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

[MIKE OSSIPOFF]

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I'd said:

>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.

Markus said:

The matrix of pairwise defeats looks as follows:

   A:B=103: 52
   A:C= 51:104
   B:C=103: 52

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.

In my example. No beatpath to B is stronger than 51. But B has 52-strength 
beatpaths to A & to C. B is the winner.

B wins even though more than half of the voters have ranked A over B.

For that reason, BeatpathWinner fails your "SDSC", which requires that, if 
ballots are all admissible, and if more than half of the voters rank y over  
x, then x shouldn't win.

Your disagreement with my statement that BeatpathWinner fails your "SDSC" 
must result from the fact that my example numbers weren't accompanied by 
explanatory text. Now I've supplied that explanatory text, and now I'm sure 
that you agree that BeatpathWinner fails your "SDSC".

You continued:

If you mean Steve Eppley's "minimal defense" with "your 'SDSC'"

I reply:

No. 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.

Mike Ossipoff

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