[EM] Mr. Schulze, please prove you applied some seven M.O. rules

[MIKE OSSIPOFF]

>From: Markus Schulze <schulze at sol.physik.tu-berlin.de>
>Reply-To: election-methods-list at eskimo.com
>To: election-methods-list at eskimo.com
>Subject: Re: [EM] Mr. Schulze, please prove you applied some seven M.O. 
>rules
>Date: Tue, 12 Sep 2000 14:15:09 +0200
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>Dear Craig,
>
>you wrote (12 Sep 2000):
> > 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.
>
>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.
>
>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.
> >
> > 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.  In particular, consider the following
> > situation.  First, either one or more pairwise ties are occurring, or
> > no pairwise ties are occurring.  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.
> > 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.  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". 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.
> >
> > 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).
> >
> > 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).
> >
> > To me, this analysis raises three issues.  First, is it correct?  If
> > 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.  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.
> >
> > 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 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.
>
>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. 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.
>
>Markus Schulze
>schulze at sol.physik.tu-berlin.de
>schulze at math.tu-berlin.de
>markusschulze at planet-interkom.de
>

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