Markus said:
you wrote (25 Feb 2005):
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.
You were asked several times to define WDSC, SDSC, and FBC in terms of cast preferences. You always refused to do so.
I reply:
Perhaps you misread my request. I said "Tell the people what you think is unclear about my definitions of my criteria."
I didn't ask you how you'd like to define different criteria. I asked you in what way you believe that the defensive strategy definitions are unclear.
By "in terms of cast preferences", I presume that you mean "Without mentioning preferences, as opposed to votes".
It isn't that I refused to define WDSC, SDSC & FBC without mentioning preferences. It's just that a criterion defined in that way would be a different criterion. It wouldn't be WDSC, SDSC, or FBC. However, I graciously and generously invited you to define such a criterion if you want to. At no time did I say that such a criterion couldn't or shouldn't be defined. I just assigned the task to you, since you're the one who wants such a criterion.
But are you trying to say that a criterion definition is unclear if it mentions preference, as opposed to only mentioning votes? If that's what you mean, then you should say it. And then, when saying it, you should demonstrate what is unclear about definitions that mention preference.
You used to keep asserting that definitions that don't mention preference could be written, that would be equivalent to my criteria. But when I asked you to post one, you posted something that was very obviously not equivalent to any of my criteria. You never posted a definition of a criterion defined without preference that was equivalent to my criteria.
You objected to criteria definitions that mention preference, on the grounds that your journal authors don't define criteria in that way.
Is it that you feel that preference isn't defined precisely enough? If so, then mabye you've forgotten that I posted a precise definition of preference to EM some time ago.
I'll add that definition to this posting, but first I'll comment on your other statements.
Markus continued:
And whenever someone submitted a definition for WDSC, SDSC or FBC in terms of cast preferences and asked you whether his definition corresponds with your intention of this criterion, you always refused to answer.
I reply:
No, I always answered. And always the answer was no. The criteria that you or anyone else posted, intended to be equivalent to my criteria, were always not equivalent to my criteria. But if you thiink otherwise, post yours again, and let others judge for themselves.
Again, I don't dislike the notion of criteria equivalent to mine, but without mentioning preference, and I'd welcome such a criterion. Write one by all means.
Of course I'd welcome such a criterion, because you say that the academics don't accept criteria that mention preference, and so if you could write criteria that are equivalent to mine, but which don't mention preference, that would be great. Write them. I'd be glad for such criteria to be written.
You made one attempt,and I told you why it wasn't equivalent to the criterion of mine that you said it was equivalent to. Richard made a few attempts. Most of Richard's proposals were easily demonstrated to not be equivalent to my criteria. Regarding one of Richard's criteria, his alleged FBC, I said that I didn't know if it was equivalent to FBC, but that, judging by the other attempts, there was no particular reason to believe that it was.
Markus continued;
By the way: I asked you several times to prove whether my method (aka Schwartz sequential dropping, cloneproof Schwartz sequential dropping, beatpath method, beatpath winner, Schulze method) satisfies FBC. You always refused to do so.
I reply:
No, I never refused to. I said that I didn't know. Since then, someone sent to me an example, probably 3 candidates, in which Condorcet fails FBC. I probably no longer have it.
By the way, you always say, "...my method (aka Schwartz Sequential Dropping, Cloneproof Schwartz Sequential Dropping, Beatpath Method, BeatpathWinner, Schulze method).
But you defined your method as one that could be better called Beat-or-tie-path-winner. It was defined in terms of paths consisting of defeats and pairwise ties. Wasn't that your main proposal?
Did you also propose BeatpathWinner, which uses paths of defeats?
Anyway, SSD and CSSD are not the same method. They have different stopping rules. Steve Eppley and I devised SSD and posted about it here. You probably had already posted a definition of CSSD, or something at least resembling a definition of CSSD, but neither of us had paid attention to it or knew about it at that time. No, I'm not trying to take credit by virtue of not having noticed a posting by you. Had you actually defined SSD?
You once said that you had, and posted a link to a posting of yours that allegedly defined SSD. But that definition was so vague that it defined nothing--or maybe everything.
I said I'd post a definition of preference:
Precise, abstract definition of preference:
A preference is an information record that consists of a designation of an ordered-pair of candidates and a designation of a set of voters. A preference is written in the form: "(some set of voters) prefer (some candidate) to (some other candidate)."
(End of preference definition)
A preference is often written by someone who is writing a criterion failure example, or a demonstration that a method meets a criterion.
That definition of preference is sufficient for my criteria that refer to preference.
Of course we all know what preference means in everyday usage. But the abstract definition of preference, written above, is the only one that is needed for my criteria that mention preference, for the purpose of defining those criteria and determining whether a particular method meets them.
But the everyday interpretation of preference suggests why it's desirable to meet the criteria, and that's why I used the word "preference" in the criteria definitions.
It goes without saying that I wouldn't object to improvements in that abstract definition of preference.
Mike Ossipoff
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