{"id":1592,"date":"2017-02-16T18:54:44","date_gmt":"2017-02-16T18:54:44","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/?post_type=chapter&#038;p=1592"},"modified":"2021-02-05T23:55:05","modified_gmt":"2021-02-05T23:55:05","slug":"approval-voting","status":"web-only","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/chapter\/approval-voting\/","title":{"raw":"Approval Voting","rendered":"Approval Voting"},"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 the Approval Voting method<\/li>\r\n \t<li>Evaluate the fairness of an election determined by the Approval Voting method<\/li>\r\n<\/ul>\r\n<\/div>\r\n<div class=\"textbox examples\">\r\n<h3>Study Strategy<\/h3>\r\nPro-tip: Write out each of the examples in this section using paper and pencil, trying each of the steps as you go, until you feel you could explain it to another person.\r\n\r\n<\/div>\r\nWith Approval Voting, the ballot asks you to mark all choices that you find acceptable. The results are tallied, and the option with the most approval is the winner.\r\n<div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\n<div>\r\n\r\nA group of friends is trying to decide upon a movie to watch. Three choices are provided, and each person is asked to mark with an \u201cX\u201d which movies they are willing to watch. The results are:\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>Bob<\/td>\r\n<td>Ann<\/td>\r\n<td>Marv<\/td>\r\n<td>Alice<\/td>\r\n<td>Eve<\/td>\r\n<td>Omar<\/td>\r\n<td>Lupe<\/td>\r\n<td>Dave<\/td>\r\n<td>Tish<\/td>\r\n<td>Jim<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Titanic<\/td>\r\n<td><\/td>\r\n<td>X<\/td>\r\n<td>X<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td>X<\/td>\r\n<td><\/td>\r\n<td>X<\/td>\r\n<td><\/td>\r\n<td>X<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Scream<\/td>\r\n<td>X<\/td>\r\n<td><\/td>\r\n<td>X<\/td>\r\n<td>X<\/td>\r\n<td><\/td>\r\n<td>X<\/td>\r\n<td>X<\/td>\r\n<td><\/td>\r\n<td>X<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The Matrix<\/td>\r\n<td>X<\/td>\r\n<td>X<\/td>\r\n<td>X<\/td>\r\n<td>X<\/td>\r\n<td>X<\/td>\r\n<td><\/td>\r\n<td>X<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td>X<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div>\r\n\r\nTotaling the results, we find:\r\n\r\nTitanic received 5 approvals\r\n\r\nScream received 6 approvals\r\n\r\nThe Matrix received 7 approvals.\r\n\r\nIn this vote, The Matrix would be the winner.\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div>\r\n\r\nIn the following video you will see the example from above.\r\n\r\nhttps:\/\/youtu.be\/-8put6XKw20?list=PL1F887D3B8BF7C297\r\n<div>\r\n<div class=\"textbox key-takeaways\">\r\n<div>\r\n<h3>Try It<\/h3>\r\n<\/div>\r\n<div>\r\n\r\nOur mathematicians deciding on a conference location from earlier decide to use Approval voting. Their votes are tallied below. Find the winner using Approval voting.\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>30<\/td>\r\n<td>10<\/td>\r\n<td>15<\/td>\r\n<td>20<\/td>\r\n<td>15<\/td>\r\n<td>5<\/td>\r\n<td>5<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Seattle<\/td>\r\n<td>X<\/td>\r\n<td>X<\/td>\r\n<td>X<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td>X<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Tacoma<\/td>\r\n<td>X<\/td>\r\n<td><\/td>\r\n<td>X<\/td>\r\n<td>X<\/td>\r\n<td>X<\/td>\r\n<td>X<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Puyallup<\/td>\r\n<td><\/td>\r\n<td>X<\/td>\r\n<td><\/td>\r\n<td>X<\/td>\r\n<td>X<\/td>\r\n<td>X<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Olympia<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td>X<\/td>\r\n<td><\/td>\r\n<td>X<\/td>\r\n<td><\/td>\r\n<td>X<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[reveal-answer q=\"109152\"]Solution[\/reveal-answer]\r\n[hidden-answer a=\"109152\"]\r\n\r\nSeattle has 30+10+15+5 = 60 approval votes.