[EM] Reply to Markus, Craig, & Bruce

[MIKE OSSIPOFF]

,
>
>
Craig said:

> > When Markus says that 2 of the 7 criteria or Russ Paielli and Mike
> > Ossipoff, are met or not met, by the Condorcet method, he would be
> > admitting that the rules are understood by him. So I believe that
> > Mr Markus Schulze is true follower of Mike Ossipoff. That would fix
> > a problem I have which is that Mike Ossipoff will not write ever to
> > me and state ideas into a precise form that can be written down.

No, I carefully replied to everything from Craig for as long as
possible. It became prohibitively time-consuming. During that time
I answered every one of Craig's objections to the criteria, explaining
meanings that he asked about, like the meaning of "is", etc. I
adopted Craig's suggestion to change "likes better than any result..."
to "likes better than every result...", in the interest of
unambiguity. I do my best to write criteria unambiguously, and I'm
glad to have suggestions on that.

>
>I have to admit that I wouldn't have understood these criteria if
>I had read only the http://home.pacbell.net/paielli/voting website.

Good of you to admit it, but you neglected to tell us which part
of the wording you didn't understand the meaning of. As I said, I
try to word things unambiguously, so do tell me what was ambiguous to
you.

>
>Actually already 4 years ago Bruce criticized Mike's "lesser of two
>evils" criteria. He wrote (6 June 1996):
> > The discussion of the "lesser of two evils" criterion promised above
> > follows below.  I sent an essentially equivalent discussion to Mike
> > last October.

Quite right. What I now call SDSC, I formerly called LO2E2 (Lesser-
of-2-evils-2). Bruce sent me an objection to it by individual e-mail,
and I answered his objection. Then, at least some months later, Bruce
repeated the exact same objection on EM, making no reference to my
reply that I'd sent him. I questioned the sincerity of that intentional
re-use of an answered objection without reference to the answer.
That tactic by Bruce was in violation of the stated guidelines for EM.

Anyway, now it looks as if it's necessary for me to answer that same
objection yet again, just like I did on EM before (Markus, why didn't
you posts that too), and just like I did when Bruce sent it to me
individually. I suppose I could look it up in the archives and
re-post my reply, but that would be even more time consuming. But
I suggest that we ask ourselves why Markus re-posted Bruce's old
objection, without re-posting my reply to it. By so doing, Markus is
wasting your time & mine, and, it seems to me, is violating the
EM guideline against recycling old arguments without replying to
the answers that were already given to those arguments.


Anyway, here's Markus' quotation of Bruce's objection, including
my replies, for the 3rd time:


> >
> > Concerning the lesser of two evils criterion, I think that I might
> > understand what it is saying, and, if so, then I think that what it
> > says is not very important.

I fully admit the lesser-of-2-evils problem isn't important to Bruce.

> > In particular, consider the following
> > situation.  First, either one or more pairwise ties are occurring, or
> > no pairwise ties are occurring.

That's very easy to agree to.

> >  I think that it is important to be
> > able to adequately address pairwise ties, but I don't think that "two
> > evils" is intended to be important ONLY when such ties are occurring.

Bruce is correct.

> > If I am wrong here, and, like Anderson's voting method, "two evils"
> > really is only important when pairwise ties are occurring, then I
> > don't really understand it after all.  But if I am right about this,
> > then we can assume that no pairwise ties are occurring.

I separate that paragraph from what follows because it's more
needless repetition.

> > For example,
> > assume that there is an odd number of voters, none of whom have
> > any ties or truncations in their individual rankings.  Then, given
> > any two alternatives, say A and B, either A beats B or B beats A.
> > Without loss of generally, assume that A beats B.  Then, either
> > there exists a third alternative, C, such that A beats B, B beats
> > C, and C beats A, or no such third alternative exists.  If no
> > such third alternative exists, then any method that satisfies the
> > generalized Condorcet criterion necessarily (I think) satisfies
> > "two evils".

Right. If there are only 2 alternatives, anything that meets Smith meets
SDSC. However sometimes there are more than 2 alternatives.


Therefore, to be an important addition (over just the
> > generalized Condorcet criterion), "two evils" must be important in
> > the case when A beats B, B beats C, and C beats A.

So far, so good.


> >
> > In this case, let V(A,B) be the voters who prefer A over B, and let
> > W(B,A) be the voters who prefer B over A, so #V(A,B) > #W(B,A).
> > Define V(B,C), W(C,B), V(C,A), and W(A,C) analogously.  Then, as I
> > understand it, "two evils" says that there must be some way for the
> > V(A,B) voters to cast their ballots such that: 1) none of them casts
> > a "partially reversed" ballot, 2) none of them casts a ballot that
> > ties A with an alternative ranked below A in the voter's true
> > preference (but other false ties are allowed), and 3) B cannot win
> > no matter how the W(B,A) voters cast their ballots (the W(B,A) voters
> > are allowed to use partial-reversal here).

If that's what LO2E2 said then LO2E2 wasn't SDSC. If that's so, then
I question the relevance re-posting this discussion of LO2E2. Anyway,
with the understanding that none of this has any relevance to
criteria now in use, I'll continue the reply. Let's suppose that
Bruce's above statements about LO2E2 are correct for that
long-disused criterion. But I'd add that there must be a majority
of all the voters preferring A to B.

