This draft fixes some serious flaws in the expression of the concept of
"weakest defeat", and other problems.
Please let me know if there are any additional ambiguities or other
errors.
A.6 Vote Counting
1. Each ballot orders the options being voted on in the order
specified by the voter. If the voter does not rank some options,
this means that the voter prefers all ranked options over the
unlisted options. Any options unranked by the voter are treated
as being equal to all other unranked options.
2. Options which do not defeat the default option are eliminated.
Definition: Option A defeats option B if more voters prefer A
over B than prefer B over A.
3. If an option has a quorum requirement, that option must defeat
the default option by the number of votes specified in the quorum
requirement, or the option is eliminated.
4. If an option has a supermajority requirement, that option must
defeat the default option by the ratio of votes specified in the
supermajority requirement, or the option is eliminated. That is,
if a an option has a 2:1 supermajority requirement, then there
must be twice as many votes which prefer that option over the
default option than there are votes which prefer the default
option over that option.
5. If one remaining option defeats all other remaining options,
that option wins.
6. If more than one option remains after the above steps, we use
Cloneproof Schultz Sequential Dropping to eliminate any cyclic
ambiguities and then pick the winner. This procedure and must
be carried out in the following order:
i. All options not in the Schultz set are eliminated.
Definition: An option C is in the Schultz set if there is no
other option D such that C transitively defeats D AND D does
not transitively defeat C.
Definition: An option F transitively defeats an option G if G
defeats F or if there is some other option H where H defeats
G AND F transitively defeats H.
ii. Unless this would eliminate all options in the Schultz set,
the weakest defeats are eliminated.
Definition: The strength of a defeat is represented by two
numbers: the number of votes in favor of the defeat, and
the number of votes against the defeat. A defeat with
the fewest options in favor of that defeat is a weak option.
Of the weak options, an defeat with the most votes opposed
to that defeat is the weakest defeat. More than one defeat
can be the weakest.
Definition: A defeat is eliminated by treating the count of
votes both for and against that defeat as zero in the context
of that defeat.
iii. If eliminating the weakest defeat would eliminate all votes
represented in the Schultz set, a tie exists and the person
with the casting vote picks from among these options.
iv. If eliminating the weakest defeats would not eliminate all
votes, a new schultz set is found based on the revised set
of defeats.
v. If this new schultz set contains only one option, that option
wins.
vi. Otherwise, these steps (i-vi) are repeated with this new
schultz set.
Thanks,
--
Raul
