<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<style type="text/css" style="display:none;"><!-- P {margin-top:0;margin-bottom:0;} --></style>
</head>
<body dir="ltr">
<div id="divtagdefaultwrapper" style="font-size:14pt;color:#000000;font-family:Calibri,Arial,Helvetica,sans-serif;" dir="ltr">
<p><font face="Times New Roman"></font></p>
<p style="margin: 0in 0in 8pt; line-height: normal; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-outline-level: 2;">
<span style="font-size: 12pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-bidi-font-weight: bold;"><font face="Calibri">To EM:</font></span></p>
<font face="Times New Roman"></font>
<p style="margin: 0in 0in 8pt; line-height: normal; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-outline-level: 2;">
<font face="Calibri"><span style="font-size: 12pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-bidi-font-weight: bold;">Please check the following [clarifications or corrections written within
the square brackets].<span style="mso-spacerun: yes;"> </span>Currently I see these suggestions as more clearly expressing B&L’s own intentions in the following two extracts from
</span><span style="font-size: 12pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;">M. Balinski and R. Laraki (2011)
<i style="mso-bidi-font-style: normal;">Majority Judgment</i>, MIT.<span style="mso-spacerun: yes;">
</span>Please explain if you think I have misunderstood these paragraphs:</span></font></p>
<font face="Times New Roman"></font>
<p style="margin: 0in 0in 8pt; line-height: normal; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-outline-level: 2;">
<span style="font-size: 12pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">p.14:</font></span></p>
<font face="Times New Roman"></font>
<p style="margin: 0in 0in 0pt; line-height: normal; mso-layout-grid-align: none;">
<span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">Similar reasoning shows that the majority-grade mechanism is
<i>group</i></font></span></p>
<font face="Times New Roman"></font>
<p style="margin: 0in 0in 0pt; line-height: normal; mso-layout-grid-align: none;">
<font face="Calibri"><i><span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;">strategy-proof-in-grading</span></i><span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;">.
<span style="mso-spacerun: yes;"> </span>A group of voters who share the same beliefs (e.g.</span></font></p>
<font face="Times New Roman"></font>
<p style="margin: 0in 0in 0pt; line-height: normal; mso-layout-grid-align: none;">
<span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">they belong to the same political party) has the same optimal strategy, namely, to</font></span></p>
<font face="Times New Roman"></font>
<p style="margin: 0in 0in 0pt; line-height: normal; mso-layout-grid-align: none;">
<span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">give to the candidates the grades it believes they merit. For if the group believed</font></span></p>
<font face="Times New Roman"></font>
<p style="margin: 0in 0in 0pt; line-height: normal; mso-layout-grid-align: none;">
<span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">that Royal merited better than
<i>Good</i>, and all raised the grade they gave her,</font></span></p>
<font face="Times New Roman"></font>
<p style="margin: 0in 0in 0pt; line-height: normal; mso-layout-grid-align: none;">
<span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">her majority-gauge would remain the same (<i>p
</i>does not change) [her majority-gauge would probably only be changed insignificantly when thousands are voting (<i>p would</i> probably only be changed insignificantly)]. If all lowered</font></span></p>
<font face="Times New Roman"></font>
<p style="margin: 0in 0in 0pt; line-height: normal; mso-layout-grid-align: none;">
<span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">the grade they gave her, her majority-gauge would decrease (<i>q
</i>increases), and</font></span></p>
<font face="Times New Roman"></font>
<p style="margin: 0in 0in 0pt; line-height: normal; mso-layout-grid-align: none;">
<span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">perhaps her majority-grade would be lowered (not their intent). If [instead] the group</font></span></p>
<font face="Times New Roman"></font>
<p style="margin: 0in 0in 0pt; line-height: normal; mso-layout-grid-align: none;">
<span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">believed that Royal merited worse than
<i>Good</i>, and all lowered the grade they</font></span></p>
<font face="Times New Roman"></font>
<p style="margin: 0in 0in 0pt; line-height: normal; mso-layout-grid-align: none;">
<span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">gave her, her majority-gauge would remain the same (<i>q
</i>does not change) [her majority-gauge would probably only be changed insignificantly when thousands are voting (q<i> would</i> probably only be increased insignificantly)]. If [instead] all</font></span></p>
<font face="Times New Roman"></font>
<p style="margin: 0in 0in 0pt; line-height: normal; mso-layout-grid-align: none;">