\r\n\r\nTacoma has 20+15+2+15+5 = 85 approval votes.\r\n\r\nPuyallup has 10+2-+25+5 = 50 approval votes.\r\n\r\nOlympia has 15+15+5 = 35 approval votes.\r\n\r\nTacoma wins under this approval voting.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div>\r\n<h3>What\u2019s Wrong with Approval Voting?<\/h3>\r\nApproval voting can very easily violate the Majority Criterion.\r\n<div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\n<div>\r\n\r\nConsider the voting schedule:\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>80<\/td>\r\n<td>15<\/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>B<\/td>\r\n<td>C<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>2nd choice<\/td>\r\n<td>B<\/td>\r\n<td>C<\/td>\r\n<td>B<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>3rd choice<\/td>\r\n<td>C<\/td>\r\n<td>A<\/td>\r\n<td>A<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nClearly A is the majority winner. Now suppose that this election was held using Approval Voting, and every voter marked approval of their top two candidates.\r\n\r\nA would receive approval from 80 voters\r\n\r\nB would receive approval from 100 voters\r\n\r\nC would receive approval from 20 voters\r\n\r\nB would be the winner. Some argue that Approval Voting tends to vote the least disliked choice, rather than the most liked candidate.\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\nAdditionally, Approval Voting is susceptible to strategic insincere voting, in which a voter does not vote their true preference to try to increase the chances of their choice winning. For example, in the movie example above, suppose Bob and Alice would much rather watch Scream. They remove The Matrix from their approval list, resulting in a different result.\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>Bob<\/td>\r\n<td>Ann<\/td>\r\n<td>Marv<\/td>\r\n<td>Alice<\/td>\r\n<td>Eve<\/td>\r\n<td>Omar<\/td>\r\n<td>Lupe<\/td>\r\n<td>Dave<\/td>\r\n<td>Tish<\/td>\r\n<td>Jim<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Titanic<\/td>\r\n<td><\/td>\r\n<td>X<\/td>\r\n<td>X<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td>X<\/td>\r\n<td><\/td>\r\n<td>X<\/td>\r\n<td><\/td>\r\n<td>X<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Scream<\/td>\r\n<td>X<\/td>\r\n<td><\/td>\r\n<td>X<\/td>\r\n<td>X<\/td>\r\n<td><\/td>\r\n<td>X<\/td>\r\n<td>X<\/td>\r\n<td><\/td>\r\n<td>X<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The Matrix<\/td>\r\n<td><\/td>\r\n<td>X<\/td>\r\n<td>X<\/td>\r\n<td><\/td>\r\n<td>X<\/td>\r\n<td><\/td>\r\n<td>X<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td>X<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nTotaling the results, we find Titanic received 5 approvals, Scream received 6 approvals, and The Matrix received 5 approvals. By voting insincerely, Bob and Alice were able to sway the result in favor of their preference.\r\n\r\n<\/div>\r\n<\/div>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Determine the winner of an election using the Approval Voting method<\/li>\n<li>Evaluate the fairness of an election determined by the Approval Voting method<\/li>\n<\/ul>\n<\/div>\n<div class=\"textbox examples\">\n<h3>Study Strategy<\/h3>\n<p>Pro-tip: Write out each of the examples in this section using paper and pencil, trying each of the steps as you go, until you feel you could explain it to another person.<\/p>\n<\/div>\n<p>With Approval Voting, the ballot asks you to mark all choices that you find acceptable. The results are tallied, and the option with the most approval is the winner.