[EM] Fwd: Is Condorcet The Turkey?

[Adam Tarr]

Bart wrote (at the end):

> > > Imagine these as the SENTIMENTS (these are not ballots) of the voters:
> > > 49 A>>>>B>C
> > > 2 B>>A>>>C (doesn't really matter)
> > > 49 C>>>>B>A
> > >
> > > The Condorcet ballots arising from the above sentiments:
> > > 49 A>B>C
> > > 2 B>A>C
> > > 49 C>B>A
> > >
> > > Please do not reply to this by pointing out that no one ranks B last.
> > > That is indeed a useful fact, but it has nothing to do with utility.
> >
> > Perhaps this collection of votes has been asked to carry a bigger burden
> > than it is capable of:
> > Condorcet does not support expressing the detailed sentiments that
> > are imagined above.
>
>Indeed, Condorcet is a bit limited, isn't it?

If you mean, in Condorcet's ability to respond to utility of preferences, 
vis-a-vis approval, then absolutely not (at least, not in this case).

The Condorcet ballots from the above election will be as 
follows.  Preferences written in parenthesis may or may not be expressed by 
the voter.

49% A(>B)
2% B>A
49% C(>B)

In order for B to win the election using Condorcet voting, roughly 94% of 
the 98% of the electorate in the A and C camps have to choose to express 
their very weak preference for candidate B.  If, for instance, "only" 93% 
chose to do so, like this:

47% A>B
2% A
2% B>A
3% C
46% C>B

Then A wins the election.  Contrast this to the same election with approval 
voting:

49% A(B)
2% B(A)
49% C(B)

Now, in stead of needing 94% if the main factions to cast their second 
choice, B only needs 48% to do so.  Roughly half as many.  For example:

25% A
24% AB
2% B
24% CB
25% C

B wins, with a 50% approval rating.

Now, we can speculate until we're blue in the face about whether ranking 
equally (a la approval voting) will be less likely than marking a second 
choice (a la Condorcet voting).  In all likelihood, it would be.  But half 
as likely?  That's hard to say with any certainty.  Political leaders will 
recognize these situations and steer their faction toward an optimal choice 
(for them, anyway) in BOTH cases.

Don't misconstrue what I say here to be a criticism of approval, which I 
consider to be a fine election method.  But the "turkey" scenarios for 
Condorcet stem from voters using stupid (in some sense) strategies in 
Condorcet, and then avoiding those same strategies in Approval.  The voting 
systems do look quite different, but that doesn't stop these examples from 
being false dichotomies.

It's worth noting that Forest and others have shown that when there is a 
Condorcet winner present among a group of candidates, that candidate is 
almost always the only stable approval winner equilibrium.  Approval voting 
works by finding the consensus, and the consensus nearly always points 
toward the Condorcet winner, regardless of the intensity of the preferences 
involved.

-Adam