<span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">raised the grade they gave her, her majority-gauge would increase (<i>p
</i>increases),and perhaps her majority-grade would be raised (not their intent).</font></span></p>
<font face="Times New Roman"></font>
<p style="margin: 0in 0in 0pt; line-height: normal; mso-layout-grid-align: none;">
<span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri"> </font></span></p>
<font face="Times New Roman"></font>
<p style="margin: 0in 0in 0pt; line-height: normal; mso-layout-grid-align: none;">
<span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">p.15:</font></span></p>
<font face="Times New Roman"></font>
<p style="margin: 0in 0in 0pt; line-height: normal; mso-layout-grid-align: none;">
<font face="Calibri"><span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;">One means by which it [MJ] resists [manipulation] is easy to explain. Take the example of Bayrou with a
<i>Good</i></span><span style="font-size: 12pt; mso-fareast-font-family: MTSYN; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;">+
</span><span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;">and Royal with a
<i>Good</i></span><span style="font-size: 12pt; mso-fareast-font-family: MTSYN; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;">−
</span><span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;">(see table 1.4); their respective</span></font></p>
<font face="Times New Roman"></font>
<p style="margin: 0in 0in 0pt; line-height: normal; mso-layout-grid-align: none;">
<span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">majority-gauges are
</font></span></p>
<font face="Times New Roman"></font>
<p style="margin: 0in 0in 0pt; line-height: normal; mso-layout-grid-align: none;">
<span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri"> </font></span></p>
<font face="Times New Roman"></font>
<p style="margin: 0in 0in 0pt; line-height: normal; mso-layout-grid-align: none;">
<span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">Bayrou: (44.3%,
<i>Good</i>, 30.6%) Royal: (39.4%, <i>Good</i>, 41.5%).</font></span></p>
<font face="Times New Roman"></font>
<p style="margin: 0in 0in 0pt; line-height: normal; mso-layout-grid-align: none;">
<span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri"> </font></span></p>
<font face="Times New Roman"></font>
<p style="margin: 0in 0in 0pt; line-height: normal; mso-layout-grid-align: none;">
<span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">[Given these two majority-guages] How could a voter who graded Royal higher than Bayrou manipulate? By changing</font></span></p>
<font face="Times New Roman"></font>
<p style="margin: 0in 0in 0pt; line-height: normal; mso-layout-grid-align: none;">
<span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">the grades assigned to try to lower Bayrou’s majority-gauge and to raise</font></span></p>
<font face="Times New Roman"></font>
<p style="margin: 0in 0in 0pt; line-height: normal; mso-layout-grid-align: none;">
<span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">Royal’s majority-gauge. But the majority judgment is
<i>partially strategy-proof-in-</i></font></span></p>
<font face="Times New Roman"></font>
<p style="margin: 0in 0in 0pt; line-height: normal; mso-layout-grid-align: none;">
<font face="Calibri"><i><span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;">ranking</span></i><span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;">: those voters who can
[might marginally be able to] lower Bayrou’s majority-gauge cannot [significantly] raise</span></font></p>
<font face="Times New Roman"></font>
<p style="margin: 0in 0in 0pt; line-height: normal; mso-layout-grid-align: none;">
<span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">Royal’s, and those who can [might marginally be able to] raise Royal’s majority-gauge cannot [significantly] lower Bayrou’s.</font></span></p>
<font face="Times New Roman"></font>
<p style="margin: 0in 0in 0pt; line-height: normal; mso-layout-grid-align: none;">
<span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">For suppose a voter can lower Bayrou’s. Then she must have given Bayrou</font></span></p>
<font face="Times New Roman"></font>
<p style="margin: 0in 0in 0pt; line-height: normal; mso-layout-grid-align: none;">
<span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">a
<i>Good </i>or better; but having preferred Royal to Bayrou, the voter [she probably] gave a grade</font></span></p>
<font face="Times New Roman"></font>
<p style="margin: 0in 0in 0pt; line-height: normal; mso-layout-grid-align: none;">
<span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">of better than
<i>Good </i>to Royal, so she cannot raise Royal’s majority-gauge [significantly] (cannot [significantly]</font></span></p>
<font face="Times New Roman"></font>
<p style="margin: 0in 0in 0pt; line-height: normal; mso-layout-grid-align: none;">
<span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">raise her
<i>p</i>). Symmetrically, a [different] voter who can raise [no, lower] Royal’s majority-gauge</font></span></p>
<font face="Times New Roman"></font>
<p style="margin: 0in 0in 0pt; line-height: normal; mso-layout-grid-align: none;">