<\/p>\n<div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<div>\n<p>A group of friends is trying to decide upon a movie to watch. Three choices are provided, and each person is asked to mark with an \u201cX\u201d which movies they are willing to watch. The results are:<\/p>\n<table>\n<tbody>\n<tr>\n<td><\/td>\n<td>Bob<\/td>\n<td>Ann<\/td>\n<td>Marv<\/td>\n<td>Alice<\/td>\n<td>Eve<\/td>\n<td>Omar<\/td>\n<td>Lupe<\/td>\n<td>Dave<\/td>\n<td>Tish<\/td>\n<td>Jim<\/td>\n<\/tr>\n<tr>\n<td>Titanic<\/td>\n<td><\/td>\n<td>X<\/td>\n<td>X<\/td>\n<td><\/td>\n<td><\/td>\n<td>X<\/td>\n<td><\/td>\n<td>X<\/td>\n<td><\/td>\n<td>X<\/td>\n<\/tr>\n<tr>\n<td>Scream<\/td>\n<td>X<\/td>\n<td><\/td>\n<td>X<\/td>\n<td>X<\/td>\n<td><\/td>\n<td>X<\/td>\n<td>X<\/td>\n<td><\/td>\n<td>X<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>The Matrix<\/td>\n<td>X<\/td>\n<td>X<\/td>\n<td>X<\/td>\n<td>X<\/td>\n<td>X<\/td>\n<td><\/td>\n<td>X<\/td>\n<td><\/td>\n<td><\/td>\n<td>X<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div>\n<p>Totaling the results, we find:<\/p>\n<p>Titanic received 5 approvals<\/p>\n<p>Scream received 6 approvals<\/p>\n<p>The Matrix received 7 approvals.<\/p>\n<p>In this vote, The Matrix would be the winner.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div>\n<p>In the following video you will see the example from above.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Approval voting\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/-8put6XKw20?list=PL1F887D3B8BF7C297\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<div>\n<div class=\"textbox key-takeaways\">\n<div>\n<h3>Try It<\/h3>\n<\/div>\n<div>\n<p>Our mathematicians deciding on a conference location from earlier decide to use Approval voting. Their votes are tallied below. Find the winner using Approval voting.<\/p>\n<table>\n<tbody>\n<tr>\n<td><\/td>\n<td>30<\/td>\n<td>10<\/td>\n<td>15<\/td>\n<td>20<\/td>\n<td>15<\/td>\n<td>5<\/td>\n<td>5<\/td>\n<\/tr>\n<tr>\n<td>Seattle<\/td>\n<td>X<\/td>\n<td>X<\/td>\n<td>X<\/td>\n<td><\/td>\n<td><\/td>\n<td>X<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Tacoma<\/td>\n<td>X<\/td>\n<td><\/td>\n<td>X<\/td>\n<td>X<\/td>\n<td>X<\/td>\n<td>X<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Puyallup<\/td>\n<td><\/td>\n<td>X<\/td>\n<td><\/td>\n<td>X<\/td>\n<td>X<\/td>\n<td>X<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Olympia<\/td>\n<td><\/td>\n<td><\/td>\n<td>X<\/td>\n<td><\/td>\n<td>X<\/td>\n<td><\/td>\n<td>X<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q109152\">Solution<\/span><\/p>\n<div id=\"q109152\" class=\"hidden-answer\" style=\"display: none\">\n<p>Seattle has 30+10+15+5 = 60 approval votes.<\/p>\n<p>Tacoma has 20+15+2+15+5 = 85 approval votes.<\/p>\n<p>Puyallup has 10+2-+25+5 = 50 approval votes.<\/p>\n<p>Olympia has 15+15+5 = 35 approval votes.<\/p>\n<p>Tacoma wins under this approval voting.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div>\n<h3>What\u2019s Wrong with Approval Voting?<\/h3>\n<p>Approval voting can very easily violate the Majority Criterion.<\/p>\n<div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<div>\n<p>Consider the voting schedule:<\/p>\n<table>\n<tbody>\n<tr>\n<td><\/td>\n<td>80<\/td>\n<td>15<\/td>\n<td>5<\/td>\n<\/tr>\n<tr>\n<td>1st choice<\/td>\n<td>A<\/td>\n<td>B<\/td>\n<td>C<\/td>\n<\/tr>\n<tr>\n<td>2nd choice<\/td>\n<td>B<\/td>\n<td>C<\/td>\n<td>B<\/td>\n<\/tr>\n<tr>\n<td>3rd choice<\/td>\n<td>C<\/td>\n<td>A<\/td>\n<td>A<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Clearly A is the majority winner. Now suppose that this election was held using Approval Voting, and every voter marked approval of their top two candidates.