[EM] Median bifurcation using pairwise matrix

Richard Moore rmoore4 at home.com
Tue Aug 14 19:45:41 PDT 2001

Roy wrote:
 > Median bifurcation groups candidates by whether a 
majority of voters
 > rank them in the upper half of the group they're listed 
with. It can
 > be used to completely rank candidates. It is my fondest 
wish that it
 > is functionally equivalent to Ranked Pairs, but without 
the ad hoc
 > feel of having to keep a sharp lookout for contradictions.

It does sound promising. This method is monotonic because 
ranking a candidate higher on a ballot (one more winning 
vote, one less losing vote) can never move that candidate 
from the upper group to the lower group for any given fork.

Condorcet? In any given fork, using the pairwise matrix, the
CW will always have more winning votes than losing votes. So
the CW will always be placed in the top group after each
fork, and will win in the end.

Smith? I'm not quite sure about that one. When a fork puts
one or more Smith set members into the lower group, this
could break up the members of the Smith set in the upper
group, so one of those becomes that group's CW, who will
then become the winner. But is it possible for all Smith
candidates to be swept into the lower group on a single
fork? If so, the method fails Smith, but if not, it passes.
I only have a guess at this point, but I suspect that it 
passes Smith.

Median bifurcation fails IIAC and FBC, however.


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