{"id":52,"date":"2011-07-06T11:56:55","date_gmt":"2011-07-06T15:56:55","guid":{"rendered":"http:\/\/omega.math.union.edu\/research\/2010-05-voting\/?page_id=52"},"modified":"2011-07-08T21:11:53","modified_gmt":"2011-07-09T01:11:53","slug":"profile-525200","status":"publish","type":"page","link":"https:\/\/omega.math.union.edu\/research\/2010-05-voting\/examples\/profile-525200\/","title":{"rendered":"Cross Tie"},"content":{"rendered":"<h3>Instructions:<\/h3>\n<p>Click the red point to start the simulation and observe where the point comes to rest.<\/p>\n<p>Change to &#8220;Mean&#8221; and try it again.<\/p>\n<p>Now go back to &#8220;Mediancentre&#8221; and press the &lt;0,3,3,0,1,1&gt; button below to view another profile that also produces a tie between these same rankings. Finally, press the &lt;5,5,8,2,1,1&gt; button to see the sum of these two ties.<\/p>\n<p><center><br \/>\n<input type=\"button\" id=\"525200\" value=\"&lt;5,2,5,2,0,0&gt;\" onclick=\"setProfile([5,2,5,2,0,0])\"><\/p>\n<div>+<\/div>\n<p><input type=\"button\" id=\"033011\" value=\"&lt;0,3,3,0,1,1&gt;\" onclick=\"setProfile([0,3,3,0,1,1])\"><\/p>\n<div>=<\/div>\n<p><input type=\"button\" id=\"558211\" value=\"&lt;5,5,8,2,1,1&gt;\" onclick=\"setProfile([5,5,8,2,1,1])\"><br \/>\n<\/center><\/p>\n<p>Note that adding the two ties does <i>not<\/i> result in another tie!<\/p>\n<p><script>\nfunction setProfile(P) {\n  var PQR = [\"pqr\",\"prq\",\"rpq\",\"rqp\",\"qrp\",\"qpr\"];\n  for (var i = 0; i < 6; i++) {Simulation[PQR[i]].setWeight(P[i])}\n}\n<\/script><\/p>\n<p><script>\n  Voting = {\n    V: [5,2,5,2,0,0],\n    model: \"Mediancentre\"\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 initial profile here is an example of a cross tie. Such configurations represent the only examples we have found of M<sup><small>c<\/small><\/sup>Borda ties that are not also Borda ties, and require an even number of voters.  <\/p>\n<p>The second profile exemplifies a bilateral tie.  It is easy to see that anonymity + neutrality force ties for these configurations. In particular both M<sup><small>c<\/small><\/sup>Borda and Borda yield a two-way tie between <i>p<\/i> and <i>r<\/i> for this example.<\/p>\n<p>It may seem strange that when we add two profiles, each of which individually yield a M<sup><small>c<\/small><\/sup>Borda tie between <i>p<\/i> and <i>r<\/i>, the result is a profile in which <i>r<\/i> is the sole M<sup><small>c<\/small><\/sup>Borda winner. This represents a failure of the consistency axiom.\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Instructions: Click the red point to start the simulation and observe where the point comes to rest. Change to &#8220;Mean&#8221; and try it again. Now go back to &#8220;Mediancentre&#8221; and press the &lt;0,3,3,0,1,1&gt; button below to view another profile that also produces a tie between these same rankings. Finally, press the &lt;5,5,8,2,1,1&gt; button to see [&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\/52"}],"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=52"}],"version-history":[{"count":7,"href":"https:\/\/omega.math.union.edu\/research\/2010-05-voting\/wp-json\/wp\/v2\/pages\/52\/revisions"}],"predecessor-version":[{"id":132,"href":"https:\/\/omega.math.union.edu\/research\/2010-05-voting\/wp-json\/wp\/v2\/pages\/52\/revisions\/132"}],"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=52"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}