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Re: Nov 18 draft of vote counting methodology

On Mon, Nov 18, 2002 at 02:13:01PM -0500, Raul Miller wrote:
>   A.6 Vote Counting

Evidently supermajority handling is still an open issue. FWIW, I prefer
the original way: compare against the default option and drop them early
if they don't make it.

>     2. We drop the weakest defeats from the Schwartz set until there
>        are no more defeats in the Schwartz set:
>          a. An option A is in the Schwartz set if for all options B,
>             either A transitively defeats B, or if B does not transitively
>             defeat A.
>          b. An option C transitively defeats an option D if C defeats
>             D or if there is some other option E where E defeats D AND
>             C transitively defeats E.

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.

>          c. An option F is a defeat (F,G) of an option G if N(F,G)
>             is larger than N(G,F).
>          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.


	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.

>          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.

>     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.


Anthony Towns <aj@humbug.org.au> <http://azure.humbug.org.au/~aj/>
I don't speak for anyone save myself. GPG signed mail preferred.

 ``If you don't do it now, you'll be one year older when you do.''

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