[EM] (6) To Kristofer and everyone: MJ best to ‘tolerate’

Toby Pereira tdp201b at yahoo.co.uk
Sat Sep 17 06:25:23 PDT 2016

Arguably a problem with Majority Judgement is that most voters make no difference to the overall "score" for a candidate. Because it uses the median rather than mean, it is a fairly "robust" measure, and a single vote is unlikely to shift the median. People can use that to argue in its favour - if you like or dislike a candidate you can rate them highly or lowly (above or below their current median), and it doesn't matter whether you use the extreme ratings or not. If a candidate's median is C, then I can give an honest B or an exaggerated A - the candidate's overall median won't be affected by my exaggeration.

But the flipside of being resistant to strategy in this way is that arguably it is only this way because it's resistant to voting itself! It just has much more "inertia" than other systems. In normal score voting every vote has an effect on a candidate's average. And because of this there is arguably a sense of "power" for a voter. But this isn't the case for median voting. Well, each vote would provide some sort of shift that could make a difference in a tie-break, but it's not the same.

One slightly crazy idea to ameliorate this would be to use a measure somewhere between the mean and median. The mean of a data set is the number that minimises the sum of the squared differences to the data points. The median is the number that minimises the sum of the absolute differences (so the differences^1). So maybe you could instead minimise the differences^1.1 or something. This would still be close to a median method but presumably each vote would make a difference to a candidate's "average" score using this measure. But then arguably it doesn't make sense to use letter grades with a verbal description in a system like this. It becomes about numbers again. It might also be difficult to calculate and hard for voters to understand what's going on.

On Sat, 17/9/16, C.Benham <cbenham at adam.com.au> wrote:

 Subject: Re: [EM] (6) To Kristofer and everyone: MJ best to ‘tolerate’
 To: "steve bosworth" <stevebosworth at hotmail.com>, "election-methods at lists.electorama.com" <election-methods at lists.electorama.com>
 Date: Saturday, 17 September, 2016, 5:42
     On 9/16/2016
 4:22 AM, steve bosworth
       MJ simply asks each voter to grade
             each candidate when judged against each
 voter’s own criteria
             of what an EXCELLENT candidate would look
             Any candidate judged to be less than
             be graded either as VERRY GOOD, GOOD,
             Balinski and Laraki refer to each voters
 own criteria
             for grading candidates as being ‘absolute’
 (but this is only
             in the sense that these criteria should be
 independent of
             any one set of candidates that might be seeking
       C: To begin with superficial aesthetics, the grades
 should have
       simple neutral names (like A B C D E F) and the ballot
       should be something like:
       "Give your favourite candidate or candidates an A
 and and your
       least preferred candidate or candidates an F and any
       candidates whatever
       grade you see fit. Default rating is F."
       As it is  if in a given election A , by my
 "criteria that should
       be independent of any one set of candidates that might
 be seeking
       election" , such as those doing so in election
       I rate my favourite candidate as being merely
 "Acceptable"  I
       would resent having to either  (a) accept that my
 vote will have
       less influence on the result than voters who rate
       their favourite as "Excellent" or (b)
 "lie" and falsely indicate
       that I rate my favourite as "Excellent".
       MJ  poses as being somewhat like a jury in a trial,
 or a panel
       that judges say a competitive performance of
 Gymnastics or Diving.
       But elections for powerful public political elections
 are very
       different. In those cases the jurors/judges are
       "disinterested", i.e. it doesn't really
 make any
       possible difference to their lives who wins the
 competition or
       whether the accused is jailed or set free.  In
 elections who wins
       the election could have a big effect on the
       lives of voters.   
       Also in those other cases there is usually general
 agreement what
       an excellent sporting performance looks like and what
 a terrible
       sporting performance looks like and
       what constitutes clear proof of guilt or innocence. 
 In elections
       voters often have opposing ideologies, i.e. very
 different ideas
       of what policies, priorities, political philosophy,
       diplomatic/military strategies the election winner
 should have.
       Another difference is that in those other cases the
 people on the
       jury in a trial or the panel judging a sporting
 performance base
       their decisions the same evidence. The jurors
       all hear the same evidence and arguments and base
 their verdict on
       that. Likewise the judging panel all closely watch the
       performance and give their scores based purely
       on that.
       But voters in public elections vary widely in terms of
       information they get, and the quality and quantity of
       information. And of course much of the
 "information" they
       use might be false or misleading, generated by those
 with a big
       interest in who wins the election.
       Leaving aside the strategy incentive for voters to
 only use the
       very top and very bottom grades, suppose that all the
 voters rate
       the candidates as sincerely as they can
       in the way MJ  "invites" them to.  
 Suppose that that there are
       only two candidates with any hope of winning, A and
 B.  Suppose I
       think that A is clearly better than B
       and you think the opposite.  Suppose my rating of  A
 is  Good  and
       B is  Poor, and your rating of  B is Excellent and 
 A is Rejected.
       Your pairwise preference will have greater weight than
 mine. Is
       that fair?   According to the MJ philosophy your
 vote should have
       greater weight because you are more
       "enthusiastic" in your support for B over
 A.  Does this greater
       enthusiasm mean that your opinion that B is better
 than A is more
       likely to be correct than my opposite
       Also, MJ seems to
 offer less scope for manipulative
           voting than any other method. 
       C: As Kevin has pointed out, sincere voters are less
 likely to be
       at a disadvantage than with Range  (aka Average
 Ratings) but in
       both the voter's  best strategy is to only
       use the two most extreme ratings. If all the voters do
 that the
       method is just Approval.
       What exactly is your definition of 
       I still favor MJ
 even though it is theoretically
           vulnerable to ‘Later-no-harm’
       C: I don't particularly care about
 Later-no-Harm.  It encourages
       the expression of preferences that may be very weak,
 and to the
       extent that they are decisive they
       would tend to lower the "Social Utility"
 (SU) of the winner. And
       the expressed preferences are also more likely to be
 the result of
       unprincipled mutual back-scratching
       deals between candidates. 
       I put a greater value on Later-no-Help  (which MJ,
 along with MTA
       and MCA meets). Ideally there should be weak zero-info
       But MJ has a very strong truncation incentive.
 It's compliance
       with LNHelp is in practice useless if the voters
 should all
       IRV meets both of Later-no-Help and Later-no-Harm, and
 in my
       opinion it is the best of the methods that meet
       Other methods I like fail both. That is better than
 only meeting
       LNHarm and so having a random-fill incentive, or only
       LNHelp and having a very
       strong truncation incentive.
       For reasons I might give in another post, I don't
 much like MAM.  
       A simpler Condorcet method I like is 
       Voters ignore candidates they don't approve and
 rank the rest.
       Equal-ranking allowed.   Elect the most approved
 member of the
       Smith set.
       The "Smith set" is the smallest set of
 candidate/s who all
       pairwise beat all (if any) outside-the-set members. 
       single-member "Smith set" is the 
       Condorcet winner.
       Compliance with both FBC and Condorcet is
 impossible.  MJ meets
       A MJ-like method that is simpler and in my view better
       Majority Top Approval (MTA).
       It uses 3-slot ratings ballots.  Default rating is
 Bottom. If any
       candidate is rated above bottom on more than half the
       elect (if there is more than one) the
       one of those with the highest number of top ratings.
       elect the candidate with the highest number of
       The voters' best strategy is to normally use only
 the top and
       bottom ratings slots, but the middle slot is handy if
 there is one
       or more candidate the voter is
       unsure how should rate on a 2-slot ratings ballot, or
 if the voter
       is prepared to maybe take a small strategic risk for
 the sake of
       being more expressive.
       But a more complex method I much prefer is IBIFA.
       Chris Benham

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