[EM] Jurij's example

[Forest Simmons]

On Tue, 6 Feb 2001, LAYTON Craig wrote:

> 
> Billy would also be the Condorcet winner.
>

Well, yes, no and maybe.

He would be what we might call the "Borda/Condorcet winner", i.e. the
"Condorcet winner" based on the (very likely) insincere ballots intended
for a Borda Count.  But it is not so clear that Billy would be a Condorcet
winner on ballots intended for a Condorcet scoring. 

Suppose the voting public were told just before the election that this
time the Condorcet winner would be chosen instead of the Borda Count
winner.

Then all of the voters that had been contemplating insincerely ranking LL
or RR lower than Billy would no longer have any strategic reason for doing
so. 

If most of the voters were in this category of intending to rank Billy
second insincerely (because of Borda), then under Condorcet, which gives
them no incentive to vote insincerely, Billy would probably lose. 

On the other hand, if Billy did win under the Condorcet system, then you
can be assured that most of the voters really did prefer a relatively
unknown guy to the arch rival of their favorite. This pure Condorcet
winner would be someone preferred by (two separate) majorities over each
of the other candidates. 

As Joe Weinstein said we need some better jargon. In the above context
there are at least three possible meanings for "Condorcet Winner."

(1) The one who wins when the ballots intended for Borda are used to
decide the winner according to Condorcet.

(2) The one who would win if the voters were to vote sincerely knowing
their ballots to be destined for a Condorcet decision. 

(3) In a perverse sense, the Borda Count winner is always "The Condorcet
winner" under the Borda criterion, because a Borda Count winner has a
higher Borda score than any other candidate, even when their scores are
compared pairwise. So in a certain sense the Borda Count, according to its
adherents, awards the election to the person preferred over all the other
candidates by the (diffuse) group will, as measured by the Borda Count. 

This third sense can be claimed by any method that ends up choosing a
winner by comparing total points of some kind. These methods all have the
advantage of avoiding Condorcet cycles because of the transitive property
of the strict order relation on real numbers. 

This third sense cannot be taken too seriously because the head-to-head
comparisons are by indirect inference (through total points) instead of
comparisons taken directly from the rankings. Nevertheless, it does
preserve some of the original intent of Condorcet (if we can read his
mind). 

I propose that we never use "Condorcet Winner" in this third possible
sense, and that we use it exclusively in the pure second sense (in
connection with sincere rankings) unless we clearly indicate that we
intend it in the first sense by saying Borda/Condorcet or IRV/Condorcet,
etc. depending on which method produced the rankings. 

Wouldn't this help avoid a lot of misunderstanding and sloppy thinking?

Another question.  How would voters vote under IRV in the two cases
considered above?  Again the two cases are ...

Case I : most of the voters do not actually prefer unknown Billy above
their favorite's arch rival. They just voted that way because they were
unaware that they were likely to turn a nobody into a serious contender by
overlooking a whimsical feature of their voting system. 

Case II : most voters actually do prefer Billy to their favorite's arch
rival. Their Borda votes were sincere.

Case I seems to be the original intent of the example.  In that case the
pure Condorcet method would end up awarding a win to Billy's second choice
(whomever he preferred next to himself), because the Condorcet destined
ballots would be marked very differently from the Borda destined ballots,
even though the blank ballots were identical and presented to the same
people with ostensibly the same choices.

It seems to me that IRV would give this same result in both cases, and
that Borda gives the opposite result in both cases.  Only Condorcet (among
these three methods dependent upon rankings) is appropriately responsive
to the difference in the two cases.

If IRV were modified to eliminate the candidate with the most last rank
votes instead of eliminating the candidate with the least first rank
votes, how would strategically minded voters vote in Case I ?  Would they
rank Billy last because they figured they could beat their favorite's arch
rival in the instant runoff? Or would they vote Billy second in an attempt
to get rid of the arch rival at the first stage? I think the same
psychology at work in the Borda example might favor this latter scenario. 
If so, then this modified IRV would end up giving the same result as Borda
in case I, as well as Case II.

An election based on Approval voting would almost surely yield the same
result as a pure Condorcet election in both cases. 

Lone-mark plurality would yield a tie between the two arch rivals in both
cases.

Fun example!

Some odds and ends:

In Jim Hightower's "Hightower Lowdown" discussion of IRV and PR he showed
his confusion by discussing Proportional Representation in the context of
a single winner election.  I think he got so enthused about the
possibility of something different and better than current methods that he
tripped up on the details in his excitement. "Get the readers activated
and leave the details to the experts," seemed to be his sentiments.

Thoughts about IRV's claim to have majority approval of the winner after
all of the vote transfers down the line: why not one last transfer after
the last contender is eliminated? Then we can claim that the winner was
by unanimous decision.

This could be done with plurality, too. Automatically transfer all the
other votes to the plurality winner right before the declaration of
victory. Better yet, just have the Supreme Court choose, and transfer
all of the votes to their choice.

Why limit ourselves to majority when we can have unanimity every time?

Forest