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Re: Nov 18 draft of vote counting methodology

On Wed, Nov 20, 2002 at 01:35:49AM +1000, Anthony Towns wrote:
> Ugh. I'd suggest reusing the same symbols and considering them to be "reset"
> each time you say "An option, <X>". Something like:
> 	W, X, Y, Z -- any option
> 	S          -- any option with a supermajority requirement
> 	D          -- the default option
> would probably be good.

I've been avoiding that, because 4.2 reuses Q in a meaningful fashion,
and because I want to refer to that same Q here.

> >          d. Given two options H and I, N(H,I) is the number of voters who
> >             prefer option H over option I, unless otherwise specified.
> >          e. If H is the default option and I has a supermajority
> >             requirement, N(H,I) is the number of voters who prefer option
> >             H over option I multiplied by the supermajority ratio.

> Yick.

Yeah, that's too ambiguous.

> 	d. Given two options, X and Y, N(X,Y) is the number of voters who
> 	   prefer option X to option Y.
> 	e. For any option, S, that requires an n:1 supermajority, and where
> 	   D is the default option, M(S,D) is N(S,D)/n. For all other options,
> 	   X, Y, M(X,Y) is N(X,Y).
> Yick even so. Exceptions are bad and confusing.

They're not really exceptions, they're procedure expressed as exceptions.

I'm thinking I should get rid of the "unless otherwise specified"
language and should rewrite each rule to explicitly state which other
rules take precedence over it.

> >          i. A defeat (R,S) is dropped by making N(S,R) the same as N(R,S).
> >             Once a defeat is dropped it must stay dropped.
> I preferred the "uneliminated proposition" description. "dropping defeats"
> is okay, but it's a bit confusing -- the defeat is a fundamental property
> of the votes we collected; propositions are just something we're working
> with to figure out the result.

Then again, on Ossipoff's site (specifically
http://www.barnsdle.demon.co.uk/vote/condor2.html), there's quite a bit
of talk about dropping the weakest defeats.  I figure, if it makes sense
for an expert on voting systems to use this terminology, it makes sense
for us to use this terminology.

> >     3. The winning option is picked from among the options T in the
> >        final Schwartz set where N(T,X) is larger than the quorum Q and
> >        X is the default option.
> Quroum of 40, no supermajorities:
> 	25 D A B
> 	30 B D A
> 	35 A B D
> D beats A 55:35, A beats B 60:30, B beats D, 65:25; D beats A is the
> weakest defeat, so A is the CpSSD winner, but is dropped in the final
> stage for not making quorum. Also, the largest majority would've preferred
> B to the result we ended up with.

I presume D is the default option.

The question is: is this better or worse behavior than eliminating
options which do not meet quorum before dropping weakest defeats?

Or, more specifically, do we want to bias decision making towards
further discussion or away from further discussion when significant
options can't make quorum?


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