[EM] Markus' "SDSC" isn't Steve's version. It's Markus' alleged SDSC-equivalent.

[Markus Schulze]

Dear Mike,

you wrote (4 Feb 2004):

> Not only does Plurality pass your "SDSC", but BeatpathWinner
> fails it:
>
> AB51, BC52, CA52
>
> B wins in BeatpathWinner, though more than half of the voters
> have ranked A over B.

I wrote (4 Feb 2004):

> The matrix of pairwise defeats looks as follows:
>
>    A:B=103: 52
>    A:C= 51:104
>    B:C=103: 52
>
> B and C are potential winners. The final winner depends on how
> you solve indecisive situations.
>
> If you mean Steve Eppley's "minimal defense" with "your 'SDSC'"
> then your example doesn't demonstrate a violation of this
> criterion since this majority of the voters doesn't rank
> candidate B "no higher than tied for bottom".
>
> Steve Eppley wrote (http://www.alumni.caltech.edu/~seppley):
> > Any ordering of the alternatives must be an admissible vote,
> > and if more than half of the voters rank y over x and x no
> > higher than tied for bottom, then x must not be elected.

You wrote (5 Feb 2004):

> You've misinterpreted my example, which was partly my fault,
> because I didn't accompany the numbers with any explanation.
> Here's what I meant: When I stated my example, I stated
> the strengths of 3 pairwise defeats. A beats B with 51
> votes-against. B beats C with 52 votes-against. And C beats
> A with 52 votes-against.
>
> I didn't show the rankings that give those pairwise defeats,
> but you know that rankings can achieve that set of pairwise
> defeats. Those small majorities are possible in a cycle, even
> with as few as 3 candidates.
>
> In any case, even if you didn't believe that (though I'll
> demostrate it if you don't believe it), Blake showed that any
> set of pairwise preference vote totals can be made consistent
> to some set of rankings, by adding some constant to all the
> vote totals. Doing that wouldn't change the winner of a
> BeatpathWinner count.  So, however you look at it, my example
> is possible. And, in that example, B is the clear winner.

Your example isn't possible.

Suppose d[X,Y] is the number of voters who rank candidate X
higher than candidate Y.

When a majority of the voters ranks candidate A higher than
candidate B and ranks candidate B no higher than tied for
bottom, then it is not possible that d[A,B] is smaller than
d[B,C] for some other candidate C.

A pairwise matrix is called "possible" if and only if there
is at least one set of partial individual rankings that is
compatible with this pairwise matrix. Blake proved that whenever
a pairwise matrix isn't possible then there is a constant Z
so that when you add Z to each entry of this pairwise matrix
then this pairwise matrix becomes possible. However, it isn't
guaranteed that the new set of partial individual rankings still
has the property that a majority of the voters ranks candidate A
higher than candidate B and ranks candidate B no higher than tied
for bottom.

*********

You wrote (4 Feb 2004):

> By "your SDSC", I refer to the criterion that you defined and
> proposed, as a way to write SDSC without any mention of sincere
> preferences.
>
> Why would I call Steve's version of SDSC "Markus' SDSC"???
>
> You, Markus, wrote a criterion by which you intended to show that
> it's possible to write a votes-only criterion that is equivalent
> to SDSC, as I define SDSC.
>
> Your criterion that you wrote in that posting, for that purpose
> is not equivalent to SDSC.
>
> BeatpathWinner passes SDSC, as do SSD, CSSD, RP, SMA, and
> probably NES.
>
> Plurality fails SDSC.
>
> But Plurality passes your "SDSC". And BeatpathWinner fails
> your "SDSC"
>
> But, as I've now said, it is possible to write a votes-only
> criterion equivalent to SDSC, as well as SFC, GSFC, and WDSC.
> And it's also possible to write a votes-only criterion equivalent
> to my CC.
>
> I just would rather mention sincere preferences than an
> arbitrary-sounding, discriminatory-sounding rule-stipulation.
> And my criteria speak more directly to voter concerns than their
> votes-only equivalents do. That's better than having to explain
> the motivation in a separate motivational statement.
>
> But,  in any case, your "SDSC" is definitely not equivalent to
> SDSC, because Plurality passes your SDSC, and BeatpathWinner
> fails your SDSC.
>
> (...)
>
> My posting to which you refer shows that Plurality passes your
> criterion that you posted as allegedly equivalent to SDSC.
>
> You posted that criterion of yours, to show that SDSC could be
> written without mentioning sincere preferences. I showed that
> your criteion is not equivalent to SDSD, because Plurality passes
> your criterion, though Plurality fails SDSC.
>
> Replying to your posting of your alleged SDSC-equivalent by
> showing that it is not equivalent to SDSC makes sense.
>
> What doesn't make any sense is your attempt at evasion, to which
> I'm replying now.
>
> (...)
>
> But you already did post your suggestion for how I should word
> SDSC. So it's a bit late to start following my request that you
> not tell me how to word things. And then I showed you that your
> alleged SDSC equivalent is not equivalent to SDSC, because
> Plurality passes your criterion.
>
> It turns out that there are equivalent wordings for my criteria,
> including SDSC,  that don't mention sincere preferences (though
> your criterion that you posted is not one of them). You'd prefer
> criteria that don't mention sincere preferences. You've said that
> you now don't want to tell me how to word things, so that must
> mean that you won't complain anymore that you'd prefer criteria
> that don't mention sincere preferences.
>
> (...)
>
> It isn't entirely clear what you're talking about. You posted a
> criterion that you wrote to show that a criterion equivalent to
> SDSC can be written without mentioning sincere preferences, only
> mentioning cast ballots. I was replying to that. And so it isn't
> clear why you think that how someone else words things is relevant
> to the question of whether your criterion is equivalent to SDSC.
> I made it quite clear that that was the issue to which I was
> replying.

I don't know what you are talking about. I still don't know what
you mean with "your 'SDSC'". I don't remember that I have proposed
a criterion and called it "SDSC" recently.

Markus Schulze