<html>
Tom,<br><br>
I'm pretty understood what you said, and I'm not saying that your Fresh
Egg idea is necessarily bad. What I am saying is this:<br><br>
1) Your "points" method of applying it is very similar to
Copeland, and I don't think Copeland is very good. If you want to
make it more applicable (in my mind, anyway), then measure defeats some
other way. Perhaps you should use defeat-strength like Ranked Pairs
and Beatpath do.<br><br>
2) You haven't really shown this to be anything beyond an
interesting idea. Show us an example where this produces an
(arguably) better result than the above mentioned Condorcet-compliant
methods do.<br><br>
-Adam<br><br>
At 09:18 PM 7/5/2003 -0500, Tom Ruen wrote:<br><br>
<blockquote type=cite class=cite cite><font face="arial" size=2>Hi Dave,
Adam and others,</font><br>
<br>
<font face="arial" size=2>Perhaps I wrote too much to be convincing of
anything. Let me try again and focus on my primary interest.</font><br>
<br>
<font face="arial" size=2>My primary interest is in recognizing the
existing of "degrees" of strength of a winner. Condorcet does
this too, but not quite as completely. That is, Condorcet also is
incomplete (when pairwise cycles exist), and requires refined measures to
determine a winner, and those refinements can require further
refinements! My interest is to show that perhaps Condorcet's Winner could
use some refining itself.</font><br>
<br>
<font face="arial" size=2>I think it is useful to attempt to label the
strength of a candidate in an election, even if it isn't unconditionally
used to pick the winner.</font><br>
<br>
<font face="arial" size=2>When I first started learning about EMs over
two years ago Craig Carey demanded from me to define what I meant by a
majority among 3 or more candidates (He claimed it didn't exist).
Whatever Craig's funny ideas are, it is a worthy question.</font><br>
<br>
<font face="arial" size=2>At the time, I though it was obvious - A
majority is more than half the votes, but of course that idea is of
limited value by itself among 3 or more candidates since there may be no
candidate that passes the test. Still this is a reasonable test since not
all methods satisfy it:</font><br>
<br>
<font face="arial" size=2><b>1. A
S</font><font face="Times New Roman, Times">overeign</font><font face="arial" size=2>
Majority (SM) - If a candidate exists that is never below first place
among any subset of competitors. (Also more simply defined If a candidate
exists that has more plurality votes than all others
combined.)</b></font><br>
<br>
<font face="arial" size=2>This rule is certainly a good test of an
election method, and two well known methods can break it - Approval and
Borda.</font><br>
<br>
<font face="arial" size=2>Examples: </font><br>
<font face="arial" size=2> Approval: [XY] means a vote
for both X and Y, but prefer X.</font><br>
<font face="arial" size=2>
[AC]=51%, [BC]=49% - 51% prefer A, but C wins.</font><br>
<font face="arial" size=2> Analysis: Foolish approval
"overvoting" can hide a sovereign-majority
preference.</font><br>
<br>
<font face="arial" size=2> Borda:</font><br>
<font face="arial" size=2>
Election 1: AC=65%, CA=35%</font><br>
<font face="arial" size=2>
A=2*65+1*35=165</font><br>
<font face="arial" size=2>
C=1*65+2*35=135</font><br>
<font face="arial" size=2>
Election 2: ACB=65%, CBA=35% (Same preference between A and
C)</font><br>
<font face="arial" size=2>
C=2*65+3*35=235</font><br>
<font face="arial" size=2>
A=3*65+1*35=230</font><br>
<font face="arial" size=2>
B=1*65+2*35=135</font><br>
<font face="arial" size=2> Analysis: Introducing a
losing candidate hides a top-majority preference!</font><br>
<br>
<font face="arial" size=2>This tells me that if I'm interested in
supporting a "Sovereign-Majority" (SM) criterion, I don't want
to support Approval or Borda.</font><br>
<br>
<font face="arial" size=2>Then we have another lower criterion that can
be applied if there is no sovereign-majority - Condorcet's
winner.</font><br>
<br>
<font face="arial" size=2><b>3. A Condorcet Majority (CM) - If a
candidate exists that is always above last place among all pairwise
subset elections with competitors. ("Above-last" is equivalent
to saying "first" among pairwise comparisons.)</b></font><br>
<br>
<font face="arial" size=2>I call this "Concercet Majority"
