<html><head></head><body><div style="color:#000; background-color:#fff; font-family:HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, sans-serif;font-size:12px"><div id="yui_3_16_0_ym19_1_1483570974005_6012"><span id="yui_3_16_0_ym19_1_1483570974005_7624"><font size="3" id="yui_3_16_0_ym19_1_1483570974005_7623">Hi Kristofer,</font></span></div><div id="yui_3_16_0_ym19_1_1483570974005_6016"><span><font size="3"><br></font></span></div><div id="yui_3_16_0_ym19_1_1483570974005_6011" dir="ltr"><span id="yui_3_16_0_ym19_1_1483570974005_6266"><font size="3" id="yui_3_16_0_ym19_1_1483570974005_6265">I realize you are only interpreting B&L, so I don't mean to shoot the messenger.</font></span></div><div class="qtdSeparateBR" id="yui_3_16_0_ym19_1_1483570974005_6010"><br><br></div><div class="yahoo_quoted" id="yui_3_16_0_ym19_1_1483570974005_5866" style="display: block;">  <div id="yui_3_16_0_ym19_1_1483570974005_5865"> <div id="yui_3_16_0_ym19_1_1483570974005_5864"> <div dir="ltr" id="yui_3_16_0_ym19_1_1483570974005_5863" style="font-size: 16px; font-family: HelveticaNeue, "Helvetica Neue", Helvetica, Arial, "Lucida Grande", sans-serif;"> <font size="2" face="Arial" id="yui_3_16_0_ym19_1_1483570974005_6009"> <hr size="1" id="yui_3_16_0_ym19_1_1483570974005_6017"> <b><span style="font-weight:bold;">De :</span></b> Kristofer Munsterhjelm <km_elmet@t-online.de><br> <b><span style="font-weight: bold;">À :</span></b> steve bosworth <stevebosworth@hotmail.com>; "election-methods@lists.electorama.com" <election-methods@lists.electorama.com> <br> <b><span style="font-weight: bold;">Envoyé le :</span></b> Mercredi 4 janvier 2017 6h45<br> <b><span style="font-weight: bold;">Objet :</span></b> Re: [EM] Interpreting Balinski's MJ words<br> </font> </div> <div class="y_msg_container" id="yui_3_16_0_ym19_1_1483570974005_5910" style="font-size: 16px; font-family: HelveticaNeue, "Helvetica Neue", Helvetica, Arial, "Lucida Grande", sans-serif;"><br>>> /strategy-proof-in-grading/.  A group of voters who share the same<br clear="none">>> beliefs (e.g.<br clear="none">>> they belong to the same political party) has the same optimal strategy,<br clear="none">>> namely, to<br clear="none">>> give to the candidates the grades it believes they merit. </div><div class="y_msg_container" id="yui_3_16_0_ym19_1_1483570974005_5910" style="font-size: 16px; font-family: HelveticaNeue, "Helvetica Neue", Helvetica, Arial, "Lucida Grande", sans-serif;"><br></div><div class="y_msg_container" id="yui_3_16_0_ym19_1_1483570974005_5910" style="font-size: 16px;"><span style="font-family: HelveticaNeue, "Helvetica Neue", Helvetica, Arial, "Lucida Grande", sans-serif;">You clarified </span>your original response to this in saying:</div><div class="y_msg_container" id="yui_3_16_0_ym19_1_1483570974005_5910" style="font-size: 16px;"><br></div><div class="y_msg_container" id="yui_3_16_0_ym19_1_1483570974005_5910" dir="ltr" style="font-size: 16px;"><span style="font-size: 13px;" id="yui_3_16_0_ym19_1_1483570974005_6140">>You're right that the voters can only very rarely change the outcome.</span><br clear="none" style="font-size: 13px;" id="yui_3_16_0_ym19_1_1483570974005_6141"><span style="font-size: 13px;" id="yui_3_16_0_ym19_1_1483570974005_6142">>But the point beyond this observation is, as I said, that even when they</span><br clear="none" style="font-size: 13px;" id="yui_3_16_0_ym19_1_1483570974005_6143"><span style="font-size: 13px;" id="yui_3_16_0_ym19_1_1483570974005_6144">>can, it's detrimental for them to do so.</span><br clear="none" style="font-size: 13px;" id="yui_3_16_0_ym19_1_1483570974005_6145">><br clear="none" style="font-size: 13px;" id="yui_3_16_0_ym19_1_1483570974005_6146"><span style="font-size: 13px;" id="yui_3_16_0_ym19_1_1483570974005_6147">>That is assuming they're strategizing in grades, i.e. want Royal to get</span><br clear="none" style="font-size: 13px;" id="yui_3_16_0_ym19_1_1483570974005_6148"><span style="font-size: 13px;" id="yui_3_16_0_ym19_1_1483570974005_6149">>a Good rather than Royal to win.</span><br></div><div class="y_msg_container" id="yui_3_16_0_ym19_1_1483570974005_5910" dir="ltr" style="font-size: 16px;"><span style="font-size: 13px;"><br></span></div><div class="y_msg_container" id="yui_3_16_0_ym19_1_1483570974005_5910" dir="ltr"><font size="3" id="yui_3_16_0_ym19_1_1483570974005_6450">Do you find it easy to imagine a scenario where a group of like-minded voters has this as a strategic goal? </font></div><div class="y_msg_container" id="yui_3_16_0_ym19_1_1483570974005_5910" dir="ltr"><font size="3" id="yui_3_16_0_ym19_1_1483570974005_6920">At the very least, this description of the goal would be quite abbreviated from what the actual thought must be.