{"id":61,"date":"2011-07-06T12:05:55","date_gmt":"2011-07-06T16:05:55","guid":{"rendered":"http:\/\/omega.math.union.edu\/research\/2010-05-voting\/?page_id=61"},"modified":"2011-07-08T21:12:22","modified_gmt":"2011-07-09T01:12:22","slug":"profile-113002","status":"publish","type":"page","link":"https:\/\/omega.math.union.edu\/research\/2010-05-voting\/examples\/profile-113002\/","title":{"rendered":"Irresolute OWM Failure"},"content":{"rendered":"<h3>Instructions:<\/h3>\n<p>Move a vote from <i>p<\/i><span class=\"gt\">&gt;<\/span><i>r<\/i><span class=\"gt\">&gt;<\/span><i>q<\/i> to <i>q<\/i><span class=\"gt\">&gt;<\/span><i>r<\/i><span class=\"gt\">&gt;<\/span><i>p<\/i> by clicking the &#8220;Change Vote&#8221; button below, and let the red point come to rest.<\/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 prq = Simulation.prq, qrp = Simulation.qrp;\n  var W = (prq.weight == 1 ? [0,1] : [1,0]);\n  prq.setWeight(W[0]); qrp.setWeight(W[1]);\n}\n<\/script><\/p>\n<p>Click the button again to change it back.<\/p>\n<p>Now add a vote to <i>q<\/i><span class=\"gt\">&gt;<\/span><i>r<\/i><span class=\"gt\">&gt;<\/span><i>p<\/i> by clicking on its point. What happens to the outcome with this additional vote?  How is the winner related to the ranking of the additional vote?<\/p>\n<p><script>\n  Voting = {\n    V: [1,1,3,0,0,2],\n    model: \"Mediancentre\",\n    position: \"(169.3, 254.2)\",\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\">\nSuppose all ties are to be broken via alphabetical order. Then the voter here with sincere preferences <i>p<\/i><span class=\"gt\">&gt;<\/span><i>r<\/i><span class=\"gt\">&gt;<\/span><i>q<\/i> might wish to flip his ranking upside down, casting <i>q<\/i><span class=\"gt\">&gt;<\/span><i>r<\/i><span class=\"gt\">&gt;<\/span><i>p<\/i>.  Pre-flip, the winner is <i>r<\/i>.  Post-flip, a three-way tie is broken in favor of <i>p<\/i>, the manipulating voter&#8217;s top choice.  This situation represents a failure of irresolute half-way monotonicity, hence of irresolute one-way monotonicity.\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Instructions: Move a vote from p&gt;r&gt;q to q&gt;r&gt;p by clicking the &#8220;Change Vote&#8221; button below, and let the red point come to rest. &nbsp;&nbsp; Click the button again to change it back. Now add a vote to q&gt;r&gt;p by clicking on its point. What happens to the outcome with this additional vote? How is the [&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\/61"}],"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=61"}],"version-history":[{"count":5,"href":"https:\/\/omega.math.union.edu\/research\/2010-05-voting\/wp-json\/wp\/v2\/pages\/61\/revisions"}],"predecessor-version":[{"id":133,"href":"https:\/\/omega.math.union.edu\/research\/2010-05-voting\/wp-json\/wp\/v2\/pages\/61\/revisions\/133"}],"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=61"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}