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 math.temple.edu/~wds/homepage/works.html ---- Election-Methods mailing list - see http://electorama.com/em for list info
