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<DIV><FONT face=Arial size=2>Greetings,</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>I've not written to EM list much, mostly because
the debate is overwhelming and so often seems far from practical level methods
that have a chance to be implemented in political elections.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>However I've been developing a useful line of
thought and I hope it might be worthy of discussion. My personal agenda is
towards Condorcet, but considering practical steps away from plurality that are
almost as good as Condorcet.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Given any election method, I can ask the
question, "How many candidates can be guaranteed to be treated
fairly?"</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>I decided to classify different methods on
limitations on "fairness" in the Condorcet sense of direct competition without
distraction.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>ELIMINATION LIMITED FAIRNESS - eliminated
candidates fail to get equal treatment.</FONT></DIV>
<DIV><FONT face=Arial size=2>1. Plurality - Trivially treats 1 candidate fairly
(top-one!)</FONT></DIV>
<DIV><FONT face=Arial size=2>2. Top-two runoff - Treats at least 2 candidates
fairly (top-two!)</FONT></DIV>
<DIV><FONT face=Arial size=2>3. Bottom-up runoff - Treats at least 2 candidates
fairly (Possibly a different two from the top-two runoff)</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT><FONT face=Arial size=2><FONT face=Arial
size=2></FONT> </DIV></FONT>
<DIV><FONT face=Arial size=2>PAIRWISE LIMITED FAIRNESS - Fair treatment,
but candidates can win without being anyone's favorite.</FONT></DIV>
<DIV><FONT face=Arial size=2>
<DIV>1. Condorcet (Ignoring cycles for now) - Treats ALL candidates
fairly</DIV>
<DIV><FONT face=Arial size=2>
<DIV><FONT face=Arial size=2> </DIV></FONT></FONT></DIV>
<DIV>
<DIV><FONT face=Arial size=2>APPROVAL LIMITED FAIRNESS - "Equal treatment", but
not "Fair treatment" since lower preference votes can hurt higher ones
(comparing levels of preference truncation).</FONT></DIV><FONT face=Arial
size=2>
<DIV><FONT face=Arial size=2>
<DIV><FONT face=Arial size=2>1. Approval - No rankings</FONT></DIV>2.
Borda</FONT></DIV>
<DIV>3. Bucklin</DIV></FONT></DIV>
<DIV> </DIV>
<DIV>I'm sure there's many other interesting methods and variations, but I just
wanted to give some basic differences. I admit others might group them
differently. Plurality and Approval might not fit any single classification with
the others.</DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV>
<DIV><FONT face=Arial size=2>I included "approval methods", but find myself
unable to deal well with analysis here. They are "fair" in the sense of no
elimination, but unfair since they DEMAND strategic truncation by most
voters to guarantee a majority winner be identified. Voters who have better
polling data have more influence for knowing better how to truncate their
choices to affect the winner. Approval elections are a game of chicken,
always depending other voters to truncate less. (I know I'll get
slammed for my opinions here, and they aren't worth any further debate for
me.)</FONT></DIV>
<DIV><FONT face=Arial size=2>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV>
<DIV><FONT face=Arial size=2>Primarily I looked at the idea of
fairness in consideration of runoff methods which eliminate
candidates.</FONT></DIV>
<DIV> </DIV></DIV></FONT></DIV>
<DIV><FONT face=Arial size=2>I think it is valuable to recognize that
all runoffs, instant or not, (with a 50% majority requirement) are limited
to guaranteed fair treatment of two candidates - the final two
survivors. If the Condorcet candidate is in that final two-set, he'll be
guaranteed to win, and other candidates don't get that same
opportunity.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>This is a significant failing, but at least it is
clear that it is better than plurality which offers no minimum support needed to
win, besides the trivial (non)limit: (votes/candidates+1) - approaches zero as
candidates gets larger.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>I also think it is interesting to notice that
on these simple grounds a "top-two" runoff is "just as fair" as a
"bottom-up" runoff - both only promise that two candidates will have
undistracted competition. The only way to go beyond TWO candidate fairness is to
go to Condorcet-style competition where there are no
distractions.</FONT></DIV>
<DIV> </DIV>
<DIV>Now I don't want at all to be critical of Condorcet's approach, but I can
see Plurality and Condorcet as opposites with different valuable
properties. Plurality counts reward candidates that can stand out
as special among full competition. Condorcet rewards candidates that
stand out only under pairwise competition. I can imagine that without
limits to competition, there is no incentive in pure Condorcet for voters
and candidates to unify before the election. Condorcet offers no incentive for
parties to organize or rally behind one choice.</DIV>
<DIV> </DIV>
<DIV>I consider perhaps it is more conservative to offer compromise
