[EM] Defensive Strategy Definition

[MIKE OSSIPOFF]

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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