[EM] Hybrid Beats-All/Approval v. Straight Approval

[Rob LeGrand]

Forest wrote:
> As I see it, checking for a beats all winner (and saving the
> approval winner for tie breaker) relieves some of the stress
> associated with strategic voting (i.e. the worry that you may be
> basing your strategy on inaccurate horse race information).

Excellent way to put it!  That's why I see Forest's CR pairwise method
(see http://groups.yahoo.com/group/election-methods-list/message/8008) 
as the brightest new idea here for quite a while.  It's hard for me to
imagine a better combination of Approval and Condorcet.

> I like your Example 3 showing that the beats all loser (i.e. reverse
> beats all winner) can be the Approval winner even when there are
> four candidates.

To me, Approval's advantages are its simplicity, its approximation of
CR when voters are clueless and its approximation of Condorcet when
voters are well-informed.  However, I'm worried that voters might be
motivated to lie to manipulate polls, and inaccurate polls would
surely be worse than none at all.  I imagine there to be plenty of
research to do in this area.

On the other hand, the best Condorcet methods, while imperfect,
usually make it extremely difficult for a voter to take advantage of
voting insincerely no matter what information he has.  I'd rather have
a method that doesn't depend on polls.  On the other hand,
Condorcet's 
(and CR pairwise's) requirement of new voting equipment is a huge
disadvantage; the U.S. government spends far too much taypayers' money
as it is!  Approval's simplicity can't be beat.

> Someday, someone with a lot of time on his/her hands should dig
> through these archives and publish all of the good examples and
> counter examples in a book like the classic book of examples and
> counterexamples in topology.

Good idea; it would make a fun project.  But note that most Condorcet
methods perform significantly better in my sincere-ballot simulations
than Approval, which should be seen as a *very* rough approximation of
CR.  I think we should be very careful drawing conclusions from
individual contrived examples.

--
Rob LeGrand
honky98 at aggies.org
http://www.aggies.org/honky98/