James wrote:
I have a quick question. You write a lot about offensive versus defensive strategy, and I'm a bit embarrassed to admit that I don't know precisely what these terms mean. Could you please give a definition for each?
I reply:
That's completely excusable, because that definition won't be found in any publication, and defensive strategy has been a term used only by some people, rather than a universally used term like CW, etc.
Here's my definition of defensive strategy:
Strategy that is intended to protect the win of a CW, or to protect majority rule.
[end of defensive strategy definition]
But it remains to define majority rule:
A candidate has a majority pairwise defeat (MPD) if another candidate is voted over him/her by a majority of all the voters.
[end of MPD definition]
An MPD is "nulllified" if it is in a cycle of MPDs, all of which are at least as strong as it is.
[end of nullification definition]
(I believe that these "end of definition" notations help clarify that the next definition isn't part of the previous one).
Majority rule is violated if a candidate wins who has an un-nullified MPD, when there's at least one candidate in the Smith set who doesn't have an unnulified MPD.
To protect majority rule is to prevent a violation of majority rule.
[end of majority rule protection definition]
(The part about the Smith set could be optional, but I add it so as not to penalize Smith Criterion complying methods).
About offensive strategy, that's strategy intended to take victory from a CW, or to make someone win in violation of majority rule.
Mike Ossipoff
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