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Nov 17 draft of voting mechanics

This is a major rewrite, with changes suggested by Clinton, Anthony
Towns and Jochen Voss.  

Also, note that supermajority requirement isn't called supermajority
requirement elsewhere in the constitution.  Once we've nailed down
the language of how votes are counted, I think I'll also be
proposing that supermajority requirement be talked about using
the same terms throughout the constitution.

If anyone feels this 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 an order which
       represents the voter's preferences.  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 in default.

       Definition: Option A defeats option B if the
       preference (A,B) is greater than the preference (B,A).

       Definition: a preference (C,D) is the number of voters who
       prefer option C over option D.

    3. To avoid default, an option has a quorum requirement, Q must be
       preferred to the default option by at least Q more voters than
       preferred the default option to it.

    4. To avoid default, an option has a supermajority requirement
       must defeat the default option by the specified ratio of votes.
       That is, if 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 all options are in default, the default option wins.

    6. Otherwise, we use Cloneproof Schwartz Sequential Dropping to
       pick the winner.  This procedure must be carried out in the
       following order:

       i. If only a single option remains in the Schwartz set,
          it is the winner.

          Definition: An option E is in the Schwartz set if, for
          all other options G, either E transitively defeats G or
          G does not transitively defeat E.

          Definition: An option F transitively defeats an option H if F
          defeats H or if there is some other option J where J defeats
          H AND F transitively defeats J.

       ii. Unless this would eliminate all propositions in the Schwartz
           set, the weakest propositions are eliminated.

           Definition: A weakest proposition is a proposition that has
           no other proposition weaker than it. There may be more than
           one such proposition.

           Definition: A proposition (N,K) is weaker than a
           proposition (L,M) if the preference (N,K) is less than
           the preference (L,M).  Also, a proposition (N,K) is
           weaker than a proposition (L,M) if the preference (N,K)
           is equal to the preference (L,M) and the preference (K,N)
           is greater than the preference (M,L).

           Definition: A proposition is a pair of options with a
           non-zero preference (S,T) for at least one of the options.
           The proposition is a defeat for one of the options unless
           the preference (S,T) equals the preference (T,S).

       iii. If eliminating the weakest propositions would eliminate
            all propositions of 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 propositions, a new Schwartz set is found based on the
           newly revised set of propositions.

       v. Otherwise, these steps (i-v) are repeated with this new
          Schwartz set.



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