> >
> > However, "two evils" necessarily requires that, in this very same
> > election, it must also be simultaneously possible for the V(B,C)
> > voters to cast their ballots such that:  1) none of them casts a
> > "partially reversed" ballot, 2) none of them casts a ballot that ties
> > B with an alternative ranked below B in the voters true preferences,
> > and 3) C cannot win no matter how the W(C,B) voters cast their ballots.
> > Further, "two evils" necessarily requires that, in this very same
> > election, it must also be simultaneously possible for the V(C,A) voters
> > to cast their ballots such that:  1) none of them casts a "partially
> > reversed" ballot, 2) none of them casts a ballot that ties C with an
> > alternative ranked below C in the voters true preferences, and 3) A
> > cannot win no matter how the W(A,C) voters cast their ballots.
> >
> > Thus, for "two evils" to be important, it must be important to guarantee
> > that the W(A,B) voters are necessarily able to ensure that B loses, and
> > to simultaneously guarantee that the W(B,C) voters are necessarily able
> > to ensure that C loses, and to simultaneously guarantee that the W(C,B)
> > voters are necessarily able to ensure that A loses, all under the same
> > false-ties and partial-reversal conditions in the same election (as
> > stated above).

Wrong. I never said that all 3 majorities have be able to simultaneously
use the power that the criterion specifies and make all 3 candidates
lose. Bruce is a mathematician, and mathematicians try to be very
literal. And so I was disappointed when Bruce invented a requirement
that wasn't in my wording.

"All in the same election" seems to mean that Bruce says that I
want all of those 3 majorities to be able to simultaneously use their
LO2E2 powers. But maybe Bruce didn't mean that, and only meant that
each of those majorities should be able to do that if it wants to,
without any requirement that it's can happen that all 3 of those
overalapping majorities can simultanously use that power.

> >
> > To me, this analysis raises three issues.  First, is it correct?  If

If Bruce merely means that each one of those majorities should have
the ability to use the power that LO2E2 says they should have, without
inventing a requirement, unstated by me, that they all can do that
simultaneously, then that statement sounds correct.

Look, say there
are 3 kids sitting on the ground, and there's one marble in front of
them. I say "Each of those kids has a way of taking that marble home."
I hope that Bruce won't then say that I said that all of those 3
kids should simultaneously be able to take the marble home (if they
don't live in the same home).

If that distinction seems obvious, and if you expect a mathematician
to be literal, then read on and be disappointed.

> > not, then why not?  If it is correct, then the second issue is:

>Given
> > the analysis above, is it important to satisfy the "two evils" criterion
> > in addition to satisfying the generalized Condorcet criterion?
> > Obviously, I don't think so.

Yes, we heard that part.

In fact, it seems to me that the more one
> > thinks about the implications of this criterion when a strict majority
> > of the voters prefer A to B, a strict majority prefer B to C, and a
> > strict majority prefer C to A, the more ludicrous this criterion
> > appears to be.  The reasonably of any criterion is basically a matter
> > of personal judgment -- my judgment, based on the above, is that "two
> > evils" is an unreasonable addition to the generalized Condorcet
> > criterion.

Bruce can repeat that claim as many times as he wants to, but it
would be better if he could justify it. In any case, as I said,
LO2E2, if it's as Bruce stateed it, has long ago been replaced by
SDSC. But Bruce's misunderstanding about all 3 of those kids being
able to simultaneously take the marble home applies just as well to
LO2E2 and to SDSC.

With more than 2 candidates, most methods that meet Smith fail SDSC.

> >
> > The third issue is:  If others feel that satisfying "two evils" is
> > important, then what methods have been proven to satisfy "two evils,"
> > what methods have been proven to fail "two evils," and where can these
> > proofs be found?

I've demonstrated on EM what methods meet which of our defensive
strategy criteria. Early this year I showed why any method that
meets BC meets SFC, GSFC, WDSC, & SDSC. BC is met by Beatpath Winner
(which Markus may or may not be the initial proposer of), SSD,
Tideman(wv), among others.

Why is Markus posting this outdated message from Bruce?

I know that many claims have been made, and it is not
> > wrong to state conjectures provided these statements are clearly labeled
> > as conjectures.  I have seen neither such proofs nor such labeling.

My statements about compliance with the defensive strategy aren't
conjectures.


Markus says:

>
>The problem is that Mike writes his "lesser of two evils" criteria in
>the form that if there is a candidate with certain properties due to the
>sincere preferences then there must be a strategy with certain properties
>such that if this strategy is used then this candidate doesn't win.

Markus, maybe you didn't notice this, but you forgot to say what the
problem with that is.

>It
>would have been significantly more simple if he had written his criteria
>in the form that if there is a candidate with certain properties due to
>the casted preferences then he must not be elected.

Quite possibly it would be simpler to write some criteria than to
write other criteria. I wanted to write the ones that I wrote.
Is that quite alright, Markus?

Markus is again repeating an answered objection. I don't want to say
that B should automatically lose, because then, in Bruce's example,
A, B, & C would have to simultaneously lose. Like those 3 kids all
taking the marble home simultaneously. I don't want to say that
all 3 candidates should have to lose simultaneously. Again, Markus,
if you like that, then you write it.

Mike


>
>Markus Schulze
>schulze at sol.physik.tu-berlin.de
>schulze at math.tu-berlin.de
>markusschulze at planet-interkom.de
>

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