[EM] Markus, 19 March, '05, 0230 GMT

[MIKE OSSIPOFF]

I tried to post this last night, but found that it didn't arrive, and so I'm 
re-sending it:

Dear Markus--
You said:

I wrote (16 March 2005):
    I replied that it cannot be said that you proposed wv
methods in general because you didn't propose a general
concept.


You wrote (17 March 2005):
    But I did propose a "general concept". As I said in my
previouis posting about this, I clearly and unmistakeably
introduced and proposed wv as a way of measuring the
strength of defeats, and advocated wv as the best way
to measure the strength of defeats. And I told of the
advantages of wv as a measure of defeat-strength.


You say today:

You proposed wv, but only in connection with the MinMax
tie-breaking strategy.

I reply:

Wrong. I didn't propose wv in connection with MinMax, because I don't know 
what MinMax means. But, guessing that you might mean PC when you say MinMax, 
PC was not the only method that could use wv or margins. Smith//PC too could 
use wv or margins.

What would you want me to have done? Proposed wv in connection with 
BeatpathWinner and Ranked-Pairs? I didn't do that because neither of those 2 
methods was known on EM yet.

Or maybe you'd have liked me to say, "I also propose wv for all the 
Condorcet versions that haven't been proposed yet on EM, but which are going 
to be proposed here". Would I have to say that in order for you to not deny 
that I proposed wv in general? I didn't know that additional Condorcet 
versions were going to be proposed on EM.

But I spoke of wv and margins as ways of measuring the strength of pairwise 
defeats. I discussed their merits in general, not just for the purpose of 
any particular method(s).

You might have a point if every sentence about wv's advantages over margins 
contained the words "if the method is PC or Smith PC". But those words 
weren't included in all my discussion of wv's advantages over margins, or my 
discussions in general  of the great benefits gained by the wv measure of 
defeat strength.

When I introduced and proposed wv, the methods that could use wv or margins 
were PC and Smith//PC.  I didn't say: "I propose wv specifically and only 
for PC" and for Smith//PC" I spoke in general about why wv gives advantages 
that margins doesn't give.

You continue:

You didn't propose wv in general,
since GMC isn't satisfied by other wv methods than MinMax(wv).

I reply:

Markus, this is why I eventually start asking if something is wrong with 
you. I just finished pointing out to you the following (among others 
things):

I introduced and proposed wv years before I defined GMC. Therefore you 
aren't making any sense when you try to say that GMC has bearing on what I 
meant when I introduced and proposed wv.

What Markus is doing here is repetition of what he said before. copying, 
re-use, recycling and repetition of statements that have been rebutted in 
the message to which Markus (maybe thinks that he) is replying to.

But Markus isn't replying. Markus is monologing. It doesn't matter what I 
say. It doesn't matter if I point out why Markus's conclusions don't make 
any sense. Markus will just keep on repeating what he likes to repeat.

You (Markus) continue:

If you don't agree with this then please post a reference
where you propose wv before 1997 for another tie-breaking
strategy than the MinMax tie-breaking strategy.

I reply:

I didn't propose wv for MinMax. MinMax is a term that I didn't use then and 
don't use now, due to its ambiguity.

But there were two methods that had been proposed on EM, which could use wv 
or margins: PC and Smith//PC.

I must admit that I've now lost count of how many times I've told you this: 
At the time when I introduced wv, there were only 2 methods known on EM that 
could use wv or margins: PC and Smith//PC. I didnt advocate the use of wv 
for BeatpathWinner or for Ranked-Pairs, because those methods were unknown 
on EM at that time.

When I told why wv gives strategic benefits when used as the measure of 
defeat-strength, I pointed out things like the fact that wv, as the measure 
of the strength of the X>Y defeat,  records and preserves the number of 
people who ranked X over Y. I pointed out that that's why wv honors majority 
rule, because majority numbers are recorded and counted. Majorities are 
honored.

That's a general fact about wv. I was speaking in general about wv as a way 
of measuring defeat-strength.

That fact is  just as true whether the method is PC, Smith//PC, 
BeatpathWinner, SD, SSD, CSSD, or Ranked-Pairs.

I pointed out that wv does better in regards to the lesser-of-2-evils 
problem because the people who prefer Compromise to Worst, and whose 
greatest concern is that Worst might win,  can vote that preference, with 
the assurance that it will remain fully counted and recorded by the count 
rule.
...the assurance that their vote against Worst will remain recorded, and, if 
there are sufficiently many similar ones, will thereby make Worst less able 
to win, in the ways guaranteed by WDSC and SFC compliance.

I pointed out that margins, by its subtraction, forgets about majority 
numbers, and forgets how many people voted Compromise over Worst.

