Markus said:
Dear Russ,
I interpret Mike Ossipoff's "Strategy-Free Criterion" (SFC) and "Generalized Strategy-Free Criterion" (GSFC) as follows:
"X >> Y" means that a majority of the voters strictly prefers candidate X to candidate Y.
SFC: Suppose (1) A >> B and (2) the partial individual rankings can be completed in such a manner that candidate A is a Condorcet candidate. Then candidate B must be elected with zero probability.
I reply:
I donīt know where you got that. If you were trying to write SFC with different letter-designations, youīd say that A is the CW, not that the partial individual rankings can be completed in such a manner that A is a CW.
Additionally, you left out the requirement that no one falsifies a preference.
Additionally, you left out the stipulation that the members of that majority vote sincerely.
So, if you donīt mind, Iīll be the one to define my criteria. However, I invite you to define any criteria you want to, including the one written by you that I quoted above. It isnīt SFC, but we can call it Markusīs Non-SFC.
You continued
GSFC: Suppose (1) A >> B and (2) the partial individual rankings can be completed in such a manner that candidate A is in the Schwartz set and candidate B is not in the Schwartz set. Then candidate B must be elected with zero probability.
I reply:
The same objections that I stated for your Non-SFC apply to your Non-GSFC. But, additionally, you have changed the sincere Smith set to the Schwartz set. The Schwartz set is different from the Smith set. And the sincere Smith set differs even more from the Schwartz set, because the sincere Smith set is about preferences, while the Schwartz set is about voting results.
So your Non-GSFC differs from GSFC even more than your Non-SFC differs from SFC.
As I said, then, Iīll be the one to define my criteia, if you donīt mind.
SFC:
If no one falsifies a preference, and if a majority prefer the CW to candidate Y, and vote sincerely, then candidate Y shouldnīt win.
[end of SFC definition]
If you have a problem with that criterion, if you donīt know what some part of it means, then ask. If you find, in my definition (not yours) some ambiguity, unclarity, etc., tell exactly what is ambiguous or unclear about it.
But, better yet, post a situation (configuration of candidates, voters, and votersīpreferences) such that it isnīt possible to say definitely whether or not some method passes the criterion. (Or post that for any of my criteria).
GSFC:
If no one falsifies a preference, and if X is in the sincere Smith set, and Y is not in the sincere Smith set, and if a majority of the voters prefer X to Y and vote sincerely, then Y shouldnīt win.
[end of GSFC definition]
*********
Markus said:
I could ask Mike Ossipoff whether my interpretation of his criteria is correct.
I reply:
Your interpretation of my criteria is not correct. If you want to discuss my criteria, discuss the ones that I have defined, not the ones that you have defined.
Markus continues:
But I guess that I won't get an answer.
I reply:
You got an answer, just as you always did. At least Iīve always answered things you said the first time you said them. In fact Iīve often answered things that youīve said repeatedly as you kept repeating them.
In fact some people say that I shouldnīt keep answering you when you repeat things. Donīt expect more answeres to repeated statements or questions.
Markus continues:
(Maybe Mike fears that he could be nailed.
I reply:
Sure, thatīs why Iīve been repeatedly asking you to tell exactly what you believe is ambiguous, uncler, or undefined about any of my criteria. :-) That must also be why I keep asking you to post a situation (configuration of candidates, voters, and votersīpreferences) with which some method canīt definitely be said to pass or not pass one of my criteria.
Markus continues:
Maybe he fears that the reader observes that his criteria are only relaxations of my majority beatpath criterion of 1997.)
I reply:
Your majority beatpath criterion doesnīt bear the slightest resemblence to any one of my criteria, much less to all of them. To mention just one big difference, though there are no similarities, my defensive strategy criteria mention preference, and you donīt do so, because you believe that criteria shouldnīt mention preference.
But if you have a criterion that you believe that my criteria are derived from, post it and tell us why you think that my criteria are derived from it.
Mike Ossipoff
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