>I don't consider the house nonmonotonicity to be a problem, however,
>because that's just part of STV. So yes, the complexity issue
>is the more decisive one.
>
>As for the single-winner method for the 1st count, where N=1,
>sure, it would be unlikely to win just 1 seat. In any case, it
>could be argued that it's simpler to use the same method for
>each N, meaning that (ugh!) STV would be what people would expect
>the procedure to use for N=1. You'd have to weigh the simplicity,
>avoiding the use of a different rule for N=1, and the improbability
>of using the N=1 result, against the aesthetic aspect of even
>having STV with N=1 in the rules. Again, having one less thing
>to explain could outweigh the aesthetics.
>
>But, on the other hand, you can't get away from having to use
>some kind of single-winner method. Because, in the event that
>house nonmonotonicity _does_ occur, even Rank STV(NL) has to
>choose which of the entirely new candidates among the latest N
>shall get the Nth place in the list.
>
>Again, considering the rarity of house-nonmonotonicity, there's
>certainly a case for saying to just go by which one has the
>most 1st choice votes.
>
>But I claim that it would go beyond unaesthetics, and would
>set a bad precedent, if IRO were specified by the procedures
>rules for choosing which new STV winner gets the Nth seat.
>Consistency doesn't require use of STV for that single-winner
>choice, since it isn't part of the sequence of N-candidate STV
>elections. It's a special single-winner election for a rare
>occurrence.
>
>I realize that introducing a new rank-balloting count rule
>for a rare occurence would create a whole additional explanation,
>and possibly a time-consuming & consensus-threatening debate.
>The rarity of nonmonotonicity suggests just giving the Nth seat
>to whichever not-previously-listed candidate among the latest
>N has the most 1st choice votes.
>
>Because, either you want to go for simplicity or merit. IRO
>wouldn't give either. The reason for using IRO instead of
>most-first-choice-votes (FPP) would be if you believe that that
>rarely-needed sw choice matters enough to not use FPP. But if
>you believe that, then IRO doesn't make the grade either.
>
>So, simplicity of definition & explanation seems to point toward
>giving the Nth seat, in the nonmonotonic situation, to the
>new STV winner with the most 1st choice votes.
>
>***
>
>As for Tideman's method, as I understand it, it doesn't offer
>anything that Schulze's method doesn't offer. Its rule is
>probably more difficult to explain or describe. Tideman may
>meet Independence from Clones, but it seems to me that it
>, in a different (& more likely) subcycle situation, causes
>a worse violation than the one that it avoids. That's why
>I haven't mentioned it when listing EM's better methods.
>I personally don't count it among those.
>
>***
>
>Mike Ossipoff
>
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