<\/p>\n<p>A would receive approval from 80 voters<\/p>\n<p>B would receive approval from 100 voters<\/p>\n<p>C would receive approval from 20 voters<\/p>\n<p>B would be the winner. Some argue that Approval Voting tends to vote the least disliked choice, rather than the most liked candidate.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>Additionally, Approval Voting is susceptible to strategic insincere voting, in which a voter does not vote their true preference to try to increase the chances of their choice winning. For example, in the movie example above, suppose Bob and Alice would much rather watch Scream. They remove The Matrix from their approval list, resulting in a different result.<\/p>\n<table>\n<tbody>\n<tr>\n<td><\/td>\n<td>Bob<\/td>\n<td>Ann<\/td>\n<td>Marv<\/td>\n<td>Alice<\/td>\n<td>Eve<\/td>\n<td>Omar<\/td>\n<td>Lupe<\/td>\n<td>Dave<\/td>\n<td>Tish<\/td>\n<td>Jim<\/td>\n<\/tr>\n<tr>\n<td>Titanic<\/td>\n<td><\/td>\n<td>X<\/td>\n<td>X<\/td>\n<td><\/td>\n<td><\/td>\n<td>X<\/td>\n<td><\/td>\n<td>X<\/td>\n<td><\/td>\n<td>X<\/td>\n<\/tr>\n<tr>\n<td>Scream<\/td>\n<td>X<\/td>\n<td><\/td>\n<td>X<\/td>\n<td>X<\/td>\n<td><\/td>\n<td>X<\/td>\n<td>X<\/td>\n<td><\/td>\n<td>X<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>The Matrix<\/td>\n<td><\/td>\n<td>X<\/td>\n<td>X<\/td>\n<td><\/td>\n<td>X<\/td>\n<td><\/td>\n<td>X<\/td>\n<td><\/td>\n<td><\/td>\n<td>X<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Totaling the results, we find Titanic received 5 approvals, Scream received 6 approvals, and The Matrix received 5 approvals. By voting insincerely, Bob and Alice were able to sway the result in favor of their preference.<\/p>\n<\/div>\n<\/div>\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-1592\">\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>Revision and Adaptation. <strong>Provided 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 class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Approval voting . <strong>Authored by<\/strong>: Lippman, David. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/-8put6XKw20?list=PL1F887D3B8BF7C297\">https:\/\/youtu.be\/-8put6XKw20?list=PL1F887D3B8BF7C297<\/a>. <strong>Project<\/strong>: Open Course Library. <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":21,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Approval voting \",\"author\":\"Lippman, David\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/-8put6XKw20?list=PL1F887D3B8BF7C297\",\"project\":\"Open Course Library\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Revision and Adaptation\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"e0c9ac8c-a0ef-4417-8435-a68990d2c6a6","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1592","chapter","type-chapter","status-web-only","hentry"],"part":1040,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/1592","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/users\/21"}],"version-history":[{"count":13,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/1592\/revisions"}],"predecessor-version":[{"id":3832,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/1592\/revisions\/3832"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/parts\/1040"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/1592\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/media?parent=1592"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=1592"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/contributor?post=1592"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/license?post=1592"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}