## Common language
-The Majority Judgment asks us to judge each choice in an absolute way
+The Majority Judgment asks us to answer to a specific, operationally pertinent,
+question about several choices, by judging each choice in an absolute way
(i.e. such that the removal or addition of choices
does not change our evaluation of the other choices)
by giving them a grade (or level) on a common scale.
## Judging one choice
For each choice taken separately,
-the initial common scale (whose grades are all of equal length 1)
-is dilated such that the length of each grade is multiplied
-by the number of individual judgments of this grade obtained by this choice.
-Like this, the only level which is defended by an absolute majority
+each grade of the scale is associated to the number
+of individual judgments which have given this grade to this choice.
+(eg. for 5 judges: [“Insufficient”, “Acceptable”, “Acceptable”, “Good”, “Good”])
+This forms a dilated scale where each grade is expanded (resp. shrunk)
+when more (resp. less) supported than the others.
+Like this, the only grade which is defended by an absolute majority
begining from one side of the scale,
without being rejected by an absolute majority
beginning from the other side of the scale,
-is the one which spans over the middle of this dilated scale.
+is the one which spans over the middlemost
+of this dilated scale (here: “Acceptable”).
This is the most consensual majority grade for this choice.
-If the number of individual judgments is small and even,
+If the number of individual judgments is small and even
+(eg. for 6 judges: [“Insufficient”, “Acceptable”, “Acceptable”, “Good”, “Good”, “Good”]),
there is however a probability that two different grades
-border the middle of this dilated scale,
-but only the lower grade rewards consensus,
+border the middlemost of this dilated scale (here: [“Acceptable”, “Good”]).
+But only the lower grade (here: “Acceptable”) rewards consensus,
and thus is considered to be the most consensual.
Indeed, if any other choice obtains less scattered judgments
-all enclosed to this two grades,
+(eg. [“Acceptable”, “Acceptable”, “Acceptable”, “Acceptable”, “Good”, “Good”])
+all enclosed into these two grades,
it will obtain a most consensual majoritary grade
-greater or egal to the one of this choice.
-Which would not necessarily be the case with the greater grade.
+greater or egal to the one of this choice (here: “Acceptable”).
+Which would not necessarily be the case with the greater grade (here: “Good”).
## Ranking many choices
increasing (resp. decreasing) the rank of a choice with respect to another choice,
can not decrease (resp. increase) the rank of this other choice.
-- not Condorcet-consistent except when the electorate is “polarized”
- (when the higher (resp. the lower) a judge evaluates one choice the lower (resp. the higher)
- she/he evaluates the other, so there can be no consensus)
+- not Condorcet-consistent:
+ not guarantying the selection of a choice
+ which is preferred by a majority against every of the others separately.
+
+ Except when the electorate is “polarized”:
+ when the higher (resp. the lower) a judge evaluates one choice the lower (resp. the higher)
+ she/he evaluates the other, so there can be no consensus;
hence when judges are most tempted to manipulate.
+
+ This property is judged undesirable, by Michel Balinski and Rida Laraki,
+ as they prove how easily the Majority Rule can go wrong when voting
+ on but two candidates, let alone more.
-- not excluding the no-show paradox (when it is better for a judge not to judge
+- not excluding the no-show paradox:
+ it may be better for a judge not to judge
than to express her/his opinion sincerely because her/his vote
- can tip the scales against his favorite choice).
+ can tip the scales against his favorite choice.
This property is judged insignificant, by Michel Balinski and Rida Laraki,
when compared with the serious problems of methods of election,
the Arrow and Condorcet paradoxes and strategic manipulation.
+ Moreover, the only methods based on measuring that exclude
+ the no-show paradox are point-summing methods,
+ which, amongst other drawbacks, are highly manipulable.
+
+## Resources
+- [Majority Judgment: Measuring, Ranking, and Electing](http://libgen.io/book/index.php?md5=BF67AA4298C1CE7633187546AA53E01D) (en)
+- [Majority Judgment vs. Majority Rule](http://www.lamsade.dauphine.fr/sites/default/IMG/pdf/cahier_377.pdf) (en)
+- [Judge : Don't Vote!](https://1007421605497013616-a-1802744773732722657-s-sites.googlegroups.com/site/ridalaraki/xfiles/BalinskiLarakiJudgeDontVotecahierderecherche2010-27.pdf) (en)
+- [Jugement majoritaire versus vote majoritaire (via les présidentielles 2011-2012)](https://www.cairn.info/revue-francaise-d-economie-2012-4-page-11.htm) (fr)
+- [Majority Judgment vs. Majority Rule](http://www.lamsade.dauphine.fr/sites/default/IMG/pdf/cahier_377.pdf) (en)
+- [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)
+- [Condorcet-Consistent and Approximately Strategyproof Tournament Rules](https://arxiv.org/pdf/1605.09733.pdf) (en)
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