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Nov 18 draft of vote counting methodology

I'd like to especially thank Anthony Towns for helping me avoid shooting
myself in the foot too many times before I got it out of my mouth.

As always, if there are any flaws in my thinking or in my presentation,
please tell me.  This is a fairly complete rewrite so please scrutinize
it suspiciously.


  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. 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.

         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.

            For example, if option I has a majority requirement of 2:1
            and H is the default option then each vote preferring H over
            I is counted twice in this context.

         f. A defeat (J,K) is weaker than a defeat (L,M) if N(J,K) is
            less than N(L,M).  Also, (J,K) is weaker than (L,M) if N(J,K)
            is equal to N(L,M) and N(K,J) is greater than N(M,L).

         g. A weakest defeat is a defeat that has no other defeat weaker
            than it. There may be more than one such defeat.

         h. A defeat is in the Schwartz set if both of its options are
            in the Schwartz set.

         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.

    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.  Q is 1 unless otherwise specified.
       If there's more than one option to pick from, the person with the
       casting vote picks the winner from these options.  If there's no
       options to pick the default option wins.




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