EM list-- The critical part of my claim about what it means to meet a criterion is my definition of an example. The configuration from Bruce that Markus re-posted, a configuration of candidates, voters, & voters'sincere preferences-- I'll call that an "election configuration". When applying a criterion to some actual field of candidates, or to a hypothetical election configuration like Bruce's, obviously one can call any ordered pair of candidates A & B. In fact, whatever the criterion requires about A & B must be true for every ordered pair (A,B) taken from the set of candidates in the actual candidate field of an actual election or from a hypothetical election configuration like Bruce's. That has greatly confused Markus, and I claim that such an election configuration is an unnecessary departure from what the criterion is directly talking about, and that there's no need for anyone to confuse themselves in that fashion. Looking specifically at WDSC & SDSC, what do they mean by A & B? They're saying, "For any 2 candidates, whom we'll call A & B..." A is one candidate. B is one candidate. And the criterion is saying something about what must be true for those 2 candidates. So the obvious kind of example for testing methods for such a requirement would be an example in which there's an A, and there's a B. A specific A & a specific B. Markus's excursion into election configurations where any ordered pair of the candidates in a set can be A & B is irrelevant & unnecessary. And of course, in general, there could be, and are, criteria that say different things about different votes, when a certain 2 candidates are A & B. For instance, WDSC says that, for any majority preferring A to B, they should have a way of defeating B without order-reversal. But, for everyone else, the criterion says nothing about their votes, specified no condition about them, and so the example writer can configure them as he wishes. When Markus wants to look at a candidate configuration and talk about something simultaneously true for each ordered candidate pair, that approach isn't generally-applicable. I suppose Markus likes that approach because it can't say anything about a criterion like WDSC. Then he'll therefore be able to claim that WDSC is ambiguous. But it's only ambiguious if "example" is misconstrued to mean "election configuration", as I've defined the term. So the example definition that I use is generally applicable, and Markus's candidate configuration suits his purposes by not being able to deal with WDSC, which Markus would like to call "ambiguous". General appicability isn't the only advantage of my definition of an example. Let me restate something that I said above: Looking specifically at WDSC & SDSC, what do they mean by A & B? They're saying, "For any 2 candidates, whom we'll call A & B..." A is one candidate. B is one candidate. And the criterion is saying something about what must be true for those 2 candidates. So the obvious kind of example for testing methods for such a requirement would be an example in which there's an A, and there's a B. A specific A & a specific B. So Markus's excursion into election configurations and simultaneous different uses for the names "A" & "B" is unnecessary, and is a way for Markus to confuse himself. The criterion is talking about one candidate called A and one candidate called B, and so why should an example be otherwise? In general, as opposed to just speaking of WDSC & SDSC, anytime a criterion speaks of A, B, C..., the criterion is talking about one candidate A, one candidate B, etc. The criterion doesn't say, "Consider every candidate, each of whom we'll call A" or "Consider every majority-beaten candidate, all of whom we'll call B". The criterion means A to refer to a certain candidate in the scenario that it discusses. I merely use that scenario as an example. When an example is defined in that way, Markus's alleged ambiguity vanishes. The ambiguity is in Markus's notion of what it means to meet a criterion. Mike Ossipoff _________________________________________________________________________ Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com. Share information about yourself, create your own public profile at http://profiles.msn.com.