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

[Markus Schulze]

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