Ranked Pairs

MIKE OSSIPOFF nkklrp at hotmail.com
Thu Mar 21 18:52:01 PST 2002

Blake said:

I note that you don't usually define the Schwartz set as a procedure.
Your usual definition of SSD is really a combination of the two

I reply:

True, now that you mention it. The goal definition is briefer, in
both instances. I really like the brevity of the goal definition of
Ranked Pairs (RP). I guess mention of a ranking avoids the need of
mentioning cycles. But many people will wonder what an output ranking
has to do with the selection of a single winner. Of course any defeat
that's in a cycle is contradicted, nullified by the other defeats in
the cycle, and that justifies getting rid of all cycles, and
that could be said in an explanation of why we're interested in
a transitive ranking of the candidates.

Still, I wonder if people wouldn't accept it better in the
procedure form, which is also fairly brief, and which needn't mention
a ranking, but does have to speak of cycles, or contradiction among
defeats. I didn't like the relative vagueness of speaking of
contradiction, but, as you may have said, someone can always ask
how a defeat can be contradicted by other defeats, and is easily
answered by showing him/her a cycle.

So maybe I'd use the procedure that I posted, but replace the
cycle wording with "keep the defeat if it isn't contradicted by
already-kept defeats". Maybe that's the most acceptable RP definition.

Blake continued:

I think that ease of implementation is a very weak argument. It isn't
as if we don't know how to implement Ranked Pairs, we do. Check out (
http://vote.sourceforge.net/rpweb/rpweb.html). And programmers should
be willing to implement a harder algorithm if it makes it simpler for
the general public. For a successful method, the number of people who
write software to tabulate it will be minuscule compared to the number
who will want to know how it's making its selection.

I reply:

I agree if you're talking about public elections. But when you propose
a voting system to a small committee, the committeemembers' acceptance
is going to be related to how complicated the count is. And RP is
plenty complicated in small committees. Complicated, elaborate count
rules, and long program, compared to CSSD or BeatpathWinner. Committee-
members considering a new count rule are much closer to the count
than public voters are.

I believe that RP(wv) is a fine proposal for public elections. Only polling
will really tell whether RP(wv), CSSD, or SSD is more acceptable for
public elections. I'd expect that, for public elections, where SSD
& CSSD choose the same, SSD's stopping rule is more obvious, making
it a better public proposal. But since CSSD is better for committees,
and committees & organizations provide precedent, maybe CSSD would
make it to public acceptance before SSD would. Maybe RP(wv) will win
in the public polling, because of its brief definition. Every bit as
brief & simple as IRV.

Blake continued:

One of the reasons I like the goal-based definition of Ranked Pairs, is
that it encourages people to view the complete ranking as a satisfactory
result. If they want, they can check it against the definition, which
is easier than finding the correct ranking. If you describe a method in
terms of a procedure, people are going to want to have every step of the
procedure as the result.

I reply:

True, if people don't have a problem about an output ranking.

Blake continued:

That's a problem, because you say you want to advocate CSSD, but then
use the BeatpathWinner implementation, which I assume means Floyd's
algorithm. But Floyd's algorithm won't let you see the procedure being
carried out, it just gives you a final answer.

I reply:


When I've recommened CSSD to small committees, I've always suggested
the BeatpathWinner implementation, because committeemembers are
closer to the count than public voters are. In public elections,
programmers could of course implement CSSD by its own defining procedure
if they wanted to. Or the BeatpathWinner procedure could be used, and
,if necessary, people could testify that BeatpathWinner always chooses
the same winner that CSSD chooses.

As you said, though, RP's output ranking is easily checked.

I'd said:

>Also, CSSD always chooses from the initial Schwartz set, but
>Tideman doesn't. But in public elections Tideman virtually always

Blake replied:

I don't see why anyone should care one way or the other. If you could
convince me that there was some practical problem with choosing outside
the Schwartz set, I'd agree with you. Even if I could imagine the
public caring, this would be a point in your favour. But the Schwartz
set is just another obscure mathematical construct.

I reply:

I'm not saying that there's a practical problem with choosing outside
the initial Schwartz set. But choosing in the Schwartz set has
compelling plausibility, you must admit. If there's a beatpath from
A to B, but no beatpath from B to A, then the sequence of public
statements that says that A is better than B isn't contradicted. The
whole reason why we need circular tiebreakers is because of that
kind of contradiction. Without one, we have a collective public
statement that A is better W, and W is better than X and X is better
than Y, and Y is better than Z, and Z is better than B, and so it's
reasonable to say that A is indirectly better than B. Unless that's 
contradicted by a return beatpath, we should accept what that
sequence of public statements is saying.

The Schwartz set of course has 2 definitions, the beatpath definition
and the unbeaten set definition. We could look at it in terms of
an unbeaten set, and point out the special status had by
a set of candidates none of whom are beaten by anyone outside that
set. It's obvious to someone with no prior experience with voting
systems that there's something special, especially deserving of
winning, about the candidates in that unbeaten set.

Markus suggested a way to ensure that RP(wv) always chooses from
the initial Schwartz set. Other ways include deleting the non-Schwartz
candidates as soon as the count indentifies them, or saying that
their defeats must be kept. Of course that's one more rule for a method
that already is far too wordy in the form needed by small committees.
In public elections there's no need to do anything about the Schwartz
set, since RP always chooses from the Schwartz set in public elections
(absent the rare pair tie).

When I was going to count the ballots for the EM polls last summer,
it was of course necessary to ask the RP proponents to tell me how
they wanted to deal with equal defeats during the count. No one
really explained at that time how they wanted it done. I  understand
that Blake has a website article about that though.

Blake continues:

My phrasing is as follows:

Ranked Pairs gives the ranking of the options that always reflects
the majority preference between any two options, except in order to
reflect majority preferences with greater margins.

I reply:

Sounds great. Maybe that's how I'd propose it, pending more
conversations or polling. Except, of course, that I'd just say
"magnitude" or "strength", instead of "margins".

Blake continues:

I usually precede this with some description of what a ranking is, and
if I really want to be rigorous, what I mean by saying that a ranking
reflects a majority preference.

Let's say I have victories A>B 20, B>C 19, C>A 18. Now, consider the
ranking A>B>C. The only majority it doesn't reflect is C>A. But any
ranking with C>A will either not reflect A>B or not reflect B>C, both of
which are included in A>B>C. So, it's all right to have A ranked over
C, because this is done in order to reflect majority preferences with
greater margins. So, A>B>C is the Ranked Pairs ranking.

I comment:

It's interesting to look at the different ways that RP & CSSD choose.

AB2, BC3, CA10, AD20, DC30, BD10

B has by far the weakest defeat, and is chosen by CSSD, SSD & PC.
The initial Schwartz set is the whole candidate-set.

But though B's defeat is weakest, A's defeat is contradicted by the
strongest defeats. Keeping A's defeat amounts to overruling the
voters who voted for AD20 & DC30.

Dropping the weakest defeat vs keeping the strongest defeats.

When RP is worded by saying to drop the strongest defeat that's the
weakest defeat in a cycle, that wording raises unnecessary questions
about why we start by dropping a strong defeat. But, if we're
looking at it in that way, in terms of dropping, we aren't dropping
A's defeat because _it_ is stronger. We're dropping it because the
defeats that contradict it are the strongest.

As I said, I prefer wording it in terms of keeping, rather than dropping. 
Also, maybe the goal definition would be better accepted,
due to its even greater brevity, if people don't object to the output

Mike Ossipoff

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