Iīd 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:
Itīs 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. Thereīs 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, youīd recycled and re-used that misunderstanding from a posting by Bruce.
Hereīs WDSC:
If a majority of the voters prefer X to Y, then they should have a way of voting that will ensure that Y wonīt 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 donīt understand.
It says only that that majority should have a way of doing that. It doesnīt 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 canīt be majority who vote for Y and not for X, because there canīt be a majority that is disjoint with another majority. Y canīt get as many votes as X gets. Y canīt 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 Condorcetīs 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:
Bīs margin of defeat is 249 - 100 = 149.
Aīs margin of defeat is 199 - 150 = 49.
Cīs margin of defeat is 150 - 99 = 51
What if the 99 C voters rank B equal to C, to protect B? Then Bīs margin of defeat would be only
150 - 100 = 50.
Candidate A still wins.
You can look, but thereīs 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 Iīve 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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