[EM] Runoff terminology --> Seeded Condorcet

[Richard Moore]

Forest Simmons wrote:

> "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.

If there is a Condorcet winner then single elimination is sufficient to find
that winner.

If there is no Condorcet winner, then the single elimination winner will
depend on the order of elimination. If there is an A > B > C > A cycle,
then if A and C meet in an early round, A is eliminated and B will
win. If A and B meet in an early round, B is eliminated and C will
win. And so on.

> 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.

That's true in tennis. I don't know about team sports.

If there is no Condorcet winner, then seeding postpones the early elimination
of top candidates, but they still have to meet sooner or later.

> 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?

These ideas sound like good ones, though I haven't given it much thought
yet. This could be a way to get the best of both methods (Condorcet and
approval), but I like the simplicity of pure approval.

 -- Richard