[EM] Condorcet and other authors on Condorcet (and how does range voting fit in?)

[Abd ul-Rahman Lomax]

At 03:13 PM 5/17/2010, Kevin Venzke wrote:
>Hi Warren,
>
>--- En date de : Lun 17.5.10, Warren Smith <warren.wds at gmail.com> a écrit :
> > I just started looking in the library
> > to answer the historical
> > question "what did Condorcet himself (and other authors
> > about
> > Condorcetness) have in mind?"
> >
> > Albert Wiele: "Democracy," St Martins Press NY 1999
> > on p133 defines "A condorcet-winner is that alternative
> > that could
> > defeat every other alternative in a pair-wise contest."
> > Note: this can be interpreted as saying "range voting is a
> > condorcet
> > system" or "not."
> >
> > It is ambiguous.
>
>It's only ambiguous if he didn't define "pair-wise contest." Did he?
>
>Personally I know what I mean when I say "pairwise contest" and it
>doesn't concern me that if I spoke less precisely then something else
>could be understood.

Here is the issue. Is the "pairwise contest" some 
*other election*, where the two candidates face 
off against each other? But this is a completely 
different election! It's a theoretical construct, 
not an actual procedure to follow with ballots.

The question is whether the ballots are changed! 
If the original election ballots have:
51: A 6, B 5
49: A 0, B 10

Who wins that "pairwise election?" Surely it 
depends on the rules! But it was assumed that 
preference was the information provided:

51: A>B
49: B>A

A wins, no doubt about it (if plurality is the 
rule, and in this case, it's even a majority.).

The idea that only preference information is 
extracted from the ballots in order to construct 
this "pair-wise contest," neglects much election 
reality. The idea that Range fails the Condorcet 
Criterion is based on an assumption that the 
internal preferences will remain the same in this 
"pairwise election," not that the pairwise 
election is determined by ignoring all other 
votes from the full election (Range, in this 
case). Since we can see that 51% of voters prefer 
A to B, we assume that they will vote this way.

But in real elections, they might not vote at 
all, so weak is their preference. Easily, if we 
took that pairwise election and did actually run 
it -- and I've proposed exactly that, we could 
find that B wins the runoff. I predict it, except 
in one case, where the A supporter votes were 
distorted by some artifact, perhaps the presence 
of some irrelevant candidates that seriously 
distracted the 51%. (I'm assuming that A and B 
are indeed the frontrunners, there may be massive 
vote splitting among the favorite and worst as seen by the 51%.)

No, where a ballot does allow full preference 
expression, and Range of sufficient resolution 
does that, I see no problem with asserting that 
Range will always pick *by definition* the 
Condorcet winner, and it isn't troubled by cycles 
(only by the much more remote possibility of ties.)

What is truly offensive is when both the Range 
and Condorcet winner, by true preferences and 
strengths, lose, because of quirks of a voting 
system like IRV. I.e., assume true preferences 
(with or without normalization, and it's most 
offensive when the utilities are normalized), 
derive sincere votes from them in a Range method 
of sufficient resolution to express all 
preferences, and the Range winner and the 
Condorcet winner are the same (as will normally 
happen), but this candidate loses in, say, IRV, 
because of insufficient first preference votes, 
so the candidate is eliminated before a strong 
showing for second rank appears (which could even 
be unanimous, a truly good outcome), whereas the 
IRV outcome, in theory, could be strongly opposed 
by two-thirds of the voters. (That's extreme, of 
course, but it's not hard to understand center 
squeeze and, in fact, it's quite predictable when 
there are three major parties.)

For the long term, I'm suggesting implementing 
methods that collect Range data, but always 
including a Condorcet winner apparent from the 
votes in a runoff, if a runoff is needed. Then, 
ultimately, efficient voting systems can be 
designed based on real election data. I'm 
suggesting Bucklin as the method, using a Range 
ballot with 50% rating being approval cutoff, no 
candidate would be elected in a primary unless 
they have at least a majority of voters rating 
them at 50% or higher. As a Bucklin method, it 
would be clearly Majority criterion compliant. 
But it is possible that it could miss some minor 
Condorcet winners, due to multiple majorities 
appearing in a Bucklin counting round. That's a 
relatively harmless Condorcet violation, and my 
guess is that it would be rare. But good ballot data would show it.

And as to the runoff, I just point out that it 
could be arranged that a condorcet winner would 
always be included. So we actually would have 
that real pairwise contest! My theory would be 
demonstrated or shown to be bogus. In fact, I 
expect that *usually* the Range winner would 
prevail, but I've also noted that exceptions 
could exist due to unwise exaggeration or 
normalization error in a primary. In other words, 
the Range winner only *appeared* to be the 
utility maximizer due to quirks in the voting.