{"id":34,"date":"2011-07-06T11:40:54","date_gmt":"2011-07-06T15:40:54","guid":{"rendered":"http:\/\/omega.math.union.edu\/research\/2010-05-voting\/?page_id=34"},"modified":"2011-07-08T21:09:53","modified_gmt":"2011-07-09T01:09:53","slug":"profile-201011","status":"publish","type":"page","link":"https:\/\/omega.math.union.edu\/research\/2010-05-voting\/examples\/profile-201011\/","title":{"rendered":"Smallest McBorda Manipulation"},"content":{"rendered":"<h3>Instructions:<\/h3>\n<p>Move a vote from <i>q<\/i><span class=\"gt\">&gt;<\/span><i>p<\/i><span class=\"gt\">&gt;<\/span><i>r<\/i> to <i>q<\/i><span class=\"gt\">&gt;<\/span><i>r<\/i><span class=\"gt\">&gt;<\/span><i>p<\/i> (or back) by clicking on the &#8220;Change Vote&#8221; button below.  What happens to the winner if one voter makes this change?<\/p>\n<p><center><br \/>\n<input type=\"button\" id=\"change\" value=\"Change Vote\" onclick=\"changeVote()\">&nbsp;&nbsp;<br \/>\n<\/center><\/p>\n<p><script>\nfunction changeVote() {\n  var qpr = Simulation.qpr, qrp = Simulation.qrp;\n  var W = (qpr.weight == 1 ? [0,2] : [1,1]);\n  qpr.setWeight(W[0]); qrp.setWeight(W[1]);\n}\n<\/script><\/p>\n<p>Repeat the experiment with the &#8220;Mean&#8221; button selected below the simulation. How does the situation differ?<\/p>\n<p><script>\n  Voting = {\n    V: [2,0,1,0,1,1],\n    model: \"Mediancentre\",\n    position: \"(300.8, 386.0)\",\n    start: true\n  }\n<\/script><\/p>\n<h3 class=\"explanation\" onclick=\"toggleExplanation(this)\"><span id=\"triangle\">&#x25B7;<\/span> Explanation:<\/h3>\n<div id=\"explanation\" style=\"height:0px\">\nThe <i>q<\/i><span class=\"gt\">&gt;<\/span><i>p<\/i><span class=\"gt\">&gt;<\/span><i>r<\/i> voter initially votes sincerely, and <i>p<\/i> is elected.  Clicking the &#8220;Change Vote&#8221; button switches her ballot to the insincere <i>q<\/i><span class=\"gt\">&gt;<\/span><i>r<\/i><span class=\"gt\">&gt;<\/span><i>p<\/i>, and achieves a win for her most favored alternative <i>q<\/i>.  This switch is thus a &#8220;strong&#8221; M<sup><small>c<\/small><\/sup>Borda manipulation with 5 voters (the fewest possible). <\/p>\n<p>Toggling to the Mean position shows that the same switch yields a Borda manipulation as well, but it is of the &#8220;weak&#8221; type, because the sincere vote yields a two-way tie between <i>p<\/i> and <i>q<\/i>.  <\/p>\n<p>Should a weak manipulation be considered less serious than a strong one?  The <i>Crossing Boundaries link<\/i> (on the right) explores this question, using a variant of the profile you see here.\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Instructions: Move a vote from q&gt;p&gt;r to q&gt;r&gt;p (or back) by clicking on the &#8220;Change Vote&#8221; button below. What happens to the winner if one voter makes this change? &nbsp;&nbsp; Repeat the experiment with the &#8220;Mean&#8221; button selected below the simulation. How does the situation differ? &#x25B7; Explanation: The q&gt;p&gt;r voter initially votes sincerely, and [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":5,"menu_order":0,"comment_status":"open","ping_status":"open","template":"","meta":[],"_links":{"self":[{"href":"https:\/\/omega.math.union.edu\/research\/2010-05-voting\/wp-json\/wp\/v2\/pages\/34"}],"collection":[{"href":"https:\/\/omega.math.union.edu\/research\/2010-05-voting\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/omega.math.union.edu\/research\/2010-05-voting\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/omega.math.union.edu\/research\/2010-05-voting\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/omega.math.union.edu\/research\/2010-05-voting\/wp-json\/wp\/v2\/comments?post=34"}],"version-history":[{"count":9,"href":"https:\/\/omega.math.union.edu\/research\/2010-05-voting\/wp-json\/wp\/v2\/pages\/34\/revisions"}],"predecessor-version":[{"id":128,"href":"https:\/\/omega.math.union.edu\/research\/2010-05-voting\/wp-json\/wp\/v2\/pages\/34\/revisions\/128"}],"up":[{"embeddable":true,"href":"https:\/\/omega.math.union.edu\/research\/2010-05-voting\/wp-json\/wp\/v2\/pages\/5"}],"wp:attachment":[{"href":"https:\/\/omega.math.union.edu\/research\/2010-05-voting\/wp-json\/wp\/v2\/media?parent=34"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}