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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