[EM] Response to critique of MJ (MCA subtype) procedure by Felsenthal & Mac

[Warren Smith]

Jameson Quinn says
"the objection that 'Seriously nonmajoritarian results are possible if
most preferences between two candidates do not straddle the median' is
easily addressed by offering only 3 rating levels."

It seems to me however, that MJ with 3 levels would in practice usually yield
an N-way tie with every candidate median-rated "middle," whereupon the
Balinski+Laraki
tiebreak procedure would reduce to "elect the candidate with the most
top-ratings"
otherwise known, basically, as "approval voting."

(This claim by me is not quite correct, but I think substantially true.)

=========================================

You may be amused by the following snooty email I sent to Felsenthal & Machover.

Just saw your paper
http://eprints.lse.ac.uk/24213/1/The_Majority_Judgement_voting_procedure_%28LSERO%29.pdf

which cited my "blog"
http://www.rangevoting.org/MedianVrange.html

Well first of all, this is not a "blog," it is a "web page" that is
part of the rangevoting.org website.

While it is true I am the main author of that website (at least so
far) there are many other contributors.

In particular the quote "dismissed from consideration as a voting
system" was not due to me, as you misleadingly implied, but was due to
Rob Lanphier, as it had said on the web page precisely because I did
not wish to say that, I just wished to record Rob Lanphier's written
opinion, in a web post he made considerably before either you or
Balinski+Laraki ever said anything on the subject.    It helps to
actually read my words before complaining about them.  If you had
quoted somebody saying "Hitler is great" would you appreciate me
saying "Felsenthal and Machover implied they thought Hitler was great"?

As I documented, this Median-based method, B&L's main theorem about it
(which in fact is due to Bart Ingles), and many of its properties and
deficiencies were already discussed by and invented by internet voting
methods community years before either you or B&L came along, and I in
my more cynical moments wonder if your main contribution is to try to
obscure that history.

You then continue on to remark (also misleadingly) that I had "failed
to note" that range voting also can elect Y even though a voter
majority prefers X over Y.
Actually, I was perfectly well aware of that and it was discussed in
many many other pages at the rangevoting.org website.  For example (to
name just one among many)
  http://www.rangevoting.org/FishburnAntiC.html

In   http://www.rangevoting.org/AppCW.html
a simple theorem is pointed out showing that range voting will always
elect a Condorcet winner whenever one exists provided a certain simple
model of strategic voting applies.
This causes Condorcet winners actually to be elected MORE often with
range voting
than with Condorcet voting (!!!) if the voters are strategic.

On the other hand if the voters are honest, then range voting outperforms
Condorcet methods because Condorcet winners can be bad.  E.g. the
"kill the Jews" vote:
  option a: kill all Jews and steal their money and use it to reduce
taxes for non-Jews
  option b: do not kill the Jews
  option c: ...
where this is 1935 Germany and Jews are about a 6% minority.
If all voters honestly vote what is best for them, then (a) wins and
is a Condorcet winner.
If all voters honestly report numerical range votes so all Jews vote a=0
but nonJews honestly report that yes, it would be a little better for
them taxwise to
do a than b...   then this MIGHT be enough to allow (a) to lose.
Only range voting (among commonly proposed voting systems) can thus
overcome the "tyranny of the majority" provided there are
enough honest voters.

http://rangevoting.org/rangeVcond.html
discusses that and notes that under a nontraditional definition of
"Condorcet winner" (which actually might have been what Condorcet
himself had in mind!) both average-based and median-based Range voting
are Condorcet methods.

You then say "in the absence of empirical data we are unable" to tell
whether median-based or average-based range voting is more likely to
elect a Condorcet winner.
Actually, had you bothered to employ the search tool at
rangevoting.org, you would soon have discovered we already had such
data years before Balinski & Laraki:
  http://www.rangevoting.org/StratHonMix.html
and in one study reported there, range (average-based)
delivered 11796 Condorcet winners while median-based delivered 11012.
In another, average gave 13279 while median gave 12472.
See also table 2 here:
http://rangevoting.org/RandElect.html
See also some of the pictures here:
http://www.rangevoting.org/IEVS/Pictures.html
which makes it fairly clear average based range is "more like"
Condorcet than median-based in positional models.

The rangevoting.org website makes available a public source computer
program called IEVS which hopefully makes it easy for anybody to
produce such data.

You then note the "main disadvantage" of average-based range voting is
it is "considerably more prone to strategic voting" than median-based.
 Unfortunately you give no evidence at all for this statement.

Unlike you, who simply made this bald assertion with no evidence for
it, my http://www.rangevoting.org/MedianVrange.html
page actually did provide a fair amount of discussion of that issue,
see section titled 'What about "strategy"?'  and there is also the
"strategic voting causes range voting to elect condorcet winners"
theorem in http://www.rangevoting.org/AppCW.html

It is not clear to me the strategic vulnerability issue matters in
real life for median vs average.   Are you aware of any real world
example where median and average returned different winners?   Are you
aware of any evidence voters behave differently with median versus
with average-based?   On the latter question I am aware of evidence
that indicates
the voters behave the same.  E.g. see
http://www.rangevoting.org/French2007studies.html


-- 
Warren D. Smith
http://RangeVoting.org  <-- add your endorsement (by clicking
"endorse" as 1st step)
and
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