"hybrid theory" violates monotonicity

[Raul Miller <moth@debian.org>]

[I've been working with random elections to examine how well various
voting mechanisms conform to monotonicity.]

"Hybrid theory" violates monotonicity if we consider the default
option as a candidate:

Using the "hybrid theory" proposal, the j wins the election where a and
b require 3:1 majority and j is the default option, and the votes are:

ba
bc
ca
jb

If the "ca" vote is changed to "ac", c wins.

If we drop a and b before calculating the schwartz set (since in both
cases neither satisfy supermajority), c wins both elections.

I've not been able to prove, to my satisfaction, that "drop options
which don't satisfy supermajority" satisfies monotonicity, but after
simulating over a million elections I have not been able to find any
cases where it fails to satisfy monotonicity.

[As an aside: the ballots I'm testing with are quite a bit more
complicated than this example -- problems tend to show up more often on
complicated ballots.  I just went with a simple example for presentation
purposes.]

FYI,

-- 
Raul