[EM] Cramster question

[Terry Bouricius]

Warren,

However, using first-choice plurality to settle Condorcet cycles could 
easily elect the Condorcet-loser (the candidate who loses in every 
pairwise match-up). There are many far superior cycle breakers. I 
personally favor ranked-pairs because it is both reasonable, and 
relatively easy to explain to lay people (unlike many cycle breakers).

Terry Bouricius

----- Original Message ----- 
From: "Warren Smith" <warren.wds at gmail.com>
To: "election-methods" <election-methods at electorama.com>
Sent: Thursday, May 14, 2009 3:35 PM
Subject: [EM] Cramster question


Question:
Condorcet’s method has many nice properties, and some supporter’s of
former Vice President Al Gore pointed out that Al Gore was very likely
the Condorcet winner. The problem with Condorcet’s method is that it
does not produce a winner often. Thus, let us propose a combination of
the Condorcet’s
method and the plurality system: This combined system deems the
Condorcet winner as the winner. In case that the Condorcet’s method does
not produce a winner, then use plurality method to select the winner.

Q1) Does the Condorcet-plurality system produce winner more often than
Condorcet’s method? Explain.

--A1: yes.   Every time a Condorcet winner fails to exist (i.e. about 9% 
of
time in random 3-canddt elections), it elects plurality winner.  Only
fails in cases where
BOTH CW fails to exist AND plurality tie.

2) Does the Condorcet-plurality system satisfy the Pareto condition?
Explain.

--A2: yes. Unanimous first-choices always win.

3) Does the Condorcet-plurality system satisfy Condorcet winning
Criterion? Explain.

--A3: yes, by defn.

4) We know that both Condorcet and plurality systems are monotone. Is
the Condorcet-plurality combined system still monotone? Explain.

--A4: Yes. In a rank-order vote containing "A>B" change it
to "B>A."   Can that ever stop B from winning?  Not if B was a CW,
and not if B was a plurality winner either.

5) Is the Condorcet-plurality system manipulable? If your answer is
manipulable,
give an example of an election where manipulation can be done. If your
answer is not
manipulable, prove it.

--A5: manipulable.  Example
http://rangevoting.org/IncentToExagg.html

-- 
Warren D. Smith
http://RangeVoting.org  <-- add your endorsement (by clicking
"endorse" as 1st step)
and
math.temple.edu/~wds/homepage/works.html
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