Condorcet vs Approval

[Tony Simmons]

>> From: Joe Weinstein
>> Subject:  Re:  Condorcet vs Approval

>> For me, Condorcet breaks down at the very beginning, in
>> the simplest case, a 2-candidate contest between A and B,
>> where Condorcet Winner A beats B over a majority of the
>> voters by very shallow preference, but B beats A over the
>> remaining voters by heavy preference.  E.G.,  suppose (on
>> a grade scale of 100) the voters grade the candidates as
>> follows:

>>     55% of voters:  A(80) B(75)
>>     45% of voters:  A(40) B(80)

>> To me it is clear that the deserving winner is B, the
>> candidate with a higher grade average (which some people
>> equate exactly, and I roughly, to higher 'social
>> utility').  Of course, one might argue (in my view,
>> correctly) that - for purposes of true social utility - a
>> grade of 40 is surely worth more than just exactly half of
>> a grade of 80, etc.  However, even if grades were in some
>> way convex-transformed to reflect this view, before being
>> averaged, B would still be the clear winner.

(1) Is it a problem that can be solved?  (2) Is it really a
problem at all?

The example, because of its simplicity, highlights the
difficulty of resolving such a problem.  How do we find out
the utilities?  Do we ask voters to express how strongly they
prefer one candidate over another?  If I prefer A slightly
over B, can I be expected to mark on the ballot that it's not
such a big preference, and the election should probably be
decided by those who really care?

I've actually done that in real elections, by not voting on a
particular matter.  But if I have a preference, and, as is the
case when there are only two candidates, the strategy for
winning is obviously to mark the ballot in a way that gives
my candidate the best advantage.  If we expect people to be
honest about the strength of their preferences, the most
honest will be turning over the electoral power to those who
are the most dishonest.  That can't be a good thing.

As much as I hate to admit it, the only way out that I can
see is to admit that as far as voting strategy goes, honesty
for the sake of honesty is a weakness.

Perhaps it only makes sense to weight votes when each voter
carries the same total weight, or when voters are expected to
normalize their preferences, and feel free to put the
favorite at the maximum score and the least favorite at the
minimum.

I can also see the value of logrolling in a situation like
this.  Implementing it in a general election might actually
make tremendous sense, since it's an important mechanism for
dealing with the strength of preferences, but that's its own
major can of worms.