[EM] Definitions of majority rule, defensive strategy, offensive strategy

[MIKE OSSIPOFF]

Donald said:

It's like when
MikeO talks about his special defination of `Majority', he too doesn't feel
he is saying anything wrong.

I reply:

My definition of majority isn't special. It's the usual standard
definition: More than half of the voters.

>From that, we say that Smith has a majority agains Jones if more
than half of the voters vote Smith over Jones.

And we say that Smith has a majority preference against Jones if
more than half of the voters prefer Smith to Jones.

But if you want a really funny definition of majority, consider
the IRV-promoters' definitions that I quoted in my reply to James.
When IRV peole claim that IRV elects a majority-winner, they're using
their own unusual definition of a majority winner.

But Don could be referring to my definition of majority rule, which
isn't something that we've seen before. It seems to me that I made
an error when I posted that definition, but didn't want to bother the
list with a corrected version.

My definition is based on GMC and Beatpath GMC. In fact, it
defines a criterion that I'd call improved Beatpath GMC.


But here's how I define majority rule:

X has a majority vote against Y if more than half of all the voters
vote X over Y.

The strength of a majority vote for X against Y is measured by
the number of voters who vote X over Y.

A majority vote is nullified if it is in a cycle of majority votes
that are all at least as strong as it is.

Majority rule is violated if we elect someone who has an unnulified
majority vote against him/her.

[end of definition]

A method that violates majority rule, as defined above, fails
improved Beatpath GMC.

As I said before, the fact that Plurality meets Beatpath GMC &
improved Beatpath GMC isn't a problem, because it's accepted that
Plurality doesn't violate voted majority wishes, though it certainly
fails important criteria.

It might sound arbitrary or artificial to speak of cycles when
defining majority rule, but what could nullify a majority vote
against someone but a cycle of majority votes at least as strong?

Likewise, my posted definitions of offensive & defensive strategy
might have had errors that I didn't want to bother the list by
correcting. But here are definitions of those terms:

A voter votes offensive strategy if s/he votes in a way intended to
take victory away from a CW, or to elect someone in violation of
majority rule.

X has a majority pairwise preference (MPP) against Y if more than half
of the voters prefer X to Y.

The strength of an MPP for X against Y is meaured by the number of
voters who prefer X to Y.

An MPP is nullified if it's in a cycle of MPPs that are all at least as
strong as it is.

Majority preference is violated if we elect someone who has an
unnulified MPP against him/her.

A voter votes defensive strategy if s/he votes in a way intended to
protect the win of a CW, or to prevent a violation of majority preference.

[end of definition]



Mike Ossipoff








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