Condorcet-Ossipoff (was Coombs: Full count, etc)

[Mike Ossipoff]

DEMOREP1 at aol.com writes:
> 
> Mr. Ossipoff wrote- 
> I have no idea what Prof. Coombs said about unranked alternatives.  I'd guess
> that, most likely, he didn't say anything about it, since the academic
> assumption has always been that everyone ranks all of the alternatives.  Just
> as Condorcet probably didn't say anything about that question.  In both
> methods, I define them in the way that actually works. Similarly, that's why
> I define Condorcet's method in terms of votes-against, though Condorcet, as I
> understand it, didn't specify how defeats should be measured.
> ----
> D- Thus, since Mr. Condorcet is no longer alive to comment about unranked
> alternatives, should Condorcet on this list be actually Condorcet-Ossipoff ?

I've been calling it Condorcet(EM) now, because now it's more than
1 person's Condorcet version; it's EM's recommendation.

> 
> Since there are other possible tie breakers in the head to head matrix of all
> candidates when there is no single head to head winner in all of his/her
> pairings (such as total votes for, total votes against, total votes for minus
> total votes against, etc.), there can also be Condorcet-Eppley,
> Condorcet-Lanphier, Condorcet-Demorep, Condorcet-Davidson (?), etc., etc.

Of course there could, but EM recognizes that votes-against
accomplishes something that other Condorcet versions don't accomplish.

> 
> Again, I note that Mr. Arrow says that any election method (with its tie
> breaker) has strategy problems. 

What strategy problems? If you cite it, then name it. Otherwise it
sounds more like an incantation than a citation. We frequently hear
people using the name of Arrow's theorem as some kind of incantation
to discredit the voting-systems endeavor.

So what strategy problems are you referring to??

As much as I'd like to wait for you to answer that, I'm going
to give you an answer: Bruce pointed out that Arrow's IIAC
(Independence from Irrelevant Alternatives Criterion) is actually
another way of saying Steve's No Spoilers Criterion. So Arrow
showed that you can't have No Spoilers, and still have a few
other desirable criteria. Well let me say what they are. I'm
more or less quoting something from Bruce here, but re-wording
it in terms of a single-winner, because it's worded in terms of
a "collective ranking" output.

Apparently Arrow listed 4 criteria:

Strutural: The input is a finite positive number of rankings
, from 1st choice to last choice, of a finite positive number
of alternatives. But only mathematicians would feel that it's
necessary to include "finite positive...". I must note that
a real public election is going to have lots of ballots that
_don't_ list from 1st choice to last choice, but this definition
that I'm quoting does allow ties, and so everyone you don't rank
can be considered tied for last in your ranking. The output
is a single winner (in Bruce's version here, it's a collective
ranking).

No-Dictator: When there are 3 or more voters & 3 or more
alternatives, there's no voter who can in principle determine
the winner every time. (greatly simplified wording)

[These 1st 2 criteria are so obvious that we (you & I) don't
even regard them as criteria, but obvious starting-point conditions
that don't even need mentioning. The last 2 criteria are more
criterion-like]

Independence from Irrelevant Alternatiaves: Removing from the
election someone who didn't win shouldn't change who wins.

Pareto Criterion: Never elect an alernative that has another
alternative ranked over it by everyone.

[Pareto sounds like GMC but is much weaker. Every method we've
discussed meets Pareto, but only 2 (Condorcet & Simpson-Kramer)
meet GMC]

***

So those are Arrow's criteria. His impossibililty theorem says
that those criteria can't all be met.

I've listed this for a reason: Now please don't be invoking
Arrow without making a specific point. 

So I ask you again, Demorep, name a specific strategy problem
that you were referring to, that Arrow's theorem implies will
always be present. Or here's another question: What was your
point in invoking Arrow? That's something that wasn't clear.
If your point was that there can be no good methods, and so
even the lousiesr proposals here are ok--that's the kind of
bullshit way Arrow is usually used against electoral reformers.

No, actually Arrow's theorem, combined with the Gibbard-Satterthwaite
theorem, form a _very_ high ceiling for the possible merit of methods.
No method proposed so far pushes those limits. There are some ideal-
sounding criteria that apparently could be met without violating
Arrow or Gibbard-Satterthwaite, even though no such methods have been
proposed yet.

Besides, of the methods that have been proposed, there are very
dramatic & drastic differences in merit. Some of the methods,
like MPV, are crap. Other methods, like Condorcet, Smith//Condorcet,
&, to a slightly lesser degree, Simpson-Kramer, are virtually
ideal for all practical purposes. So then, what's this
"Arrow says all methods have strategy problems " intended to mean?

All methods have strategy problems? Do they have strategy problems
as bad as the combination of majority disapproval with Condorcet? Not
by a long shot. I & others have named those strategy problems, and
so I won't repeat them here.

By the way, having mentioned Gibbard-Satterthwaite, I should
say something about it. All I know is what Bruce said, and I've
never seen the actual theorem (Bruce, could you post it?).

But, from what I've heard, that theorem says that there can't
be a method in which no one would ever benefit from mis-
representing his preferences.

(In Condorcet an order-reverser would have to be lucky, and would
be taking a great risk)

Have with put the Arrow invocation to rest yet?

> 
> Which tie breaker will make the most sense to the public (who will be asked
> in the States to vote on constitutional amendments for single and/or multiple
> winner election reforms for executive and judicial offices) ?

Executive & judicial? Don't forget legislative. SW is easier to get
than PR.

But that paragraph of yours sounds terribly passive. Do we just
offer people what they're already most familiar with, or do we
offer them what we consider the best? And if it's good enough 
that we consider it the best then it will make sense to anyone
who seriously looks at it.


Mike

> 
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