[EM] Justification of my example definition

[MIKE OSSIPOFF]

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


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