Change in defensive strategy definition

[MIKE OSSIPOFF]

I'd said:

>The strength of a majority pairwise for X over Y is measured by
>the number of people who prefer X to Y.

Dave Ketchum replied:

Seems like that sentence is missing something:
Suppose 10 people prefer X to Y.
Shouldn't strength then be affected according to whether 5 or 55
prefer Y to X?

I reply:

First, let me clarify that, by "majority", I mean a majority of
all the voters in that election.

If 55 prefer Y to X, and 10 prefer X to Y, then we certainly can't
say that X has a majority pairwise preference to Y. I agree with
you on that. If a majority of all the voters prefer X to Y, then
only a smaller number can prefer Y to X.

But say that the number preferring Y to X is smaller than the
number preferring X to Y, as it must be in order for X to have
a majority preference against Y. You're asking if we should
consider that smaller number who prefer Y to X, when evaluating
the strength of the majority pairwise preference.

But what's the obvious way to judge the strength or size of
a majority? By how _big_ a majority it is. And so it's irrelevant how
many people prefer Y to X. As soon as we say "majority", we're
talking about a majority-size group. The only majority size group,
as regards X & Y, is the one that prefers X to Y.

We compare 2 majorities by asking which is the larger majority.
If 60% prefer X to Y, and 55% prefer Y to Z, then the XY majority
is a bigger majority than the YZ majority. That's true without regard
to whether a person is a wv advocate or a margins advocate, though I
admit that it creates a difficult justification problem for a
margins advocate.

Mike Ossipoff




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