Nov 16 draft of voting mechanics
More silliness fixed: The word "tie" is now only used in one context.
The definition of "transitive defeats" is fixed. The language defining
propositions has been cleaned up.
If anyone feels that draft is too hard to understand, please write me
a letter indicating the first part that you have trouble understanding,
and something about the nature of the problem you're having.
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 Schwartz 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 Schwartz set are eliminated.
Definition: An option C is in the Schwartz set if there is no
other option D such that D transitively defeats C AND C does
not transitively defeat D.
Definition: An option F transitively defeats an option G if F
defeats G 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 Schwartz set,
the weakest propositions are eliminated.
Definition: A proposition is a pair of options J and K
from the Schwartz set which are considered along with
the number of voters who prefer J to K and the number
of voters who prefer K to J.
Definition: The dominant strength of a proposition is the
count of votes in a proposition which is not smaller than
the other vote count in that proposition.
Definition: a weak proposition is a proposition which
has a dominant strength greater than zero and no larger
than that of any other proposition.
Definition: a weakest proposition is a weak proposition where
the vote count in the proposition which is not larger than
the other vote count is also no smaller than that of any
other weak proposition.
Definition: A proposition is eliminated by treating both
of its vote counts as zero from this point forward.
iii. If eliminating the weakest propositions would eliminate all
votes represented in the Schwartz set, a tie exists and the
person with the casting vote picks from among the options
represented in this Schwartz set.
iv. If eliminating the weakest propositions would not eliminate
all votes, a new Schwartz set is found based on the newly
revised set of propositions.
v. If this new set of propositions allows one option to
defeat all other options in the Schwartz set, that
vi. Otherwise, these steps (i-vi) are repeated with this new