[EM] Bad Condorcet winners?

[Forest Simmons]

I have some comments on Mike's response to Bart. See below.

On Sat, 17 Mar 2001, MIKE OSSIPOFF wrote (in part):

> My 2 main points about the Condorcet badexample apply here:
> 
> 1. The voter median will be a popular & crowded place, and if you think
> the only candidate there will be someone who is despised by 97% of the
> voters, it's very much to your advantage to convince someone else to
> run, another voter median centrist. By the way, "centrist" can be
> easily misunderstood. I think we're merely using it as shorthand for
> "voter median". Now, in the media, "centrist" is taken to mean someone
> who is between the Democrat & the Republican, at the media-defined
> "center", regardless of where the voter median really is.
> 
> So it's implausible to just one candidate, someone despised by 97%
> of the voters, with the voter median position all to himself.
> 
> 2. Aside from that, supposing that the example showed a genuine possibility 
> that's likely enough to be concerned about, the occasionial
> disutility isn't the important thing. The important thing is the
> _average_ SU. That's what determines your expectation in some future
> election where we don't know who the candidates will be. Your expectation is 
> better if we're going to use a voting system with a
> better _average_ SU. Pairwise-count methods have all other methods
> (except maybe Borda, with the assumption of sincere Borda voting)
> beaten in terms of average SU. In particular, Condorcet's method
> is best at electing CWs, and CWs are typically the SU maximizers.
> 

This fact, that pairwise-count methods have all other methods beat in
social utility, is what led me to generalize Approval Voting in the
direction of Dyadic Approval, which still relies on pairwise counts.

I say "still" because ordinary Approval can be formulated as a pairwise
count method, too.  Approval inherits its "no need to vote lesser above
favorite" property from this pairwise counting aspect of its nature, while
the rareness of ties is inherited from the additive point system aspect of
its nature.

Any system (like Borda) that cannot be equivalently formulated as a
pairwise counting method will invite strategic reversal of preferences in
real elections where a sense of the relative popularity of the candidates
is known. 

The tension that induces these reversals is in more or less direct
conflict with maximizing social utility, like two mules yoked to the same
plow but pulling in different directions; they cannot plow with the same
power that would be possible if they were pulling parallel to each other.

That's why it is a waste of social utility (not to mention sanity) to
defend methods that require you to vote your favorite below somebody else
for strategic purposes.

Dyadic Approval is a high resolution method, so it can easily discern the
occasional "bad centrist."

On the other hand, it is based on pairwise comparisons, so it doesn't
waste its energy on the internal frictions and tensions of strategic order
reversals.

Forest

> Bart's example of "bad Condorcet": 
> 
> >my basic "bad Condorcet" example (actually a low-utility
> >Condorcet example).  It doesn't seem particularly implausible to me, but
> >requires that utility include a non-policy component.  For example, the
> >middle candidate could be a centrist but unpopular for other reasons.
> >
> >In the following example, voter ratings are used to show an
> >approximation of utility.  Candidates A, B, and C are voter-rated on a
> >scale of from 0-10, with 10 being the voter's favorite, and 0 the least
> >favorite:
> >
> >Votes             Candidate (rating)
> >-----     ---------------------------------
> >  49%       A(10)                 B(1)  C(0)
> >   3%       B(10)  A(9)                 C(0)
> >  48%       C(10)                 B(1)  A(0)
> >
> >Without trying to make too much of the average or aggregate voter
> >ratings, it seems obvious that 97% of the voters despise candidate B,
> >even though B is the Condorcet winner.
> >
> >Bart
> >
>