{"id":8301,"date":"2023-09-29T14:32:41","date_gmt":"2023-09-29T14:32:41","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/?post_type=chapter&#038;p=8301"},"modified":"2024-10-18T20:58:36","modified_gmt":"2024-10-18T20:58:36","slug":"apportionment-learn-it-1","status":"web-only","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/chapter\/apportionment-learn-it-1\/","title":{"raw":"Apportionment: Learn It 1","rendered":"Apportionment: Learn It 1"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li>Define apportionment and its importance in political representation in the United States and other representative democracies<\/li>\r\n\t<li>Identify various methods of apportionment, including Hamilton's method, Jefferson's method, Webster's method, Huntington-Hill method, and Lowndes' method<\/li>\r\n\t<li>Understand the apportionment process for legislative districts<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Apportionment<\/h2>\r\n<p><strong>Apportionment<\/strong> is the problem of dividing up a fixed number of things among groups of different sizes. In politics, this takes the form of allocating a limited number of representatives amongst voters.<\/p>\r\n<section class=\"textbox keyTakeaway\">\r\n<div>\r\n<h3>apportionment<\/h3>\r\n<p><strong>Apportionment<\/strong> is the process of allocating seats in a legislative body, such as a parliament or congress, based on a specific formula that usually takes into account population size or other demographic factors.<\/p>\r\n<p>&nbsp;<\/p>\r\n<p>In politics, apportionment is crucial for ensuring fair representation, as it determines how many elected officials will represent a given area, influencing the balance of power and policy decisions.<\/p>\r\n<\/div>\r\n<\/section>\r\n<p>This problem, presumably, is older than the United States, but the best-known ways to solve it have their origins in the problem of assigning each state an appropriate number of representatives in the new Congress when the country was formed. States also face this apportionment problem in defining how to draw districts for state representatives. The apportionment problem comes up in a variety of non-political areas too, though.<\/p>\r\n<p>We face several restrictions in this process:<\/p>\r\n<section class=\"textbox keyTakeaway\">\r\n<div>\r\n<h3>apportionment rules<\/h3>\r\n<ol style=\"list-style-type: decimal;\">\r\n\t<li>The things being divided up can exist only in whole numbers.<\/li>\r\n\t<li>We must use all of the things being divided up, and we cannot use any more.<\/li>\r\n\t<li>Each group must get at least one of the things being divided up.<\/li>\r\n\t<li>The number of things assigned to each group should be at least approximately proportional to the population of the group. (Exact proportionality isn\u2019t possible because of the whole number requirement, but we should try to be close, and in any case, if Group A is larger than Group B, then Group B shouldn\u2019t get more of the things than Group A does).<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/section>\r\n<p>In terms of the apportionment of the United States House of Representatives, these rules imply:<\/p>\r\n<ol style=\"list-style-type: decimal;\">\r\n\t<li>We can only have whole representatives (a state can\u2019t have [latex]3.4[\/latex] representatives).<\/li>\r\n\t<li>We can only use the (currently) [latex]435[\/latex] representatives available. If one state gets another representative, another state has to lose one.<\/li>\r\n\t<li>Every state gets at least one representative.<\/li>\r\n\t<li>The number of representatives each state gets should be approximately proportional to the state population. This way, the number of constituents each representative has should be approximately equal.<\/li>\r\n<\/ol>\r\n<section class=\"textbox tryIt\">\r\n<p>[ohm2_question hide_question_numbers=1]13083[\/ohm2_question]<\/p>\r\n<\/section>\r\n<p>We will look at four ways of solving the apportionment problem. Three of them (Lowndes\u2019s method is the exception) have been used at various times to apportion the U.S. Congress, although the method currently in use (the Huntington-Hill method) is significantly more complicated.<\/p>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Define apportionment and its importance in political representation in the United States and other representative democracies<\/li>\n<li>Identify various methods of apportionment, including Hamilton&#8217;s method, Jefferson&#8217;s method, Webster&#8217;s method, Huntington-Hill method, and Lowndes&#8217; method<\/li>\n<li>Understand the apportionment process for legislative districts<\/li>\n<\/ul>\n<\/section>\n<h2>Apportionment<\/h2>\n<p><strong>Apportionment<\/strong> is the problem of dividing up a fixed number of things among groups of different sizes. In politics, this takes the form of allocating a limited number of representatives amongst voters.