{"id":41,"date":"2011-07-06T11:48:05","date_gmt":"2011-07-06T15:48:05","guid":{"rendered":"http:\/\/omega.math.union.edu\/research\/2010-05-voting\/?page_id=41"},"modified":"2011-07-08T21:10:44","modified_gmt":"2011-07-09T01:10:44","slug":"profile-124033","status":"publish","type":"page","link":"https:\/\/omega.math.union.edu\/research\/2010-05-voting\/examples\/profile-124033\/","title":{"rendered":"Central Profile"},"content":{"rendered":"<h3>Instructions:<\/h3>\n<p>Drag the red dot away from the center and release it and start the simulation. Note that it always returns to the center.<\/p>\n<p>Change to &#8220;Mediancentre&#8221; and try it again.<\/p>\n<p><script>\n  Voting = {\n    V: [1,2,4,0,3,3],\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\">\nA profile is <i>central<\/i> if it can be decomposed as a sum of elementary reversals (such as<br \/>\n&lt;0,0,1,0,0,1&gt;) and elementary cycles (such as &lt;1,0,1,0,1,0&gt;).  Such a decomposition may not be unique (but is unique for the one shown here).  It is exactly the central profiles that yield 3-way Borda ties.  The same holds for M<sup><small>c<\/small><\/sup>Borda (except that we haven&#8217;t decided what M<sup><small>c<\/small><\/sup>Borda does for 2-split profiles, some of which are central).\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Instructions: Drag the red dot away from the center and release it and start the simulation. Note that it always returns to the center. Change to &#8220;Mediancentre&#8221; and try it again. &#x25B7; Explanation: A profile is central if it can be decomposed as a sum of elementary reversals (such as &lt;0,0,1,0,0,1&gt;) and elementary cycles (such [&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\/41"}],"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=41"}],"version-history":[{"count":8,"href":"https:\/\/omega.math.union.edu\/research\/2010-05-voting\/wp-json\/wp\/v2\/pages\/41\/revisions"}],"predecessor-version":[{"id":130,"href":"https:\/\/omega.math.union.edu\/research\/2010-05-voting\/wp-json\/wp\/v2\/pages\/41\/revisions\/130"}],"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=41"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}