because it defines a unique winner, in parallel how the SM works. Two
candidates can never simultaneously satisfy this criterion, although in
some elections (with cyclic preferences), there may again be no candidate
that satisfies it.</font><br>
<br>
<font face="arial" size=2>Whether I want to use this rule for picking a
winner, it is a real measure of a candidate. AND we all know that IRV can
break this rule and pick a different candidate sometimes.</font><br>
<br>
<font face="arial" size=2>So, if I'm interesting in ALWAYS picking the CM
winner, then IRV is not a method I want to support.</font><br>
<br>
<font face="arial" size=2>I misnumbered the CM as (3) above because there
is an intermediate criterion which I chose to call the "Fresh Egg
Majority".</font><br><br>
<font face="arial" size=2><b>2. A Fresh Egg Majority (FEM) - If a
candidate exists that is always above last place along all subset
elections with competitors.</b></font><br>
<br>
<font face="arial" size=2>Looking at FEM is similar to CM, except it is a
more strict requirement. Sometimes a CM winner won't exist, but more
often a FEM winner won't exist.</font><br>
<br>
<font face="arial" size=2>On the surface this would appear to be
back-stepping, being less decisive than CM, less useful in practice,
however I choose to see it as being more careful, more demanding, and
choosing to recognize the difference between a candidate that can merely
do well in pairwise contests, and one that also does well in the
plurality set and other subsets.</font><br>
<br>
<font face="arial" size=2>This criterion suggests to me that the
Condorcet Majority definition, however nice, is not the end-all-be-all
rule for picking a winner, and that it is reasonable to consider election
methods that don't always pick the Condorcet winner.</font><br>
<br>
<font face="arial" size=2>As I said before an interesting result of the
FEM definition is that when it exists, both Condorcet AND IRV must agree
on this winner.</font><br>
<br>
<font face="arial" size=2>I don't think I should have to define FEM as a
concept that is meaningful for recognizing candidate's strength, although
I admit many may not consider it useful for defining a better
method.</font><br>
<br>
<font face="arial" size=2>For me it is interesting to me to define these.
I call them "majorities" but only the first (SM) REALLY
qualifies as a true (50%+1) majority. The FEM and CM criteria succeed by
defining a unique winner sometimes, and uncertainty elsewhere. These are
perhaps best called pseudo-majorities for being a pass/fail test that can
have at most one winner. Condorcet supporters might talk of
"strongest majority", although I'd call that phrase as
overstepping their case since a measure of what is strongest can be
subjective.</font><br>
<br>
<font face="arial" size=2>Obviously other such criteria may be named, for
example: </font><br>
<font face="arial" size=2><br>
<b>1+1/2. A Noble Majority (NM) - If a candidate exists that is always
above the average vote along all subset elections with competitors.
(Average = total_votes/subset_candidates)</b></font><br>
<br>
<font face="arial" size=2>Avoiding last place (FEM) is a good sign of a
winner, but ALWAYS being above the middle is even stronger. This
criterion is between SM and FEM. It occurs more often than SM but less
often than FEM.</font><br>
<br>
<font face="arial" size=2>I'm note sure if this one has any use, but it
is an attractive criterion to satisfy.</font><br>
<br>
<font face="arial" size=2>I think it is useful for recognizing some
winners will be stronger than others, AND it may be useful to grade
winners in this way. Condorcet is the method that first demanded this
complexity of giving degrees of winners, and there is still disagreement
in the hardest cases. I am merely continuing his story and seeing what
Condorcet chose to ignore.</font><br>
<br>
<font face="arial" size=2>If I have a point, it is to suggest that
Condorcet may be more negligent than supporters wish to admit, and even
if everyone agrees that Condorcet picks a best winner, I'd like
recognition when a pairwise winner is picked without core support of
plurality counts.</font><br>
<br>
<font face="arial" size=2>Thanks for listening.</font><br>
<br>
<font face="arial" size=2>Sincerely,</font><br>
<font face="arial" size=2>Tom Ruen</font><br>
</blockquote></html>