[EM] range versus condorcet & others; practical purposes

[Warren Smith]

In some sense the range versus Condorcet debate is a red herring
since Condorcet methods have, I think, no chance of actual adoption
by governments.  And range does have a chance.  So for practical purposes,
forget Condorcet.  Why do I say that?

Well, in our real-world-voter study of range & approval:  USA voters
by statistically clear margins, told us they wanted to stay with plurality and
NOT switch to either range or approval voting.  This makes it sound 
(correctly) like range will have a hard time getting adopted!
Now as far as I and the other pollsters could imperfectly see from listening to them,
the top reason the USA voters felt this way, was complexity.  They felt range and 
approval were too complicated.  But range voting is actually quite simple.
>From this my coauthor Doug Greene concluded that
discussing methods significantly MORE complicated than range was
just "mental masturbation" with no hope of actual political success.

That to me is a big reason to go with range:  it seems to me to be
by far the simplest method out there that much improves upon
plurality voting.  Approval voting is even simpler than range (though not as simple
as plurality).  So that may be a reason to go with approval.  However,
my feeling is that 
(1) despite the simplicity advantage of approval, USA third parties
would be foolish to support it because range experimentally gives them HUGELY
more votes than approval.
(2) if we cannot get - at the very least - the USA third parties to support a method,
there is no chance to get it adopted!
So it seems to me range is clearly more likely to be adopted by the USA because
it, but not approval, has a good hope of getting at least a mildly large support base.  
In fact my tactical plan is exactly to try to mobilize the third parties.

So it seems to me that from a practical point of view of maximizing our chances 
(as voting reform advocates) of success, there is only one reasonable
choice: range voting.  Not approval or IRV (not good enough to third parties)
and not advanced condorcet (too complicated for USA voters to accept).

To illustrate what I mean about advanced Condorcet methods being "complicated",
let me now describe a Schulze-beatpaths method, which Tarr favors,
with the wv and equality-allowing enhancements, which both Tarr and I consider
essential.  I assume Tarr will correct me if I make any errors in exposition:

(1) votes are orderings of the candidates of the form
A>B>C=D>E (equalities are permitted).  All candidates must be ordered
and none omitted (if any are omitted, the system either refuses to
accept your vote, or tells you it will assume all the unlisted
candidates aare ranked coequal last - either way you have no
way to express ignorance about any candidate).

(2) For each pair of candidates (a,b) we compute the "winning vote count"
for a over b, which is the number of voters whose vote said a>b,
assuming this number exceeds the count for b>a.  The result is a
"directed graph" with N vertices where each vertex corresponds to
one of the N candidates.  For each pair (a,b) of candidates
an arc is drawn pointing from the loser (call it b) to the winner (here a)
of that pairwise sub-election, and the arc is labeled
with the numerical value of the winning-vote count we just described.

(3) Now, in this directed graph, a "beatpath" is a directed path
of edges, always walking in the direction of an arc-arrow, which
leads from some candidate L to some other W.  The "strength"
of this beatpath is the minimum value of the numerical labels on its arcs.

(4) If the strongest path from L to W, is stronger than, or at least as strong
as, the strongest path from W to L, and if this is simultaneously true for EVERY L, then
W is a "Schulze winner".  Schulze proved the theorem that such a W always
exists (at least using margins, I am confused re the winning-votes enhancement).

(5) Usually, W will be unique, but ties for winner are possible.
In that case, Schulze advocates breaking the ties by a rather complicated
procedure which I thoughtfully will spare you from having to know!

In this procedure, it perhaps it possible or desirable to further enhance it
by permitting partial-order-type votes so voters can express ignorance/no-opinion.
Some such votes would be illegal since they contain a preference cycle.
They would have to be detected and rejected. 
That would add considerable additional complexity.

So.  OK, what do you think?  Does this method strike you
as simple enough, compared to range voting, to allow its adoption by the public?
Holy cow.  I think it has some beautiful ideas, but... no.

Also, aside from the complexity and tactical advantages re actually getting it adopted
- I just mentioned of range voting,
range also has the advantage it, in vast computer simulations, performs better than
all the others (tried about 30 competitors), robustly, measured by Bayesian regret.
In particular it has significant advantages over approval in situations with a decent 
honest-voter fraction and a large number of candidates (those situations
are a highly-exploitable weakness for approval).
So it seems to me this is a wonderful alignment of the planets
in range's favor.  Now I admit my computer simulations have been
attacked by (whom I regard as) sore losers, and I would like to
do an even huger future sim study addressing all their quibbles as best we can.  
But frankly, going on what we know now, range is objectively the best system, and going
on what we may learn in the future huge sim study, range is unlikely to
ever be beaten by a significant amount.   I think perhaps maybe it can be beat,
but I am not worried the beating will be severe since I just cannot see any major
exploitable weaknesses of range.

So while I want the mental masturbation to continue unabated, I think we have to unify
as a practical matter behind range voting.  And that is why I created both the
range voting list
   http://groups.yahoo.com/group/RangeVoting
and the CRV;  I meanwhile recommend continuing the mental masturbation
(i.e. study and endless debate over all voting methods) on the EM-list.  
I encourage all  EM-ers who feel similarly to also join the CRV.  As some have
already found, we also have interesting mental masturbation here on CRV!

wds  (CCing to EM list)