[EM] Fwd: Is Condorcet The Turkey?

[Bart Ingles]

Adam Tarr wrote:
> 
> 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).

Actually my offhand comment was aimed more at the implied assertion that
"if sentiments cannot be expressed in a Condorcet ballot, they are only
imaginary."


> 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, instead 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.

The likelihood of marking a second choice would of course depend on (1)
the amount of strategic information available, (2) the actual degree of
preference for B, and (3) how uniform these sentiments are within the
groups.

I agree that it's a question of degree.  The difference between the two
methods is in the incentives they provide.  As you pointed out recently,
the only incentive that Condorcet provides for strategic truncation (at
least with wv) is through collusion between the A and C factions (then
again, the same might even be true with AV in some situations).

You raise an interesting point though-- could Condorcet actually be
*more* likely to dump a sincere Condorcet winner in certain situations? 
Suppose the original scenario above represents averages for each
faction, so that some A voters have a strong 2nd-choice preference for
B, while others are indifferent between B and C, and so on.

15%  A>B=C
25%  A>B>C
20%  B>A=C
25%  C>B>A
15%  C>A=B

Under AV, B could receive as much as 70% approval, vs. no more than 40%
for A or C.

Under Condorcet, the sincere truncators have no incentive to truncate
(other than convenience). Instead they are free to use pure strategy. 
If 6% of the indifferent A and C factions vote to bury B, they increase
their probability of success from 0% up to whatever their chances would
be in an A vs. C matchup (it wouldn't have to be very high, since the
consequences of failure are nil).

Of course there are counter-strategies.  The B voters might get together
and throw 2nd choice support to either A or C, to try to reduce the
strategy payoff for the remaining side.  Or some of the A>B>C and C>B>A
voters could vote A=B>C or C=B>A, essentially duplicating the Approval
results.  It seems kind of a messy way to there, though.

Bart


> 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
> 
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