{"id":3227,"date":"2026-05-13T16:33:11","date_gmt":"2026-05-13T14:33:11","guid":{"rendered":"https:\/\/geekosas.com\/?p=3227"},"modified":"2026-05-23T12:46:36","modified_gmt":"2026-05-23T10:46:36","slug":"como-se-repartieron-los-votos-en-la-segunda-vuelta-en-chile","status":"publish","type":"post","link":"https:\/\/geekosas.com\/index.php\/2026\/05\/13\/como-se-repartieron-los-votos-en-la-segunda-vuelta-en-chile\/","title":{"rendered":"How were the votes distributed in the runoff election in Chile?"},"content":{"rendered":"<p>Acknowledgments: I would like to begin this article by thanking Hernan Aburto (huaburto@gmail.com) for his assistance. We worked together to refine the model and polish the conclusions. His version of the article on his blog: <a href=\"https:\/\/www.grialprofano.cl\/flyto\/97\/que-paso-con-los-votos-de-la-primera-vuelta-en-el-balotaje\/\">https:\/\/www.grialprofano.cl\/flyto\/97\/que-paso-con-los-votos-de-la-primera-vuelta-en-el-balotaje\/<\/a><\/p>\n<h2>How were the votes distributed?<\/h2>\n<p>In the most recent elections held on Sunday, December 19, 2021, candidate Boric won by a wide margin over candidate Kast.<br \/>\nThis was a rather unexpected result, given that if one ran the numbers assuming voters would follow their candidates\u2019 recommendations, one might have expected a result in the second round close to that shown in the following table:<\/p>\n<h4>Table 1, second-round projections.<\/h4>\n<p><img data-recalc-dims=\"1\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/www.geekosas.com\/wp-content\/uploads\/2021\/12\/image-1640525923156.png?ssl=1\" alt=\"file\" \/><\/p>\n<ul>\n<li><strong>Note<\/strong> As a percentage of the total electorate<\/li>\n<\/ul>\n<p>This would have declared candidate Kast the winner by a wide margin, but that was not the actual outcome, so we ask ourselves: what really happened?<\/p>\n<p>Using a simple mathematical model that we will describe at the end, we obtained the following distribution of votes<\/p>\n<h4>Graph 1, Transfer of votes from the first to the second round<\/h4>\n<p><img data-recalc-dims=\"1\" height=\"768\" width=\"1024\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/www.geekosas.com\/wp-content\/uploads\/2021\/12\/pesos-1024x768.png?resize=1024%2C768&#038;ssl=1\" alt=\"\" \/><\/p>\n<h4>Table 2 Estimated distribution of votes<\/h4>\n<p>Thus, the votes were distributed as follows from the first round to the second:<\/p>\n<p><img data-recalc-dims=\"1\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/www.geekosas.com\/wp-content\/uploads\/2021\/12\/image-1640525829798.png?ssl=1\" alt=\"file\" \/><\/p>\n<ul>\n<li><strong>Note 1<\/strong> To make the graph meaningful, the data is shown as a percentage of the total electorate.<\/li>\n<li><strong>Note 2<\/strong> There is a margin of error because this is a model.<\/li>\n<\/ul>\n<p>This yields the election day results, declaring Boric the winner.<\/p>\n<h2>Comments<\/h2>\n<ul>\n<li>The number of votes transferred from Provoste to Kast is equivalent to those from Sichel to Boric<\/li>\n<li>Boric managed to attract 1.2% more new voters than Kast.<\/li>\n<li>The decisive factor was the votes from Parisi that went to Boric, even though Parisi recommended the opposite.<\/li>\n<\/ul>\n<p>If we reversed the transfer of votes from Parisi between the candidates Kast and Boric (simulating that his voters had followed his recommendation), the result would have been as follows:<\/p>\n<h4>Table 3: Result if Parisi\u2019s voters had followed his recommendation<\/h4>\n<p><img data-recalc-dims=\"1\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/www.geekosas.com\/wp-content\/uploads\/2021\/12\/image-1640526044599.png?ssl=1\" alt=\"file\" \/><\/p>\n<p>With Kast as the winner<\/p>\n<h2>The Model<\/h2>\n<p>This is a regression model where the betas represent the percentages of votes transferred from the first round to the second. It is assumed that vote transfer is homogeneous, so the model was run on subsets of similar polling stations. The method for creating these subsets is debatable, but the fact is that we tested different approaches and the results were similar.<\/p>\n<h4>The mathematical approach is as follows:<\/h4>\n<h5>Dimensions<\/h5>\n<p><code class=\"katex-inline\">o<\/code>: candidates or sources of first-round votes (e.g., boric_pv, sichel_pv, noVoto_pv&#8230;), note that blank, invalid, and no_voto votes are treated as a candidate.<br \/>\n<code class=\"katex-inline\">d<\/code>: candidates or destinations of second-round votes (boric_sv, kast_sv, blank_sv, invalid_sv, noVote_sv); note that blank, invalid, and no-vote are treated as a single candidate.<br \/>\n<code class=\"katex-inline\">m<\/code>: polling station m.<\/p>\n<h5>Data<\/h5>\n<p><code class=\"katex-inline\">pv_{o,m}<\/code> Votes received in the first round at each polling station.<br \/>\n<code class=\"katex-inline\">sv_{o,m}<\/code> Votes received in the second round at each polling station.