[EM] Interpreting Balinski's MJ words

[steve bosworth]

To EM:

Please check the following [clarifications or corrections written within the square brackets].  Currently I see these suggestions as more clearly expressing B&L’s own intentions in the following two extracts from M. Balinski and R. Laraki (2011) Majority Judgment, MIT.  Please explain if you think I have misunderstood these paragraphs:

p.14:

Similar reasoning shows that the majority-grade mechanism is group

strategy-proof-in-grading.  A group of voters who share the same beliefs (e.g.

they belong to the same political party) has the same optimal strategy, namely, to

give to the candidates the grades it believes they merit. For if the group believed

that Royal merited better than Good, and all raised the grade they gave her,

her majority-gauge would remain the same (p does not change) [her majority-gauge would probably only be changed insignificantly when thousands are voting (p would probably only be changed insignificantly)]. If all lowered

the grade they gave her, her majority-gauge would decrease (q increases), and

perhaps her majority-grade would be lowered (not their intent). If [instead] the group

believed that Royal merited worse than Good, and all lowered the grade they

gave her, her majority-gauge would remain the same (q does not change) [her majority-gauge would probably only be changed insignificantly when thousands are voting (q would probably only be increased insignificantly)]. If [instead] all

raised the grade they gave her, her majority-gauge would increase (p increases),and perhaps her majority-grade would be raised (not their intent).



p.15:

One means by which it [MJ] resists [manipulation] is easy to explain. Take the example of Bayrou with a Good+ and Royal with a Good− (see table 1.4); their respective

majority-gauges are



Bayrou: (44.3%, Good, 30.6%) Royal: (39.4%, Good, 41.5%).



[Given these two majority-guages] How could a voter who graded Royal higher than Bayrou manipulate? By changing

the grades assigned to try to lower Bayrou’s majority-gauge and to raise

Royal’s majority-gauge. But the majority judgment is partially strategy-proof-in-

ranking: those voters who can [might marginally be able to] lower Bayrou’s majority-gauge cannot [significantly] raise

Royal’s, and those who can [might marginally be able to] raise Royal’s majority-gauge cannot [significantly] lower Bayrou’s.

For suppose a voter can lower Bayrou’s. Then she must have given Bayrou

a Good or better; but having preferred Royal to Bayrou, the voter [she probably] gave a grade

of better than Good to Royal, so she cannot raise Royal’s majority-gauge [significantly] (cannot [significantly]

raise her p). Symmetrically, a [different] voter who can raise [no, lower] Royal’s majority-gauge

must have given her a Good or worse and thus to Bayrou a worse [no, a better] than Good;

so the voter cannot lower [no, raise] Bayrou’s majority-gauge [significantly] (cannot [significantly]increase his q [p]).



Compared with other mechanisms, the majority judgment cuts in half the

possibility of manipulation, however bizarre a voter’s motivations or whatever

her utility function. The majority judgment resists manipulation in still other

ways that other methods do not, but to see how requires information found

in voters’ individual ballots that is not shown in the elections results of table

1.4. For example, significant numbers of voters cannot contribute at all either

to raising Royal’s majority-gauge or to lowering Bayrou’s (28% of those who

graded Royal above Bayrou). Moreover, those who can manipulate have no

incentive to exaggerate very much in any case, for it does not pay to do so (a

more detailed analysis is given in chapter 19).

++++++++++++++++



Note:  If you wish to receive a copy of the whole chapter as an attachment, just ask (stevebosworth at hotmail.com).

I look forward to your comments.

Steve

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