[EM] Head to Head Comparison of Election Methods

[Paul Dumais]

I would like to propose a debate to compare my favorite election method
(I call it Dumais) and anyone else's favorite election method (for fun).
My goal is to discover which method is the best at fairly and
efficiently ranking candidates based a set of voters' choice(s). Though
I doubt any method will be universally accepted in every situation; I
think such a debate will bring interesting issues to light which may
alter people's views. I will take up this challenge with the first
serious challenger.
	Here is a description of Dumais voting.
1.  Each voter ranks one or more of the available candidates.
2.  Do a standard borda count.
3.  Divide the candidates into two groups. One group (the preferred
group) all have a Borda Count (BC) of BC > (C-1)*V/2 where C is the
number of candidates and V is the number of voters. The second group
(the non-preferred group) has BC < (C-1)*V/2.
4.  Repeat steps 2 and 3 (on the preferred group) until the preferred
group is small enough to choose the winner or winners. A complete
ranking of all candidates can also be done in this way by repeating
steps 2 and 3 on each group.

Unranked choices split the remaining borda count (or (U-1)/2 where U is
the number of unranked candidates). This method can be interpreted in
another way. Each candidate gets one point for every opponent it defeats
on a single ranking by a single voter. Each candidate gets 1/2 point for
each opponent it ties with (unranked candidates). The borda count is
equivalent to asking: "how many times does a candidate (ie A) defeat
another candiate when we compare him to every other candidate using all
the available information (ie using each voter's ranking of the
candidates)?". Elimination is required to reduce the effect of
introducing identical candidates (as a stratategy) and to allow us to
reduce the effect of "lower" candidates in our choice of the best
candidate. A borda count in the only fair way to choose candidates for
elimination, since it is the only method that takes into account all of
the voting information without predjudice.

This voting method meets the Smith criterion, condorcet criterion, and
reverse-consistancy.

-- 
Paul Dumais