[EM] briefer definitions. Condorcet Criterion.

[MIKE OSSIPOFF]

EM list--

It's occurred to me that yesterday's definition of strategy
doesn't apply easily to Plurality & Approval. Instead of fixing it,
I'd like to leave it out. Here's how I'd define defensive & offensive
strategy:

Defensive strategy:

If electing a certain candidate is the goal of a majority of the voters,
and some members of that majority vote in a way intended to elect him,
that's defensive strategy. If keeping a certain candidate from winning
is the goal of a majority of the voters, and some members vote in a way
intended to keep him from winning, that's defensive strategy.

(I'd like to add a statement that protecting the win of a SCW is
defensive strategy too, but for now, when I say "defensive strategy",
I mean it as defined above. Till such time as someone says that
it would make sense to them to add the SCW clause).


Offensive strategy:

A voter uses offensive strategy if he votes in a way intended to take
victory from a SCW & give it to someone else whom he likes better.

[end of those 2 definitions]

Again, I realize that, at least in voting systems other than Plurality,
voters seldom have only the goal of electing one particular candidate.
But hypothetical situations can be presented in which that's the case,
and in real elections people's voting often approaches that character.

Condorcet Criterion:

I'd said that that criterion is always defined to pass nothing or to
pass Plurality. It is often written that way, but I can't say it always
is. It needn't be.

With the understanding that "sincere voting" needs definition,
here's how that criterion could be stated:

If everyone votes sincerely, the SCW should win.

Seamlessly defining sincere voting to apply to all methods isn't
as easy as it sounds. Here's an initial try:

Not reversing a sincere preference, and not leaving unexpressed any
sincere preferences or ratings which the voting system would allow
to be expressed in addition to those preferences already expressed.

With that definition, the Condorcet Criterion applies to all methods,
and Plurality & Approval don't pass. The definition of sincere voting
seems to cover all methods. "Preference" means pairwise preference.
The definition applies to methods that ask for ratings, because if
you rate X higher than Y, you're voting a preference for X over Y
(in addition to actually expressing the ratings). If, in Point Ratings,
you use that method as Approval, which is the best strategy for that
method, and you vote a strategy that would be sincere in Approval,
then that strategy is still sincere in Point Ratings.

Mike Ossipoff

_________________________________________________________________________
Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com.

Share information about yourself, create your own public profile at 
http://profiles.msn.com.