{"id":8298,"date":"2023-09-29T14:32:16","date_gmt":"2023-09-29T14:32:16","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/?post_type=chapter&#038;p=8298"},"modified":"2024-10-18T20:58:35","modified_gmt":"2024-10-18T20:58:35","slug":"voting-theory-apply-it-2","status":"web-only","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/chapter\/voting-theory-apply-it-2\/","title":{"raw":"Voting Theory: Apply It 2","rendered":"Voting Theory: Apply It 2"},"content":{"raw":"<h2>Analyzing Voting Systems and Fairness Cont.<\/h2>\r\n<p>As we depart from the point allocation strategy of the Borda count, we approach Copeland's method in a neighborhood committee setting. This method introduces us to the concept of pairwise comparison and its effectiveness in capturing the collective preference of a group, presenting a unique perspective on consensus-building in elections.<\/p>\r\n<h3>Scenario 4: Neighborhood Committee Election - Copeland's Method<\/h3>\r\n<p>A neighborhood committee uses Copeland's method to select its new chair. The voting data is given below.<\/p>\r\n<p>Pairwise Voting Data:<\/p>\r\n<ul>\r\n\t<li>Aisha vs. Juan: Aisha wins [latex]60-40[\/latex]<\/li>\r\n\t<li>Aisha vs. Nia: Nia wins [latex]55-45[\/latex]<\/li>\r\n\t<li>Juan vs. Nia: Tie of [latex]50-50[\/latex]\u00a0<\/li>\r\n<\/ul>\r\n<section class=\"textbox tryIt\">\r\n<p>[ohm2_question hide_question_numbers=1]13978[\/ohm2_question]<\/p>\r\n<\/section>\r\n<p>Leaving behind the pairwise confrontations of Copeland's method, we now examine the Approval Voting method employed in a community survey. This scenario will demonstrate how this method enables voters to express their preferences in a broader context and the implications it has for gauging public opinion on multiple options<\/p>\r\n<h3>Scenario 5: Community Survey - Approval Voting Method<\/h3>\r\n<p>A community conducts a survey to choose a new public project, using the Approval Voting method. The voting data is given below.<\/p>\r\n<p>Voting Data (Number of Approvals):<\/p>\r\n<ul>\r\n\t<li>Park Renovation: [latex]120[\/latex] approvals<\/li>\r\n\t<li>Community Center: [latex]150[\/latex] approvals<\/li>\r\n\t<li>Public Library: [latex]110[\/latex] approvals<\/li>\r\n\t<li>Sports Complex: [latex]130[\/latex] approvals<\/li>\r\n<\/ul>\r\n<section class=\"textbox tryIt\">\r\n<p>[ohm2_question hide_question_numbers=1]13979[\/ohm2_question]<\/p>\r\n<\/section>\r\n<p>After exploring the Approval Voting method in the community survey, where the simplicity of choosing multiple options comes into play, we now delve into the theoretical realm with Arrow\u2019s Impossibility Theorem. This transition from practical voting methods to theoretical analysis invites us to consider the broader principles and potential limitations of voting systems as a whole. Arrow's theorem challenges us to critically think about the possibility of achieving a perfect voting system that is fair, rational, and devoid of paradoxes, bringing a new dimension to our understanding of electoral fairness.<\/p>\r\n<h3>Scenario 6: Theoretical Analysis - Arrow's Impossibility Theorem<\/h3>\r\n<p>In a theoretical discussion about voting systems, Arrow\u2019s Impossibility Theorem is brought up.<\/p>\r\n<section class=\"textbox tryIt\">\r\n<p>[ohm2_question hide_question_numbers=1]13980[\/ohm2_question]<\/p>\r\n<\/section>\r\n<p>As we conclude our exploration of various voting methods, consider the intricate balance between accurately representing voter preferences and maintaining fairness in election outcomes. Each method, from preference ballots to Approval Voting, offers unique insights into how we make collective decisions. Arrow\u2019s Impossibility Theorem further reminds us of the inherent challenges in creating a perfect voting system, highlighting the complexity of achieving both fairness and rationality in the voting process. Excellent work today!<\/p>","rendered":"<h2>Analyzing Voting Systems and Fairness Cont.<\/h2>\n<p>As we depart from the point allocation strategy of the Borda count, we approach Copeland&#8217;s method in a neighborhood committee setting. This method introduces us to the concept of pairwise comparison and its effectiveness in capturing the collective preference of a group, presenting a unique perspective on consensus-building in elections.