[EM] Ranked Pairs

Blake Cretney blake at condorcet.org
Fri Mar 15 08:42:22 PST 2002


 > Steve Eppley and Tideman have proposed briefer definitions,
 > based on goal rather than procedure, but I feel that those require
 > too much explanation, and that people want a procedure for a definition.

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 

 > Advantages of CSSD over Tideman:
 > CSSD has a more briefly & simply programmed implementation, the
 > BeatpathWinner implementation. Added to that, Tideman becomes especially
 > wordy & difficult for small committees where there can be equal
 > defeats and pairties.

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.

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.

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.

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

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.

 > Tideman's definition is somewhat briefer, and doesn't need to
 > define the Schwartz set. Some try to avoid mentioning cycles, but
 > then they have to say "...conflict with previously-kept defeats".
 > Maybe that will be better-accepted by the public than saying "cycle
 > with previously kept defeats", but I'm not sure.

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 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 try to avoid the graph theory approach, in which one imagines arrows
pointing between circles drawn on a piece of paper.  Instead, I rely on
the fact that for some combinations of pairwise decisions you can find a
ranking that agrees with all those decisions, and for some, you can't.

If people are willing to believe that it isn't always possible to find a
ranking reflecting every majority preference, then they can accept the
precedence given by Ranked Pairs, without thinking too much about
exactly why all majority preferences can't be reflected, what this looks
like, or what vocabulary might be used to describe this paradox.

Blake Cretney ( http://condorcet.org)

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