hjugement/README.md

   1 # Majority Judgment
   2
   3 ## Common language
   4
   5 The Majority Judgment asks us to answer to a specific, operationally actionable,
   6 question about several choices, by judging each choice in an absolute way
   7 (i.e. such that the removal or addition of choices
   8 does not change our evaluation of the other choices)
   9 by giving them a grade (or level) on a common scale.
  10
  11 This common scale contains as many grades as our supposed common expertise
  12 is able to distinguish, in order to faithfully represent
  13 the properties of the attribute it tries to measure.
  14 Hence, a common scale should be crafted for each different attribute.
  15 The inter-subjective meaning of each grade
  16 being reinforced by the practice of judgments.
  17
  18 ### Examples
  19
  20 Examples of common scales could be:
  21 - [“To Reject”, “Insufficient”, “Acceptable”, “Good”, “Very Good”] for quality,
  22 - [“Very Bad”, “Bad”, “Rather Bad”, “Rather Good”, “Good”, “Very Good”] for quality,
  23 - [“Strongly Against”, “Against”, “Rather Against”, “Indifferent”, “Rather For”, “For”, “Strongly For”] for adhesion,
  24 - [“Very Wrong”, “Wrong”, “Rather Wrong”, “Rather Well”, “Well”, “Very Well”] for rightness,
  25 - [“None”, “Not Enough”, “Enough”, “Much”, “Too Much”] for quantity,
  26 - [“To Do”, “Prioritized”, “Blocking”, “Urgent”, “Too Urgent”] for priority,
  27 - [“Useless”, “Interesting”, “Useful”, “Indispensable”, “Enslaving”] for utility.
  28
  29 Note that the more a scale enables to judge in the absolute,
  30 the more resistant to Arrow's paradox it is.
  31 Here, depending on the judges,
  32 some of the above scales using the “Very X”/“X”/“Rather X” structure,
  33 may be too subjective to discourage the relative comparison of choices,
  34 this said, if it is the exact expressions used in everyday parlance,
  35 it may be sensible to use them.
  36 In any case, to not confuse/skew the judgments it is important
  37 that a scale spans only on a single dimension/criteria.
  38
  39 ## Judging one choice
  40
  41 The “majority grade” is the fundamental indicator of the Majority Judgment.
  42 Located at the middle of the distribution of grades obtained by a choice,
  43 it is also known by high school students under the name “median”,
  44 that is to say, the grade such that 50% of grades are lower or egal to it,
  45 and 50% are greater or egal to it.
  46 Such that regardless the way we look at it,
  47 there is always an absolute majority among the judges
  48 which agree to defend the majority grade against any other grade.
  49 In other words: whoever among the judges is against, is necessarily in minority.
  50 Therefore, the majority grade brings the judges together by minimizing
  51 the number of unsatisfied among them.
  52 Like so, the majority grade enables us to overcome the old notion of majority
  53 expressed on the count of our scattered voices, which divides us.
  54
  55 Moreover, one can see that the farest an individual judgment is
  56 from the majoritary grade, the less impact it has on the result.
  57 This rewards honest individual judgments,
  58 by ignoring as near as may be the most cranky or strategic judgements.
  59
  60 If the number of individual judgments is small and even
  61 (eg. for 6 judges: [“Insufficient”, “Acceptable”, “Acceptable”, “Good”, “Good”, “Good”]),
  62 there is however a probability that two different grades
  63 border the middlemost of this dilated scale (here: “Acceptable” and “Good”).
  64 But only the lower grade (here: “Acceptable”) rewards consensus,
  65 and thus is considered to be the most consensual.
  66 Indeed, if any other choice obtains less scattered judgments
  67 (eg. [“Acceptable”, “Acceptable”, “Acceptable”, “Acceptable”, “Good”, “Good”])
  68 all enclosed into these two grades,
  69 it will obtain a majoritary grade
  70 greater or egal (here: “Acceptable”) to the one of this choice.
  71 Which would not necessarily be the case with the greater grade (here: “Good”).
  72
  73 ## Ranking many choices
  74
  75 The ranking of choices is done by comparing their respective majority grades.
  76 Those obtaining the same majority grade are compared further
  77 by applying again the principle of minimizing unsatisfied judges :
  78 one judgment giving this majority grade is removed of their distributions
  79 until two different majority grades are obtained,
  80 or both choices precisely have the same distribution of individual judgments.
  81 In which case, it is enough that one judge
  82 change the grade it gives to at least one of those choices,
  83 and/or it may be wise to also judge on other criterias.
