Markus--
You said:
I wrote (27 Feb 2005):
So you say that it is impossible to define WDSC, SDSC, and FBC in terms of cast preferences?
You wrote (27 Feb 2005):
Either it's impossible, or else no one has yet succeeded. Does it matter which it is?
Yes, it does matter. Election methods are defined on _cast_ preferences and not on _sincere_ preferences.
I reply:
Wrong. Now some are defined on preferences, as opposed to only votes.
Of course you can define anything any way that you want to. So you can define a criterion as a voting system Yes/No test that is doesn�t mention preference. But that would be an unnecessarily narrow definition of a criterion. A voting system criterion is a Yes/No test for evaluating voting systems. The ones that you like don�t mention preference. But, contrary to your claim, quoted above, those ones that you don�t like, which mention preference, are criteria, by any reasonable definition of that term.
You continued:
Therefore, whether a given election method passes a given criterion must depend only on how this method handles _cast_ preferences.
I reply:
...if it�s one of the criteria that you like.
I�m not asking you to like my criteria. But you need to understand that "the criteria that Markus likes" doesn�t mean "the set of all criteria".
You continue:
Therefore, a criterion can be well defined only when it can be defined without mentioning _sincere_ preferences.
I reply:
Certainly, if we accept your definition of a criterion, which says that not mentioning preference is a requiremen for criteria. But your definition is arbitrary and unjustifiable.
So that�s what it comes down to: You try to jusify your claim that my criteria are undefined because, by your definition, criteria are defined only if they don�t mention preference. I suppose one can justify any statement, by one�s chosen definitions.
Ok, now you�ve answered my question. You�ve told me why you think that my criteria are undefined. Now this discussion has concluded, because you�ve answered my question.
There�s no need for more discussion about why you believe that my criteria are undefined, unless you have another reason for believing that, or unless you can post an example of a situation (configuration of candidates, voters, and voters�preferences) with which it isn�t possible to say definitely that a some particular method passes the criterion or fails it.
You wrote (27 Feb 2005):
In a sense a method that gives the same result is the same method, but in another sense it can be said to not be the same method, if it's a completely different implementation. In any case, however, when I said that SSD is equivalent to Schulze's method, that statement wasn't entirely correct.
Nope. It is not a "completely different implementation".
I reply:
Yep. BeatpathWinner and CSSD are completely different implementations. But of course there�s also a sense in which they�re one method, which is why I often say BeatpathWinner/CSSD.
But I don�t want to debate that issue.
Mike Ossipoff
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