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.
Yick.
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.
Cheers,
aj
--
Anthony Towns <[EMAIL PROTECTED]> <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.''
