[EM] Sum-up for Ranked Pairs

[Rob LeGrand]

Blake wrote:
> The main argument that has been brought in favour of Schulze is that
> in a simulation, it achieved a slightly better approximation of
> ratings than did Ranked Pairs, both falling behind Borda.  It seems to
> me that there are problems with choosing Schulze on this basis.  There
> is no reason to believe that Schulze ratings are optimal, even
> assuming important criteria.  It puts us in the position that we may
> be advocating Schulze, only to be later faced with another method with
> an imperceptibly higher ratings score, and even greater complexity.
> Would we then abandon Schulze?  Also, such a small difference might
> very well be susceptible to changes in the model of voter preferences
> used.  In fact, although I expect it will hold out, there have not yet
> been any arguments showing statistical (let alone practical)
> significance for the results.

I've run the same simulations (99999 elections each) many times now, and the
results are very consistent.  Among the margins methods, Path Voting always
beats Minmax, and Minmax always beats Ranked Pairs by even more.  I don't see
this as an enormous difference, but it is consistent.  Recently Markus showed
that those three differences are statistically significant for the cases of 10
and 25 candidates, and that was just for those 99999 elections.  Intuitively, I
can see why Path Voting does better.  As Mike might say, it tends to overrule
fewer voters.

One reason the beatpath idea appeals to me so much, despite the fact that it's
not obviously optimal, is that it's so simple.  It may not be as intuitive as
Ranked Pairs to the average voter, but to me it's mathematically more
aesthetically pleasing, whatever that means.  There may be a Condorcet
completion method that satisfies the same criteria and is better on SU, but
somehow I doubt it.  Maybe it's my theoretical computer science training
(networks and graph theory, etc.), but to me beatpaths seem like the most
natural (smoothest?) way to resolve Condorcet paradoxes.  If Ranked Pairs were
as simple to implement and had the same intuitive appeal, I'd support it
despite its apparent SU disadvantage.

> Read my signature for a brief definition of Ranked Pairs.  Note that
> although this definition doesn't suggest an efficient procedure to
> carry out the method (though one exists), it does define the method
> and suggest a justification, which is really all you need to advocate
> it.  Some terms may require clarification, but they have the meaning
> one would expect.

Any efficient implementation of Ranked Pairs relies on tiebreakers in the
middle of the procedure and runs the risk of tripping over equal pairwise
victories to give a non-optimal ranking.  Of course, this shouldn't be a
problem for public elections.

I understand and respect the reasoning that leads Blake to favor Ranked Pairs,
and the same goes for Mike and Cloneproof SSD.  It all depends on your
assumptions and which criteria you find important.  Personally, though, I think
Path Voting is the best of both worlds.  To me, winning-votes introduces more
problems (and funny behavior) than it solves, and Ranked Pairs isn't worth its
more complex optimal implementation.  But then I'm something of a
perfectionist.

Let me say again that I think Ranked Pairs is a very, very good method.  But I
don't see any important advantages for it over Path Voting.

=====
Rob LeGrand
honky98 at aggies.org
http://www.aggies.org/honky98/

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