<\/p>\n<h5>Decision Variables<\/h5>\n<p><code class=\"katex-inline\">p_{o,d}<\/code> Percentage of votes going from a source to a destination.<\/p>\n<h5>Constraints<\/h5>\n<p>Nature of the variables<br \/>\n<code class=\"katex-inline\">0 \\le p_{o,d} \\le 1  \\forall o,d<\/code><\/p>\n<p>Conservation of votes<br \/>\n<code class=\"katex-inline\">\\sum_d p_{o,d}  = 1  \\forall o \\in origins<\/code><\/p>\n<h5>Objective Function<\/h5>\n<p><code class=\"katex-inline\">min_{p}  \\sum_{m,d}(sv_{d,m} - \\sum_o{pv_{o,m} * p_{o,d}})^2<\/code><\/p>\n<h2>Endnotes<\/h2>\n<ul>\n<li>Python with Selenium was used to retrieve data from the SERVEL website.<\/li>\n<li>R was used to manipulate the data and generate graphs.<\/li>\n<li>Finally, Julia with JuMP was used for mathematical modeling.<\/li>\n<li>The source code can be found at: <a href=\"https:\/\/github.com\/danielfm123\/presidenciales_2021\">https:\/\/github.com\/danielfm123\/presidenciales_2021<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<div class=\"mh-excerpt\"><p>Acknowledgments: I would like to begin this article by thanking Hernan Aburto (huaburto@gmail.com) for his assistance. We worked together to refine the model and polish <a class=\"mh-excerpt-more\" href=\"https:\/\/geekosas.com\/index.php\/2026\/05\/13\/como-se-repartieron-los-votos-en-la-segunda-vuelta-en-chile\/\" title=\"How were the votes distributed in the runoff election in Chile?\">[&#8230;]<\/a><\/p>\n<\/div>","protected":false},"author":1,"featured_media":3059,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[1],"tags":[],"class_list":["post-3227","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-sin-categoria"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"https:\/\/i0.wp.com\/geekosas.com\/wp-content\/uploads\/2021\/12\/FRCN3F5FY6BYLWSLIY4NSVWH5E.jpg?fit=900%2C600&ssl=1","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p8vjqF-Q3","jetpack-related-posts":[{"id":3314,"url":"https:\/\/geekosas.com\/index.php\/2017\/05\/23\/estimation-of-vote-distribution-in-the-second-round-of-the-chilean-presidential-elections-2017\/","url_meta":{"origin":3227,"position":0},"title":"Estimation of vote distribution in the second round of the Chilean presidential elections 2017","author":"Daniel Fischer","date":"2017-05-23","format":false,"excerpt":"This article was made in a hurry and with little data; the definitive one is at Who voted for each candidate? After the first round of the Chilean presidential elections, it is traditional for each candidate to begin \"auctioning off\" the votes of their followers to the candidate they feel\u2026","rel":"","context":"In &quot;Sin categor\u00eda&quot;","block_context":{"text":"Sin categor\u00eda","link":"https:\/\/geekosas.com\/index.php\/category\/sin-categoria\/"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/geekosas.com\/wp-content\/uploads\/2017\/12\/segunda-vuelta.jpg?fit=710%2C399&ssl=1&resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/geekosas.com\/wp-content\/uploads\/2017\/12\/segunda-vuelta.jpg?fit=710%2C399&ssl=1&resize=350%2C200 1x, https:\/\/i0.wp.com\/geekosas.com\/wp-content\/uploads\/2017\/12\/segunda-vuelta.jpg?fit=710%2C399&ssl=1&resize=525%2C300 1.5x, https:\/\/i0.wp.com\/geekosas.com\/wp-content\/uploads\/2017\/12\/segunda-vuelta.jpg?fit=710%2C399&ssl=1&resize=700%2C400 2x"},"classes":[]},{"id":3317,"url":"https:\/\/geekosas.com\/index.php\/2017\/05\/23\/who-voted-for-each-candidate-chilean-elections-2017\/","url_meta":{"origin":3227,"position":1},"title":"Who voted for each candidate? 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As with Video Games and Data Science, we did web scraping from www.metacritic.com to generate a database, in which, for each movie we obtained the following information: Country of Origin Genres\u2026","rel":"","context":"In &quot;Sin categor\u00eda&quot;","block_context":{"text":"Sin categor\u00eda","link":"https:\/\/geekosas.com\/index.php\/category\/sin-categoria\/"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/www.geekosas.com\/wp-content\/uploads\/2017\/03\/histogramas-300x120.png?resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/www.geekosas.com\/wp-content\/uploads\/2017\/03\/histogramas-300x120.png?resize=350%2C200 1x, https:\/\/i0.wp.com\/www.geekosas.com\/wp-content\/uploads\/2017\/03\/histogramas-300x120.png?resize=525%2C300 1.5x, https:\/\/i0.wp.com\/www.geekosas.com\/wp-content\/uploads\/2017\/03\/histogramas-300x120.png?resize=700%2C400 2x"},"classes":[]},{"id":3288,"url":"https:\/\/geekosas.com\/index.php\/2017\/05\/23\/parking-law\/","url_meta":{"origin":3227,"position":4},"title":"Parking Law","author":"Daniel Fischer","date":"2017-05-23","format":false,"excerpt":"In Chile, on February 15 (correct me if I'm wrong), the parking law was enacted, which among other things requires parking companies to: Compensate customers who are victims of theft. 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