{"id":44,"date":"2011-07-06T11:51:44","date_gmt":"2011-07-06T15:51:44","guid":{"rendered":"http:\/\/omega.math.union.edu\/research\/2010-05-voting\/?page_id=44"},"modified":"2011-07-08T21:11:31","modified_gmt":"2011-07-09T01:11:31","slug":"profile-201011a","status":"publish","type":"page","link":"https:\/\/omega.math.union.edu\/research\/2010-05-voting\/examples\/profile-201011a\/","title":{"rendered":"A Stubborn 2-Way Tie"},"content":{"rendered":"<h3>Instructions:<\/h3>\n<p>Click the red dot to release it and start the simulation. The green wedge(s) indicate the winning profile(s).<\/p>\n<p>This profile produces a tie for <i>every<\/i> scoring rule, not just the Borda rule. Is that true of M<sup><small>c<\/small><\/sup>Borda as well? Click &#8220;Mediancentre&#8221; below to find out.<\/p>\n<p>Have you seen this profile in a previous example?<\/p>\n<p><script>\n  Voting = {\n    V: [2,0,1,0,1,1],\n    model: \"Mean\"\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\">\nIt follows that Borda\u2019s behavior in the <i>Crossing Boundaries<\/i> example is duplicated by that of every scoring rule other than plurality &#8212; one observes two weak manipulations as the votes are transferred one-at-a-time, while M<sup><small>c<\/small><\/sup>Borda exhibits a single strong manipulation. In the case of Plurality voting, the transfers have no effect, with all profiles in the sequence yielding the same two-way tie. The situation suggests why it may be misleading to compare two voting rules according to how frequently they can be manipulated, unless one looks at decisiveness at the same time.<\/p>\n<p>(We are making a standard assumption here about scoring rules &#8212; that scoring weights for first, second, and third place satisfy <i>w<\/i><sub>1<\/sub> &#x2265; <i>w<\/i><sub>2<\/sub> &#x2265; <i>w<\/i><sub>3<\/sub> with <i>w<\/i><sub>1<\/sub> &gt; <i>w<\/i><sub>3<\/sub>.)\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Instructions: Click the red dot to release it and start the simulation. The green wedge(s) indicate the winning profile(s). This profile produces a tie for every scoring rule, not just the Borda rule. Is that true of McBorda as well? Click &#8220;Mediancentre&#8221; below to find out. Have you seen this profile in a previous example? [&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\/44"}],"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=44"}],"version-history":[{"count":8,"href":"https:\/\/omega.math.union.edu\/research\/2010-05-voting\/wp-json\/wp\/v2\/pages\/44\/revisions"}],"predecessor-version":[{"id":131,"href":"https:\/\/omega.math.union.edu\/research\/2010-05-voting\/wp-json\/wp\/v2\/pages\/44\/revisions\/131"}],"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=44"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}