README.md

   1 # Majority Judgment
   2
   3 ## Common language
   4
   5 The Majority Judgment asks us to answer to a specific, operationally pertinent,
   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 - [“No”, “No, but”, “Yes, but”, “Yes”] for adhesion,
  22 - [“None”, “Not Enough”, “Enough”, “Much”, “Too Much”] for quantity,
  23 - [“To Do”, “Prioritized”, “Blocking”, “Urgent”, “Too Urgent”] for priority,
  24 - [“Useless”, “Interesting”, “Useful”, “Indispensable”, “Enslaving”] for utility,
  25 - [“To Reject”, “Insufficient”, “Acceptable”, “Good”, “Very Good”, “Too Good”] for quality.
  26
  27 ## Judging one choice
  28
  29 For each choice taken separately,
  30 each grade of the scale is associated to the number
  31 of individual judgments which have given this grade to this choice.
  32 (eg. for 5 judges: [“Insufficient”, “Acceptable”, “Acceptable”, “Good”, “Good”])
  33 This forms a dilated scale where each grade is expanded (resp. shrunk)
  34 when more (resp. less) supported than the others.
  35 Like this, the only grade which is defended by an absolute majority
  36 begining from one side of the scale,
  37 without being rejected by an absolute majority
  38 beginning from the other side of the scale,
  39 is the one which spans over the middlemost
  40 of this dilated scale (here: “Acceptable”).
  41 This is the most consensual majority grade for this choice.
  42
  43 If the number of individual judgments is small and even
  44 (eg. for 6 judges: [“Insufficient”, “Acceptable”, “Acceptable”, “Good”, “Good”, “Good”]),
  45 there is however a probability that two different grades
  46 border the middlemost of this dilated scale (here: [“Acceptable”, “Good”]).
  47 But only the lower grade (here: “Acceptable”) rewards consensus,
  48 and thus is considered to be the most consensual.
  49 Indeed, if any other choice obtains less scattered judgments
  50 (eg. [“Acceptable”, “Acceptable”, “Acceptable”, “Acceptable”, “Good”, “Good”])
  51 all enclosed into these two grades,
  52 it will obtain a most consensual majoritary grade
  53 greater or egal to the one of this choice (here: “Acceptable”).
  54 Which would not necessarily be the case with the greater grade (here: “Good”).
  55
  56 ## Ranking many choices
  57
  58 To sort many choices means being able to compare them two-by-two,
  59 which is done according to their most consensual majority grade.
  60 In case of equality, the minimum individual judgments of this grade
  61 are removed from both dilated scales so that one of them has no longer any,
  62 then the comparison goes on with the new most consensual majority grades.
  63 Like this, either a choice is judged higher than the other,
  64 by the geatest number of judgments which differenciate them according
  65 to a most consensual majoritary grade,
  66 or both choices precisely have the same distribution of individual judgments.
  67
  68 One can see that the farest an individual judgment is
  69 from the most consensual majoritary grade,
  70 the less impact it has on the result.
  71 This rewards honest individual judgments,
  72 by ignoring as near as may be the most cranky or strategic judgements.
  73
  74 ## Properties
  75
  76 The Majority Judgment is:
  77
  78 - allowing anonymity:
  79   interchanging the names of judges does not change the outcome:
  80   all judges are given an equal power.
  81
  82 - neutral:
  83   interchanging the names of choices does not change the outcome:
  84   all choices are treated equally.
  85
  86 - complete:
  87   every choice is either superior or inferior
  88   to any other choice, or both when equal.
  89   Hence the Majority Judgement is not subject
  90   to Condorcet's paradox.
  91
  92 - monotone:
  93   if a choice is superior or egal to another one,
  94   and a judge increases its grade for it,
  95   it becomes strictly superior.
  96
  97 - transitive:
  98   if a first choice is superior to a second one,
  99   and this second one is superior to a third,
 100   then the first is superior to the third).
 101
 102 - coherent:
 103   it is independent of irrelevant alternatives as formulated by Nash-Chernoff:
 104   removal or addition of choices does not change
 105   the judges’ evaluations of the other choices.
 106   Hence the Majority Judgement is not subject
 107   to Arrow's paradox.
 108
 109 - strategy-proof-in-grading:
 110   judging a choice higher or lower
 111   than our intimate judgement has the opposite impact
 112   on its most consensual majority grade.
 113
 114 - partially strategy-proof-in-ranking:
 115   increasing (resp. decreasing) the rank of a choice with respect to another choice,
 116   can not decrease (resp. increase) the rank of this other choice.
 117
 118 - not Condorcet-consistent:
 119   not guarantying the selection of a choice
 120   which is preferred by a majority against every of the others separately.
 121
 122   Except when the electorate is “polarized”:
 123   when the higher (resp. the lower) a judge evaluates one choice the lower (resp. the higher)
 124   she/he evaluates the other, so there can be no consensus;
 125   hence when judges are most tempted to manipulate.
 126
 127   This property is judged undesirable, by Michel Balinski and Rida Laraki,
 128   as they prove how easily the Majority Rule can go wrong when voting
 129   on but two candidates, let alone more.
 130
 131 - not excluding the no-show paradox:
 132   it may be better for a judge not to judge
 133   than to express her/his opinion sincerely because her/his vote
 134   can tip the scales against his favorite choice.
 135
 136   This property is judged insignificant, by Michel Balinski and Rida Laraki,
 137   when compared with the serious problems of methods of election,
 138   the Arrow and Condorcet paradoxes and strategic manipulation.
 139   Moreover, the only methods based on measuring that exclude
 140   the no-show paradox are point-summing methods,
 141   which, amongst other drawbacks, are highly manipulable.
 142
 143 ## Resources
 144 - [Majority Judgment: Measuring, Ranking, and Electing](http://libgen.io/book/index.php?md5=BF67AA4298C1CE7633187546AA53E01D) (en)
 145 - [Majority Judgment vs. Majority Rule](http://www.lamsade.dauphine.fr/sites/default/IMG/pdf/cahier_377.pdf) (en)
 146 - [Judge : Don't Vote!](https://1007421605497013616-a-1802744773732722657-s-sites.googlegroups.com/site/ridalaraki/xfiles/BalinskiLarakiJudgeDontVotecahierderecherche2010-27.pdf) (en)
 147 - [Jugement majoritaire versus vote majoritaire (via les présidentielles 2011-2012)](https://www.cairn.info/revue-francaise-d-economie-2012-4-page-11.htm) (fr)
 148 - [Majority Judgment vs. Majority Rule](http://www.lamsade.dauphine.fr/sites/default/IMG/pdf/cahier_377.pdf) (en)
 149 - [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)
 150 - [Condorcet-Consistent and Approximately Strategyproof Tournament Rules](https://arxiv.org/pdf/1605.09733.pdf) (en)