solutions - methods that have one "Plurality" count to recognize the
strongest candidates under full competition, and a second Condorcet counting
round among the survivors of the first round. A single plurality-based
elimination round allows serious candidates to be separated from the less
serious ones, and encourages voters make a hard choice which candidate to
support.</DIV>
<DIV> </DIV>
<DIV>Interestingly to me a "top-two runoff" is the simplest (trivial) form of
this two round approach.</DIV>
<DIV> </DIV>
<DIV>I like the idea of supporting IRV reform, except limiting it to a
two-round (top-two) instant runoff because it has the purity of a
single elimination round of plurality-strong candidates and equal treatment of
survivors.</DIV>
<DIV> </DIV>
<DIV>This approach is most defendable to people who see virtue in the plurality
placings and fear IRV rewards weak candidates. </DIV>
<DIV> </DIV>
<DIV>Someday if too many elections like France 2002 occur, we can consider
election rules that allow more than two candidates to survive elimination.</DIV>
<DIV><A
href="http://en.wikipedia.org/wiki/French_presidential_election%2C_2002">http://en.wikipedia.org/wiki/French_presidential_election%2C_2002</A></DIV>
<DIV> </DIV>
<DIV>In that election everyone will agree there were three strong candidates
most worthy of consideration. A pure bottom-up IRV election would be horrible
due to so many rounds of elimination that would demand recounts when
eliminations were close among weak candidates. A pure 16 candidate Condorcet
election would probably be safe, but with 3% spoiled ballots, pretty much
meaningless to think voters could offer much wisdom in all pairwise contests. It
is just a little scary to perform all pairwise counts, even if it is extremely
rare for a plurality weak candidate to win Condorcet.</DIV>
<DIV> </DIV>
<DIV>What is most interesting to me to consider that the next (simplistic)
reform beyond a "top-two runoff" may NOT be "top-three runoff" as
recursion implies (or worse a recursive "bottom-up-runoff") but instead a
"top-three-Condorcet" as a plurality round followed by 3 pairwise
rounds.</DIV>
<DIV> </DIV>
<DIV>A two-round Plurality-Condorcet approach allows different methods to be
defined that can treat any desired number of candidates equally. Or more
sensibly it can have elimination rules that allow a variable number of
plurality survivors based on their judged strength in the plurality
count.</DIV>
<DIV> </DIV>
<DIV>For instance here's three sensible rules that can work together:</DIV>
<DIV>If there's no outright majority winner, let candidates survive by
rules:</DIV>
<DIV> 1. At least two candidates must survive. (top-two)</DIV>
<DIV> 2. At least the top 50% of votes for candidates must
survive (top-median)</DIV>
<DIV> 3. All candidates with at least 20% of the vote must
survive. (individual threshold)</DIV>
<DIV> </DIV>
<DIV>Rule #2 is most used when there's many candidates and none very strong. In
the French 2002 election, rule #2 would keep the top-3 candidates in the
plurality round, whom combined have 53% of the vote. Rule#3 applies more when
there's more than 2 strong candidates, allowing up two 4 strong candidates
to survive.</DIV>
<DIV> </DIV>
<DIV>Rules like these define thresholds that candidates must reach to be
guaranteed fair treatment of a Condorcet round. Nonmontonicity can
exist when a possible Condorcet winner fails the thresholds, but clear
threshold requirements at least help voters decide their strategy in how to get
at least one favored candidate into the "fairly treated" set.</DIV>
<DIV> </DIV>
<DIV>Pre-election polling data measures "plurality strength" so a direct
prediction can be made which candidates will make the first round cut. (unlike
bottom-up IRV elections which offers no guarantees to the strongest
plurality candidates unless they hold an outright majority)</DIV>
<DIV> </DIV>
<DIV>Anyway, I really like this approach of measuring methods (by how many
candidates are treated fairly) and limited one-round elimination by plurality
strength. Everyone should recognize that runoffs, however much put-down as
offering poor results in strong 3-way contests, are a major step
forward in treating two candidates equally at least.</DIV>
<DIV> </DIV>
<DIV>My reform steps for single winner elections would be:</DIV>
<DIV>1. Plurality (beats dictatorship, fair treatment for ONE top
candidate)</DIV>
<DIV>2. Top-two runoff (majority requirement, fair treatment for at
least TWO top candidates)</DIV>
<DIV>3. Plurality-Condorcet (fair treatment for a SET of
top candidates)</DIV>
<DIV>4. Pure Condorcet (fair treatment for ALL candidates)</DIV>
<DIV> </DIV>
<DIV>I offer these methods as either one election (Voting with one set of
ranked ballots) or two rounds of voting. When there are many candidates and less
informed voters, it can be distracting to have to do everything in one round. If
voters are willing I'd prefer allowing two rounds of actual voting to make sure
all preferences offered are well considered.</DIV>
<DIV> </DIV>
<DIV>Thanks for listening. I apologize for being too long-winded. :)</DIV>
<DIV> </DIV>
<DIV>Sincerely,</DIV>
<DIV>Tom Ruen</DIV>
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