{"id":1585,"date":"2017-02-16T18:46:24","date_gmt":"2017-02-16T18:46:24","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/?post_type=chapter&#038;p=1585"},"modified":"2019-05-30T16:40:19","modified_gmt":"2019-05-30T16:40:19","slug":"which-method-is-fair","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/chapter\/which-method-is-fair\/","title":{"raw":"Which Method is Fair?","rendered":"Which Method is Fair?"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Determine the winner of an election using preference ballots<\/li>\r\n \t<li>Evaluate the fairness\u00a0of an election using preference ballots<\/li>\r\n \t<li>Determine the winner of an election using the Instant Runoff method<\/li>\r\n \t<li>Evaluate the fairness\u00a0of an Instant Runoff election<\/li>\r\n \t<li>Determine the winner of an election using a Borda count<\/li>\r\n \t<li>Evaluate the fairness of an election determined using a Borda count<\/li>\r\n \t<li>Determine the winner of en election using Copeland's method<\/li>\r\n \t<li>Evaluate the fairness of an election determined by Copeland's method<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>So Where\u2019s the Fair Method?<\/h2>\r\nAt this point, you\u2019re probably asking why we keep looking at method after method just to point out that they are not fully fair. We must be holding out on the perfect method, right?\r\n\r\nUnfortunately, no. A mathematical economist, Kenneth Arrow, was able to prove in 1949 that there is no voting method that will satisfy all the fairness criteria we have discussed.\r\n<h2>Arrow\u2019s Impossibility Theorem<\/h2>\r\n<strong>Arrow\u2019s Impossibility Theorem<\/strong> states, roughly, that it is not possible for a voting method to satisfy every fairness criteria that we\u2019ve discussed.\r\n\r\nTo see a very simple example of how difficult voting can be, consider the election below:\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>5<\/td>\r\n<td>5<\/td>\r\n<td>5<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>1st choice<\/td>\r\n<td>A<\/td>\r\n<td>C<\/td>\r\n<td>B<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>2nd choice<\/td>\r\n<td>B<\/td>\r\n<td>A<\/td>\r\n<td>C<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>3rd choice<\/td>\r\n<td>C<\/td>\r\n<td>B<\/td>\r\n<td>A<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nNotice that in this election:\r\n\r\n10 people prefer A to B\r\n\r\n10 people prefer B to C\r\n\r\n10 people prefer C to A\r\n\r\nNo matter whom we choose as the winner, 2\/3 of voters would prefer someone else! This scenario is dubbed <strong>Condorcet\u2019s Voting Paradox<\/strong>, and demonstrates how voting preferences are not transitive (just because A is preferred over B, and B over C, does not mean A is preferred over C). In this election, there is no fair resolution.\r\n\r\nIt is because of this impossibility of a totally fair method that Plurality, IRV, Borda Count, Copeland\u2019s Method, and dozens of variants are all still used. Usually the decision of which method to use is based on what seems most fair for the situation in which it is being applied.","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Determine the winner of an election using preference ballots<\/li>\n<li>Evaluate the fairness\u00a0of an election using preference ballots<\/li>\n<li>Determine the winner of an election using the Instant Runoff method<\/li>\n<li>Evaluate the fairness\u00a0of an Instant Runoff election<\/li>\n<li>Determine the winner of an election using a Borda count<\/li>\n<li>Evaluate the fairness of an election determined using a Borda count<\/li>\n<li>Determine the winner of en election using Copeland&#8217;s method<\/li>\n<li>Evaluate the fairness of an election determined by Copeland&#8217;s method<\/li>\n<\/ul>\n<\/div>\n<h2>So Where\u2019s the Fair Method?<\/h2>\n<p>At this point, you\u2019re probably asking why we keep looking at method after method just to point out that they are not fully fair. We must be holding out on the perfect method, right?<\/p>\n<p>Unfortunately, no. A mathematical economist, Kenneth Arrow, was able to prove in 1949 that there is no voting method that will satisfy all the fairness criteria we have discussed.<\/p>\n<h2>Arrow\u2019s Impossibility Theorem<\/h2>\n<p><strong>Arrow\u2019s Impossibility Theorem<\/strong> states, roughly, that it is not possible for a voting method to satisfy every fairness criteria that we\u2019ve discussed.<\/p>\n<p>To see a very simple example of how difficult voting can be, consider the election below:<\/p>\n<table>\n<tbody>\n<tr>\n<td><\/td>\n<td>5<\/td>\n<td>5<\/td>\n<td>5<\/td>\n<\/tr>\n<tr>\n<td>1st choice<\/td>\n<td>A<\/td>\n<td>C<\/td>\n<td>B<\/td>\n<\/tr>\n<tr>\n<td>2nd choice<\/td>\n<td>B<\/td>\n<td>A<\/td>\n<td>C<\/td>\n<\/tr>\n<tr>\n<td>3rd choice<\/td>\n<td>C<\/td>\n<td>B<\/td>\n<td>A<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Notice that in this election:<\/p>\n<p>10 people prefer A to B<\/p>\n<p>10 people prefer B to C<\/p>\n<p>10 people prefer C to A<\/p>\n<p>No matter whom we choose as the winner, 2\/3 of voters would prefer someone else! This scenario is dubbed <strong>Condorcet\u2019s Voting Paradox<\/strong>, and demonstrates how voting preferences are not transitive (just because A is preferred over B, and B over C, does not mean A is preferred over C). In this election, there is no fair resolution.<\/p>\n<p>It is because of this impossibility of a totally fair method that Plurality, IRV, Borda Count, Copeland\u2019s Method, and dozens of variants are all still used. Usually the decision of which method to use is based on what seems most fair for the situation in which it is being applied.<\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-1585\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Which Method is Fair?. <strong>Authored by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":21,"menu_order":7,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"Which Method is Fair?\",\"author\":\"Lumen Learning\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"ab1c42d4-ea9c-4e19-8ed9-dbd2a5e49ff6","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1585","chapter","type-chapter","status-publish","hentry"],"part":1040,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/pressbooks\/v2\/chapters\/1585","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/wp\/v2\/users\/21"}],"version-history":[{"count":4,"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/pressbooks\/v2\/chapters\/1585\/revisions"}],"predecessor-version":[{"id":2997,"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/pressbooks\/v2\/chapters\/1585\/revisions\/2997"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/pressbooks\/v2\/parts\/1040"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/pressbooks\/v2\/chapters\/1585\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/wp\/v2\/media?parent=1585"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/pressbooks\/v2\/chapter-type?post=1585"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/wp\/v2\/contributor?post=1585"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/wp\/v2\/license?post=1585"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}