<\/p>\n<h3>Scenario 4: Neighborhood Committee Election &#8211; Copeland&#8217;s Method<\/h3>\n<p>A neighborhood committee uses Copeland&#8217;s method to select its new chair. The voting data is given below.<\/p>\n<p>Pairwise Voting Data:<\/p>\n<ul>\n<li>Aisha vs. Juan: Aisha wins [latex]60-40[\/latex]<\/li>\n<li>Aisha vs. Nia: Nia wins [latex]55-45[\/latex]<\/li>\n<li>Juan vs. Nia: Tie of [latex]50-50[\/latex]\u00a0<\/li>\n<\/ul>\n<section class=\"textbox tryIt\">\n<iframe loading=\"lazy\" id=\"ohm13978\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=13978&theme=lumen&iframe_resize_id=ohm13978&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><br \/>\n<\/section>\n<p>Leaving behind the pairwise confrontations of Copeland&#8217;s method, we now examine the Approval Voting method employed in a community survey. This scenario will demonstrate how this method enables voters to express their preferences in a broader context and the implications it has for gauging public opinion on multiple options<\/p>\n<h3>Scenario 5: Community Survey &#8211; Approval Voting Method<\/h3>\n<p>A community conducts a survey to choose a new public project, using the Approval Voting method. The voting data is given below.<\/p>\n<p>Voting Data (Number of Approvals):<\/p>\n<ul>\n<li>Park Renovation: [latex]120[\/latex] approvals<\/li>\n<li>Community Center: [latex]150[\/latex] approvals<\/li>\n<li>Public Library: [latex]110[\/latex] approvals<\/li>\n<li>Sports Complex: [latex]130[\/latex] approvals<\/li>\n<\/ul>\n<section class=\"textbox tryIt\">\n<iframe loading=\"lazy\" id=\"ohm13979\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=13979&theme=lumen&iframe_resize_id=ohm13979&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><br \/>\n<\/section>\n<p>After exploring the Approval Voting method in the community survey, where the simplicity of choosing multiple options comes into play, we now delve into the theoretical realm with Arrow\u2019s Impossibility Theorem. This transition from practical voting methods to theoretical analysis invites us to consider the broader principles and potential limitations of voting systems as a whole. Arrow&#8217;s theorem challenges us to critically think about the possibility of achieving a perfect voting system that is fair, rational, and devoid of paradoxes, bringing a new dimension to our understanding of electoral fairness.<\/p>\n<h3>Scenario 6: Theoretical Analysis &#8211; Arrow&#8217;s Impossibility Theorem<\/h3>\n<p>In a theoretical discussion about voting systems, Arrow\u2019s Impossibility Theorem is brought up.<\/p>\n<section class=\"textbox tryIt\">\n<iframe loading=\"lazy\" id=\"ohm13980\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=13980&theme=lumen&iframe_resize_id=ohm13980&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><br \/>\n<\/section>\n<p>As we conclude our exploration of various voting methods, consider the intricate balance between accurately representing voter preferences and maintaining fairness in election outcomes. Each method, from preference ballots to Approval Voting, offers unique insights into how we make collective decisions. Arrow\u2019s Impossibility Theorem further reminds us of the inherent challenges in creating a perfect voting system, highlighting the complexity of achieving both fairness and rationality in the voting process. Excellent work today!<\/p>\n","protected":false},"author":15,"menu_order":11,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":90,"module-header":"apply_it","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/8298"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/users\/15"}],"version-history":[{"count":5,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/8298\/revisions"}],"predecessor-version":[{"id":12443,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/8298\/revisions\/12443"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/parts\/90"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/8298\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/media?parent=8298"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapter-type?post=8298"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/contributor?post=8298"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/license?post=8298"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}