<span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">must have given her a
<i>Good </i>or worse and thus to Bayrou a worse [no, a better] than <i>Good</i>;</font></span></p>
<font face="Times New Roman"></font>
<p style="margin: 0in 0in 0pt; line-height: normal; mso-layout-grid-align: none;">
<span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">so the voter cannot lower [no, raise] Bayrou’s majority-gauge [significantly] (cannot [significantly]increase his
<i>q </i><span style="mso-bidi-font-style: italic;">[p]</span>).</font></span></p>
<font face="Times New Roman"></font>
<p style="margin: 0in 0in 0pt; line-height: normal; mso-layout-grid-align: none;">
<span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri"> </font></span></p>
<font face="Times New Roman"></font>
<p style="margin: 0in 0in 0pt; line-height: normal; mso-layout-grid-align: none;">
<span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">Compared with other mechanisms, the majority judgment cuts in half the</font></span></p>
<font face="Times New Roman"></font>
<p style="margin: 0in 0in 0pt; line-height: normal; mso-layout-grid-align: none;">
<span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">possibility of manipulation, however bizarre a voter’s motivations or whatever</font></span></p>
<font face="Times New Roman"></font>
<p style="margin: 0in 0in 0pt; line-height: normal; mso-layout-grid-align: none;">
<span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">her utility function. The majority judgment resists manipulation in still other</font></span></p>
<font face="Times New Roman"></font>
<p style="margin: 0in 0in 0pt; line-height: normal; mso-layout-grid-align: none;">
<span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">ways that other methods do not, but to see how requires information found</font></span></p>
<font face="Times New Roman"></font>
<p style="margin: 0in 0in 0pt; line-height: normal; mso-layout-grid-align: none;">
<span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">in voters’ individual ballots that is not shown in the elections results of table</font></span></p>
<font face="Times New Roman"></font>
<p style="margin: 0in 0in 0pt; line-height: normal; mso-layout-grid-align: none;">
<span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">1.4. For example, significant numbers of voters cannot contribute at all either</font></span></p>
<font face="Times New Roman"></font>
<p style="margin: 0in 0in 0pt; line-height: normal; mso-layout-grid-align: none;">
<span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">to raising Royal’s majority-gauge or to lowering Bayrou’s (28% of those who</font></span></p>
<font face="Times New Roman"></font>
<p style="margin: 0in 0in 0pt; line-height: normal; mso-layout-grid-align: none;">
<span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">graded Royal above Bayrou). Moreover, those who can manipulate have no</font></span></p>
<font face="Times New Roman"></font>
<p style="margin: 0in 0in 0pt; line-height: normal; mso-layout-grid-align: none;">
<span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">incentive to exaggerate very much in any case, for it does not pay to do so (a</font></span></p>
<font face="Times New Roman"></font>
<p style="margin: 0in 0in 0pt; line-height: normal; mso-layout-grid-align: none;">
<span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">more detailed analysis is given in chapter 19).</font></span></p>
<font face="Times New Roman"></font>
<p style="margin: 0in 0in 0pt; line-height: normal; mso-layout-grid-align: none;">
<span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri">++++++++++++++++</font></span></p>
<font face="Times New Roman"></font>
<p style="margin: 0in 0in 0pt; line-height: normal; mso-layout-grid-align: none;">
<span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><font face="Calibri"> </font></span></p>
<font face="Times New Roman"></font>
<p style="margin: 0in 0in 0pt; line-height: normal; mso-layout-grid-align: none;">
<font face="Calibri"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;">Note:
</span></b><span style="font-size: 12pt; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin;"><span style="mso-spacerun: yes;"> </span>If you wish to receive a copy of the whole chapter as an attachment, just ask (stevebosworth@hotmail.com).</span></font></p>
<font face="Times New Roman"></font>
<p style="margin: 0in 0in 8pt; line-height: normal; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-outline-level: 2;">
<span style="font-size: 12pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-bidi-font-weight: bold;"><font face="Calibri">I look forward to your comments.</font></span></p>
<font face="Times New Roman"></font>
<p style="margin: 0in 0in 8pt; line-height: normal; mso-margin-top-alt: auto; mso-margin-bottom-alt: auto; mso-outline-level: 2;">
<span style="font-size: 12pt; mso-fareast-font-family: "Times New Roman"; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-bidi-font-weight: bold;"><font face="Calibri">Steve</font></span></p>
<font face="Times New Roman"></font><br>
<p></p>
</div>
</body>
</html>