</font></div><div class="y_msg_container" id="yui_3_16_0_ym19_1_1483570974005_5910" dir="ltr"><font size="3">There's no </font><font size="3">benefit </font><span id="yui_3_16_0_ym19_1_1483570974005_7149" style="font-size: medium;">in trying to give Royal a "Good" median rating if no scenario is envisioned where Royal </span></div><div class="y_msg_container" id="yui_3_16_0_ym19_1_1483570974005_5910" dir="ltr"><span style="font-size: medium;">could win </span><span style="font-size: medium;" id="yui_3_16_0_ym19_1_1483570974005_7593">with this </span><span style="font-size: medium;">rating. </span></div><div class="y_msg_container" id="yui_3_16_0_ym19_1_1483570974005_5910" style="font-size: 16px; font-family: HelveticaNeue, "Helvetica Neue", Helvetica, Arial, "Lucida Grande", sans-serif;"><br></div><div class="y_msg_container" id="yui_3_16_0_ym19_1_1483570974005_5910" style="font-size: 16px; font-family: HelveticaNeue, "Helvetica Neue", Helvetica, Arial, "Lucida Grande", sans-serif;">>> One means by which it [MJ] resists [manipulation] is easy to explain.<br clear="none">>> Take the example of Bayrou with a /Good/+ and Royal with a /Good/− (see<br clear="none">>> table 1.4); their respective<br clear="none">>> majority-gauges are<br clear="none">>>   ...<br clear="none">>> But the majority judgment is /partially<br clear="none">>> strategy-proof-in-/<br clear="none">>> /ranking/: those voters who can [might marginally be able to] lower<br clear="none">>> Bayrou’s majority-gauge cannot [significantly] raise<br clear="none">>> Royal’s, and those who can [might marginally be able to] raise Royal’s<br clear="none">>> majority-gauge cannot [significantly] lower Bayrou’s.<br clear="none"><br clear="none">>Again, the point here isn't directly that the outcome doesn't often<br clear="none">>change. (That the outcome doesn't often change is beneficial for other<br clear="none">>reasons, some of which are related to strategy.)<br clear="none">><br clear="none">>The main point is instead:<br clear="none">><br clear="none">>Suppose some voter ranks Royal above Bayrou, like this:<br clear="none">><br clear="none">>Excellent | Good | Fair   | Poor | Reject<br clear="none">>..........|.Royal|.Bayrou.|......|.......<br clear="none">><br clear="none">>Then if the voter wants to make Royal rather than Bayrou win, she can<br clear="none">>push Royal up or Bayrou down.<br clear="none">><br clear="none">>But she can only push Bayrou down from where Bayrou is ranked on her<br clear="none">>honest ballot, and can only push Royal up from where Royal is ranked on<br clear="none">>her honest ballot.<br clear="none">><br clear="none">>And in effect, this makes only half the ballot available to do either.<br clear="none">>If the voter has ranked Royal highly, she can push Bayrou down but can't<br clear="none">>move Royal even higher. On the other hand, if the voter has ranked Royal<br clear="none">>closer to the Reject end, she can push Royal higher (up to Excellent),<br clear="none">>but can't push Bayrou very far down.<br clear="none">><br clear="none">>So a voter can only either exaggerate Royal (if she graded Royal low on<br clear="none">>the original ballot) or exaggerate Bayrou (if she graded Bayrou high),<br clear="none">>but not both at the same time.<br clear="none">><br clear="none">>The example voter above has graded Royal pretty high and so can only<br clear="none">>exaggerate by one step - by moving Royal from Good to Excellent. On the<br clear="none">>other hand, she can move Bayrou all the way from Fair to Reject.</div><div class="y_msg_container" id="yui_3_16_0_ym19_1_1483570974005_5910" style="font-size: 16px; font-family: HelveticaNeue, "Helvetica Neue", Helvetica, Arial, "Lucida Grande", sans-serif;"><br></div><div class="y_msg_container" id="yui_3_16_0_ym19_1_1483570974005_5910" style="font-size: 16px; font-family: HelveticaNeue, "Helvetica Neue", Helvetica, Arial, "Lucida Grande", sans-serif;">This sounds like they are saying that it's a noteworthy quality of MJ that an expressed preference strength can't</div><div class="y_msg_container" id="yui_3_16_0_ym19_1_1483570974005_5910" style="font-size: 16px; font-family: HelveticaNeue, "Helvetica Neue", Helvetica, Arial, "Lucida Grande", sans-serif;" dir="ltr">exceed the range of the ballot...? What method could we even compare?</div><div class="y_msg_container" id="yui_3_16_0_ym19_1_1483570974005_5910" style="font-size: 16px; font-family: HelveticaNeue, "Helvetica Neue", Helvetica, Arial, "Lucida Grande", sans-serif;" dir="ltr"><br></div><div class="y_msg_container" id="yui_3_16_0_ym19_1_1483570974005_5910" style="font-size: 16px; font-family: HelveticaNeue, "Helvetica Neue", Helvetica, Arial, "Lucida Grande", sans-serif;" dir="ltr">Kevin</div><div class="y_msg_container" id="yui_3_16_0_ym19_1_1483570974005_5910" style="font-size: 16px; font-family: HelveticaNeue, "Helvetica Neue", Helvetica, Arial, "Lucida Grande", sans-serif;" dir="ltr"><br></div> </div> </div>  </div></div></body></html>