<\/p>\n<section class=\"textbox keyTakeaway\">\n<div>\n<h3>apportionment<\/h3>\n<p><strong>Apportionment<\/strong> is the process of allocating seats in a legislative body, such as a parliament or congress, based on a specific formula that usually takes into account population size or other demographic factors.<\/p>\n<p>&nbsp;<\/p>\n<p>In politics, apportionment is crucial for ensuring fair representation, as it determines how many elected officials will represent a given area, influencing the balance of power and policy decisions.<\/p>\n<\/div>\n<\/section>\n<p>This problem, presumably, is older than the United States, but the best-known ways to solve it have their origins in the problem of assigning each state an appropriate number of representatives in the new Congress when the country was formed. States also face this apportionment problem in defining how to draw districts for state representatives. The apportionment problem comes up in a variety of non-political areas too, though.<\/p>\n<p>We face several restrictions in this process:<\/p>\n<section class=\"textbox keyTakeaway\">\n<div>\n<h3>apportionment rules<\/h3>\n<ol style=\"list-style-type: decimal;\">\n<li>The things being divided up can exist only in whole numbers.<\/li>\n<li>We must use all of the things being divided up, and we cannot use any more.<\/li>\n<li>Each group must get at least one of the things being divided up.<\/li>\n<li>The number of things assigned to each group should be at least approximately proportional to the population of the group. (Exact proportionality isn\u2019t possible because of the whole number requirement, but we should try to be close, and in any case, if Group A is larger than Group B, then Group B shouldn\u2019t get more of the things than Group A does).<\/li>\n<\/ol>\n<\/div>\n<\/section>\n<p>In terms of the apportionment of the United States House of Representatives, these rules imply:<\/p>\n<ol style=\"list-style-type: decimal;\">\n<li>We can only have whole representatives (a state can\u2019t have [latex]3.4[\/latex] representatives).<\/li>\n<li>We can only use the (currently) [latex]435[\/latex] representatives available. If one state gets another representative, another state has to lose one.<\/li>\n<li>Every state gets at least one representative.<\/li>\n<li>The number of representatives each state gets should be approximately proportional to the state population. This way, the number of constituents each representative has should be approximately equal.<\/li>\n<\/ol>\n<section class=\"textbox tryIt\">\n<iframe loading=\"lazy\" id=\"ohm13083\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=13083&theme=lumen&iframe_resize_id=ohm13083&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><br \/>\n<\/section>\n<p>We will look at four ways of solving the apportionment problem. Three of them (Lowndes\u2019s method is the exception) have been used at various times to apportion the U.S. Congress, although the method currently in use (the Huntington-Hill method) is significantly more complicated.<\/p>\n","protected":false},"author":15,"menu_order":13,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Math in Society (Lippman)\",\"author\":\"Mike Kenyon & David Lippman\",\"organization\":\"LibreTexts Mathematics\",\"url\":\"https:\/\/math.libretexts.org\/Bookshelves\/Applied_Mathematics\/Math_in_Society_(Lippman)\/04%3A_Apportionment\/4.01%3A_Introduction\",\"project\":\"4.1: Introduction\",\"license\":\"cc-by-sa\",\"license_terms\":\"Access for free at https:\/\/math.libretexts.org\/Bookshelves\/Applied_Mathematics\/Math_in_Society_(Lippman)\"}]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":90,"module-header":"learn_it","content_attributions":[{"type":"cc-attribution","description":"Math in Society (Lippman)","author":"Mike Kenyon & David Lippman","organization":"LibreTexts Mathematics","url":"https:\/\/math.libretexts.org\/Bookshelves\/Applied_Mathematics\/Math_in_Society_(Lippman)\/04%3A_Apportionment\/4.01%3A_Introduction","project":"4.1: Introduction","license":"cc-by-sa","license_terms":"Access for free at https:\/\/math.libretexts.org\/Bookshelves\/Applied_Mathematics\/Math_in_Society_(Lippman)"}],"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\/8301"}],"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":9,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/8301\/revisions"}],"predecessor-version":[{"id":14892,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/8301\/revisions\/14892"}],"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\/8301\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/media?parent=8301"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapter-type?post=8301"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/contributor?post=8301"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/license?post=8301"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}