[EM] Runoff terminology --> Seeded Condorcet

[Forest Simmons]

Thanks Richard, I'll incorporate all of your valuable suggestions one way
or another.

I guess that "Instant Runoff Voting" is intended to be a simulated version
of a certain kind of actual runoff where the voters are required to go to
the polls up to N-1 times when there are N candidates.

It's ironic that when there is an unambiguous Condorcet winner, the same
number of head-to-head votes in a single elimination tournament would find
the Condorcet winner. This could be done naturally in the base two log of
N trips to the polls. On the first trip the voters have N/2, two-way
contests to vote on. With each successive trip to the polls, (the greatest
integer in) half of the remaining candidates are eliminated, etc. 

Regular plurality ballots could be used, since it is not uncommon to have
several races on one ballot in standard plurality elections.

This is a much better kind of actual runoff than the kind that IRV
simulates, since it is more efficient and yields a better result (whenever
there is a definite Condorcet winner, and the more wasteful runoff method
would inadvertently eliminate it) yet IRV claims exclusive use of the word
"runoff".

How ironic.

Well, I guess I need a good generic word to replace "instant runoff
method" that doesn't remind us too strongly of the inferior runoff method
that IRV simulates (thereby upsetting the Boeotians), yet does bring to
mind a satisfactory decision without multiple voting episodes. 

Any good ideas?

I remember when Xerox came out with their photocopy procedure. Before
long, "to xerox" meant to photocopy, no matter the brand of copy machine.
Eventually the word "photocopy" displaced this informal use of the word
xerox.  We need a good generic word like that.

"Instant Round Robin" would convey the idea of full Condorcet to sports
fans. 

"Instant Tournament" or "Instant Playoffs" would include simulated single
elimination, double elimination, and round robin concepts.

Would "instant voteoff" be too suggestive of elimination (even though it
naturally includes full Condorcet through the round robin playoff analogy
mentioned above)?

By the way, I'm no sports fan, but I understand that the playoff
tournaments of the major leagues are "seeded" in such a way that the
highest ranking teams do not get pitted against one another in their first
games; otherwise some of the best teams could be eliminated too early, and
the final games would not be as interesting on average.

This suggests to me an idea for resolving Condorcet ambiguities: Use
Approval to seed a single elimination head-to-head voteoff.

Here's how it would work:  On their Condorcet ballots the voters provide
one additional piece of information, namely the cutoff between the
candidates they want to support and those they want to reject.

Once the voted ballots are scored, the candidates are lined up in order of
increasing level of support, bottom to top. (Break all the approval ties
with a single random ballot.)

Optional Step: Eliminate all of the candidates with less than fifty
percent approval (support).

Next, starting with the candidate with least support (at the bottom of the
list), move up the list comparing head-to-head (while eliminating losers)
until one candidate remains, the winner.

Either of the two least approved (most rejected) candidates (seeded at the
bottom) would have to be a clear cut Condorcet winner to make it all the
way to the top. On the other hand, the Approval winner would only have to
prove herself against whomever made it up through the ranks. 

Don't you think marking the boundary between supported and rejected
candidates is a small price to pay for such an elegant resolution of the
Condorcet cycle problem?

I think this method is a great improvement over any other method for
resolving Condorcet ambiguities. The standard hair splitting criteria for
resolving ambiguities seem like straightening deck chairs on the Titanic
in comparison.

In my opinion the only problem with this method is that it doesn't make
optimum use of the extra bits of information regarding "approval". (I
prefer "support"  and "reject", since these terms go along with the
strategic usage more naturally.)

In other words, this version of the seeding idea is for those that
appreciate Approval, but prefer Condorcet.

The other main faction of this EM list (those who appreciate Condorcet,
but prefer Approval), would rather have a version that makes more use of
the extra available information by weighing less heavily (in the
head-to-head comparisons) the preferences that respect (i.e. do not cross)
the support/reject boundary line on the ballot. 

If these (within group preferences) are given a weight of zero, we have
pure Approval. If they are given a weight of one, then we have regular
Condorcet (but seeded by Approval). 

So we have a one parameter family (a homotopy, if you will) of unambiguous
methods between regular Approval, and Approval Seeded Condorcet.

For me a weight of one-half is about right. 

This method naturally extends to multiple levels in Dyadic Approval. Each
level, starting with the most coarse (regular Approval), is used to seed
the next finer level. 

All head-to-head generated cycles are resolved.

What do you think?


On Fri, 9 Mar 2001, Richard Moore wrote:

> Forest,
> 
> I think on the whole it is a very good article, especially the paradox of
> elimination methods pointed out in the closing paragraphs. It has already
> been pointed out that if people interpret this in the context of the present
> political climate the rankings of Faction 1 seem unrealistic. In today's
> climate there might be a Faction 1A and a Faction 1B, with the 2nd and
> 3rd choices reversed between them, but more populous of the two
> subfactions would be the one with Rep > Dem > Green. One thought
> is to replace these with Conservative, Liberal, and Moderate. Another
> is to use Conservative, Liberal, and Progressive (since the last of the
> three is descriptive of Greens, though I don't think of Republicans as truly
> conservative or Democrats as truly liberal, in the original senses of those
> words).
> 
> The second paragraph seems to be implying that the methods you will be
> discussing are all types of runoff election. When the word "runoff" is
> mentioned, some type of elimination procedure involving two or more
> stages comes to my mind.
> 
> The only other thing I caught is the misspelling of "consensus" as
> "concensus".
> 
>  -- Richard
> 

I'll use the spell checker next time.

Forest