[EM] Markus reply

[MIKE OSSIPOFF]

I´d said:

>Bruce
>Anderson, Markus, Blake, and Richard have been kind enough
>to industriously help look for faults in the criteria,
>often very valianly and tenaciously.  But without finding
>problems in the criteria.

Markus replied:

I would rather say that I gave up asking you for clear
definitions.

I reply:

It´s easy to make a general claim like that, which is why you make it 
instead of stating what you think is unclear in the definitions. Forget 
about asking me for clear definitions or convincing me. There´s no need to 
convince me, if you can convince others. Tell the people here what you think 
is unclear about my definitions of my criteria.

Your claim was that WDSC  SDSC require that if a majority prefer X to Y, and 
a majority prefer Y to Z, and a majority prefer Z to X, then, 
simultaneously, the first majority should be able to make Y lose, while the 
2nd majority are making Z lose, while the 3rd majority are making Z lose.

As I said, you´d recycled and re-used that misunderstanding from a posting 
by Bruce.

Here´s WDSC:

If a majority of the voters prefer X to Y, then they should have a way of 
voting that will ensure that Y won´t win, without any member of that 
majority voting a less-liked candidate over a more-liked one.

[end of WDSC definition]

Tell the people which part of that you don´t understand.

It says only that that majority should have a way of doing that. It doesn´t 
say that several overlapping majorities like that should be able to 
simultaneously do so.

Why Approval meets WDSC:

Suppose that the majority who propose X to Y vote for X, and not for Y. 
There can´t be majority who vote for Y and not for X, because there can´t be 
a majority that is disjoint with another majority.  Y can´t get as many 
votes as X gets. Y can´t win.

That majority have accomplished that without voting a less-liked candidate 
over a more-liked one.

[end of demonstration that Approval meets WDSC]

Why margins Condorcet fails WDSC:

This will be shown via a failure example:

349 voters.

199, a majority, prefer B to A. Those are the B voters and the C voters. The 
100 B voters prefer A to C.

Though this sentence is irrelevant to the use of this example to prove 
margins Condorcet´s noncompliance with WDSC, this can be regarded as an 
order-reversal example in which the A voters are using offensive 
order-reversal against B, the CW.

150: ACB
100: B
  99: CBA

The margins:

B´s margin of defeat is 249 - 100 = 149.

A´s margin of defeat is 199 - 150 = 49.

C´s margin of defeat is 150 - 99 = 51

What if the 99  C voters rank B equal to C, to protect B? Then B´s margin of 
defeat would be only
150 - 100 = 50.

Candidate A still wins.

You can look, but there´s nothing that the B and C voters can do to keep A 
from winning, short of reversing a preference.

The definition of WDSC might be clearer when accompanied by a use of the 
criterion, which is why I included that. Also, Russ asked about 
demonstrations of compliance and noncompliance. Though I´ve already sent a 
complete set to Russ, this is an example of such demonstrations.

Margins Condorcet fails this, and the other majority defensive strategy 
criteria, because its subtraction, to calculate the margins, destroys 
information about majorities.

Mike Ossipoff

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