All that is true, regardless of whether the method is PC, Smith//PC, 
BeatpathWinner, SD, SSD, CSSD, or Ranked-Pairs.

The fact that that majority defeat of Worst is recorded and counted, instead 
of forgotten by subtraction, affects Worst's chances of winning, in the way 
described by WDSC & SFC,  regardless of whether the method is PC, Smith//PC, 
BeatpathWinner, SD, SSD, CSSD, or Ranked-Pairs.

To summarize, the reasons that I gave for why wv honors majority rule, and 
avoids the lesser-of-2-evils problem are just as true whether the method is 
PC, Smith//PC, BeatpathWinner, SD, SSD, CSSD, or Ranked-Pairs.

For instance, let's talk about why BeatpathWinner meets WDSC:

WDSC's premise says that a majority of the voters prefer X to Y.  WDSC's 
requirement says that they must have a way to ensure that Y loses, without 
reversing a preference.

If that majority rank X over Y, then Y has a majority defeat. A majority 
defeat is a 1-defeat majority beatpath. Therefore there's a 
majority-strength beatpath from X to Y.

Can there be a majority-strength beatpath from Y to X? Well, say that that 
majority don't rank Y. That means that they aren't ranking Y over anyone. 
That means that X can't pairwise-beat anyone by majority. Since every 
beatpath must start out with a defeat, that means that there can't be a 
majority beatpath from Y to anyone, including X.

And that means that there's a majority-strength beatpath from X to Y, but 
not from Y to X. The strongest beatpath from X to Y is stronger than the 
strongest beatpath from Y to X. That means that Y can't win, because someone 
(X) has a beatpath win against Y.

That majority were able to make Y lose merely by ranking X over Y, and not 
ranking Y over anyone. They didn't have to reverse a preference in order to 
make Y lose.

[end of demonstration that BeatpathWinner meets WDSC]

While we're at it, how about why BeatpathWinner meets SFC:

SFC compliance is tested only in examples in which there's a CW, because its 
premise mentions a CW.

The premise of SFC says that no one falsifies a preference, and that a 
majority prefer the CW to Y and vote sincerely. The requirement says that Y 
shouldn't win.

By my definition of sincere voting, if voters are allowed to rank as many 
candidates as they want to, a sincere ranking must vote all of the voter's 
preferences.

So the stipulation that a majority prefer the CW to Y and vote sincerely 
means that that majority rank the CW over Y.

As before, that gives Y a majority defeat, which is a 1-defeat majority 
beatpath from the CW to Y.

Can Y have a majority defeat to the CW?

In the previous demonstration, I mentioned that a majority beatpath 
obviously must start with a majority defeat, since all of its defeats must 
be majority defeats. Likewise, a majority beatpath must end with a majority 
defeat. For a beatpath from Y to the CW to end with a majority defeat, the 
CW must have a majority defeat.

Can the CW have a majority defeat if no one falsifies a preference? If for 
any candidate Z other than the CW, it must be that more prefer the CW to Z 
than prefer Z to the CW. That's the definition of a CW. That means that 
there can by no majority preferring someone to the CW. And, if no one 
falsifies a preference, then there can be no majority voting someone over 
the CW. That means that the CW can't have a majority defeat. Since a 
majority beatpath must end with a majority defeat, that also means that 
there can be no majority beatpath from anyone to the CW.

Since there's a majority beatpath from the CW to Y, and there can't be a 
majority beatpath from lY to the CW (because there can't be a majority 
beatpath from anyone to the CW), then the CW has a beatpath win against Y. 
That disqualifies Y from winning, by the definition of BeatpathWinner.

So, as required by SFC's requirement, when SFC's premise conditions are met, 
and the method is BeatpathWinner, candidate Y can't win. BeatpathWinner 
meets SFC.

[end of demonstration that BeatpathWinner meets  SFC]

In my earliest advocacy of wv, I pointed out that Worst's majority defeat 
will be recorded, preserved, and always counted. I pointed out that that 
means that majority rule will be honored, and that lesser-of-2-evils voters 
will be reassured that their pairwise vote against Worst will be recorded 
and preserved, as will its effect in reducing Y's winnability, as described 
by WDSC and SFC.  I pointed out that those things aren't so in margins. 
Those things affect Worst's ability to win in BeatpathWinner just as surely 
as they do in PC or Smith//PC, as shown by the demonstration above.
Those are general facts about wv, arguments in general for wv.

As I said in an earlier reply: Though voting systems are important, I'm only 
doing this because I like to, with no goals regarding results. That's 
because what someone else does or doesn't do isn't my department. But it's 
fun to find out what kind of opposing arguments I get. The lengths to which 
some people, like Markus, will go are remarkable, and often hilarious, and 
provide much entertainment.

Mike Ossipoff

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