[EM] IRV inconsistency plus Beyond Etiquette (at no extra cost)

[Forest Simmons]

"The Tragedy of the Inconsistent Oracle"... touching story, that.

Here's my entry to Blake's Greek Tragedy Writing Contest:

Once upon a time Sparta and Athens decided to try joining together against
their common enemies.  They wanted to elect a common leader from among
three likely candidates ... Hercules, Achilles, and Sopha_so_good_cles,
hereafter referred to as H, A, and S (respectfully).

The Oracle of Delphi recommended using the latest rave election method ...
IRV which (unbeknownst to the citizens) stood for Insane Results Voting. 

The election was staged, and the ballots were to be delivered to the
oracle to be counted. However, on the way to Delphi, the Spartans stopped
and counted the ballots from Sparta, and noted that Hercules was the
definite winner according to the rules of IRV. 

Sparta's results:

1900 SHA
1400 HAS
1200 AHS

They noted that by the rules of IRV, H beat S by a decisive majority of
2600 to 1900 transferred votes.

They took a secret vow that if the oracle were to give the win to S or A,
they would stir up the Spartans to attack Athens and enslave the surviving
citizens.

The results from Athens were ...

1500 SHA
1700 HAS
2300 AHS

which the Athenians delivering the ballots to the oracle made note of
during their trek to the temple of Delphi.

Again the results were decisive by the rules of IRV: H beat A 3200 to 2300
transferred votes.

No secret vow was taken by the citizens of Athens, who were not men of
blood. (There were a few women of blood in the company, but they held
their peace.) 

Presently the Oracle of Delphi announced the results:

A beat S by a decisive majority of 6600 to 3400 transferred votes.

The Athenians were surprised because they knew that Hercules was well
liked among the Spartans, and that he had a decisive victory among the
Athenians. Nevertheless, they all accepted the result passively (except a
few women of blood).

The Spartans, who knew nothing of the Athenian tally, went ballistic.

They attacked Athens with raging fury, destroying almost every man, woman,
and child, subjecting the rest to slavery for many generations.

The Oracle of Delphi was heard to mutter, "Tut, tut." 

(Why the Oracle was thinking about King Tut at a time like this is beyond
me.)

[Greek Chorus chants tale of woe, and nobody lives happily ever after.]

Well, the point of this sad tale is that IRV advocates believe that these
victories are indeed decisive, majority victories. So according to their
own belief system, Hercules has decisive majority victories in both Sparta
and Athens.  At the same time their belief system says that Hercules loses
to Achilles by an even more decisive majority when the ballots are
combined. 

How do they resolve this blatant inconsistency? Write another Greek
Tragedy? Quote Arrow? Blame it on the fickleness of the public?

Their belief system is inconsistent.

Now how about people who believe in the Condorcet Criterion. Is their
belief system inconsistent?

Only to the extent that they take their Condorcet completion methods too
seriously, claiming decisive results. 

Taking Condorcet completion methods too seriously is an Achilles heel of
the EM list, causing a lot of nitpicking and bickering that gives IRV
supporters (in their blissful solidarity) an unwarranted political
advantage.

I would like to make a couple of suggestions that go beyond mere
etiquette.

(1) Let's try to avoid nitpicking. 

Nitpicking means detracting from someone's posting by trying to shoot it
down on the basis of some tangential issue.

When the temptation is too great (as it is for me sometimes) let's try to
use good humor (or else sarcasm so heavy that it parodies itself) and/or
acknowledge that what we are doing is nitpicking by saying something like,
"I don't want to detract too much from this otherwise excellent posting,
but I would like to point out blah, blah, blah."

(2) Let's give the writer a way to save face gracefully rather than
unmercifully nailing him to the wall..

We all hate to see hard feelings come out of these differences of opinions
whether they are just differences in word usage or more substantial
differences.

It's probably a good working hypothesis to assume that everyone
subscribing to this EM list is trying to help the cause of truth and
fairness go forward, no matter how thick headed they might seem at times.

Let's cool off before clicking the SEND button.

Whoever is the first to break off a pointless chain of attacks and counter
attacks by some good natured suggestion of a truce is a hero in my
estimation. 

Any other suggestions "beyond etiquette?"

Forest


On Thu, 17 May 2001, Blake Cretney wrote:

> On Mon, 14 May 2001 15:45:33 -0700 (PDT)
> Forest Simmons <fsimmons at pcc.edu> wrote:
> 
> > Here's an inconsistency of IRV that I wish somebody had told me
> about
> > before I submitted my article to the Green Voice.
> > 
> > It is possible for a candidate to "win" every precinct without
> winning the
> > election.
> > 
> > In other words, if the "winner" of each precinct is calculated by
> applying
> > the rules of IRV to the ballots from each individual precinct before
> > applying IRV to the entire collection of ballots, it can happen that
> > candidate B wins in every precinct while some other candidate wins
> the
> > election.
> > 
> > This weirdness cannot happen in Approval, for example.
> 
> I'm always suspicious of the Weirdness Avoidance Standard.  My
> impression is that a lot about public choice doesn't fit with our
> intuitions.  So, our intuitions aren't always reliable.
> 
> Since Consistency violation can occur in Condorcet methods too,
> including Ranked Pairs, I defend it on my web site.  Here's the
> defense.  I'm going to suggest a similar, although purely hypothetical
> situation, and show that the intuition against consistency violation
> can lead to error.
> 
> Imagine that you are asking a magical oracle about which is the best
> candidate. The oracle only accepts questions comparing two candidates.
>  The oracle is sometimes wrong, but always gives an accurate
> prediction of its likelihood of being correct.  This is meant to be
> vaguely similar to the situation of relying on majority decisions to
> get a best guess for best winner.
> 
> The oracle claims
> A>B has a 80% chance of being correct
> B>C has a 70% chance of being correct
> C>A has a 60% chance of being correct 
> 
> Clearly the oracle is wrong about one of these answers.  Since the
> oracle is least certain about C>A, it makes sense to guess that this
> is where the mistake is made.  We can then declare A the likely best
> candidate.  
> 
> Now, someone else goes to the oracle to ask about the same candidates.
>  The oracle gives the following information 
> 
> A>C 51%
> A>B 100%
> C>B 100%
> 
> On the basis of this information alone, A appears to be the best
> candidate. 
> 
> Let me point out, that the two sessions with the oracle are not
> inconsistent.  They may be unlikely, but they both could happen.  
> 
> Now, by consistency, we would expect that A should also win if the
> information from the two interviews are combined.  The combined
> information gives these responses: 
> 
> A>B 80% chance
> B>C 70% chance
> C>A 60% chance
> A>B 100% chance
> C>B 100% chance 
> 
> Since we know the 100% statements are true, the B>C can be dropped as
> false, and the A>B 80% can be dropped as redundant.   This gives,
> 
> A>B 100% chance
> C>B 100% chance
> A>C 51% chance
> C>A 60% chance 
> 
> So, clearly, since C>A is more likely than A>C, if follows that C is
> most likely the best candidate.   This of course violates consistency,
> but in this case, appears reasonable.
> 
> ---
> Blake Cretney
> 
>