  84
  85 ## Properties
  86
  87 The Majority Judgment is:
  88
  89 - allowing anonymity:
  90   interchanging the names of judges does not change the outcome:
  91   all judges are given an equal power.
  92
  93 - neutral:
  94   interchanging the names of choices does not change the outcome:
  95   all choices are treated equally.
  96
  97 - complete:
  98   every choice is either superior or inferior
  99   to any other choice, or both when equal.
 100   Hence the Majority Judgement is not subject
 101   to Condorcet's paradox.
 102
 103 - monotone:
 104   if a choice is superior or egal to another one,
 105   and a judge increases its grade for it,
 106   it becomes strictly superior.
 107
 108 - transitive:
 109   if a first choice is superior to a second one,
 110   and this second one is superior to a third,
 111   then the first is superior to the third).
 112
 113 - coherent:
 114   it is independent of irrelevant alternatives as formulated by Nash-Chernoff:
 115   removal or addition of choices does not change
 116   the judges’ evaluations of the other choices.
 117   Hence the Majority Judgement is not subject
 118   to Arrow's paradox.
 119
 120 - strategy-proof-in-grading:
 121   judging a choice higher or lower
 122   than our intimate judgement has the opposite impact
 123   on its most consensual majority grade.
 124
 125 - partially strategy-proof-in-ranking:
 126   increasing (resp. decreasing) the rank of a choice with respect to another choice,
 127   can not decrease (resp. increase) the rank of this other choice.
 128
 129 - not Condorcet-consistent:
 130   not guarantying the selection of a choice
 131   which is preferred by a majority against every of the others separately.
 132
 133   Except when the electorate is “polarized”:
 134   when the higher (resp. the lower) a judge evaluates one choice the lower (resp. the higher)
 135   she/he evaluates the other, so there can be no consensus;
 136   hence when judges are most tempted to manipulate.
 137
 138   This property is judged undesirable, by Michel Balinski and Rida Laraki,
 139   as they prove how easily the Majority Rule can go wrong when voting
 140   on but two candidates, let alone more.
 141
 142 - not excluding the no-show paradox:
 143   it may be better for a judge not to judge
 144   than to express her/his opinion sincerely because her/his vote
 145   can tip the scales against his favorite choice.
 146
 147   This property is judged insignificant, by Michel Balinski and Rida Laraki,
 148   when compared with the serious problems of methods of election,
 149   the Arrow and Condorcet paradoxes and strategic manipulation.
 150   Moreover, the only methods based on measuring that exclude
 151   the no-show paradox are point-summing methods,
 152   which, amongst other drawbacks, are highly manipulable.
 153
 154 ## Resources
 155 - [Majority Judgment: Measuring, Ranking, and Electing](http://libgen.io/book/index.php?md5=BF67AA4298C1CE7633187546AA53E01D) (en)
 156 - [Majority Judgment vs. Majority Rule](http://www.lamsade.dauphine.fr/sites/default/IMG/pdf/cahier_377.pdf) (en)
 157 - [Judge : Don't Vote!](https://1007421605497013616-a-1802744773732722657-s-sites.googlegroups.com/site/ridalaraki/xfiles/BalinskiLarakiJudgeDontVotecahierderecherche2010-27.pdf) (en)
 158 - [Jugement majoritaire versus vote majoritaire (via les présidentielles 2011-2012)](https://www.cairn.info/revue-francaise-d-economie-2012-4-page-11.htm) (fr)
 159 - [Majority Judgment vs. Majority Rule](http://www.lamsade.dauphine.fr/sites/default/IMG/pdf/cahier_377.pdf) (en)
 160 - [What Should “Majority Decision” Mean?](https://1984f707-a-62cb3a1a-s-sites.googlegroups.com/site/ridalaraki/xfiles/BalinskiLaraki%28ElsterBook%292014.pdf?attachauth=ANoY7cqCY4F_kQdtBc2d9EtUDNNPqtuoOYj98ThvPFukdXBkzogggu_WcKe2SryAQ9tq0P1HaGHHhD6sOdBNQ-ttaQ9XJUjVPHVCsMp4PDuX_DlvMv8MYqG6SGy_m39Q9tztOWezturc9q50RMHs0CKEGqiBqnRlyP4BFo5i4PqHDT5nD2v0HTsINWs6PooIz-bZpeuUXST1A30ojKDQ_b5xsK50RFMkJT7LG-p441cGlUOQWIGYikd2XglJdBJr0N5YuL80ZePd&attredirects=0) (en)
 161 - [Condorcet-Consistent and Approximately Strategyproof Tournament Rules](https://arxiv.org/pdf/1605.09733.pdf) (en)