{"id":57597,"date":"2021-05-03T08:34:20","date_gmt":"2021-05-03T07:34:20","guid":{"rendered":"https:\/\/datascientest.com\/?p=57597"},"modified":"2023-11-09T14:07:27","modified_gmt":"2023-11-09T14:07:27","slug":"loi-des-grands-nombres-et-vote-democratique","status":"publish","type":"post","link":"https:\/\/datascientest.com\/loi-des-grands-nombres-et-vote-democratique","title":{"rendered":"Loi des grands nombres et vote d\u00e9mocratique"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"57597\" class=\"elementor elementor-57597\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-58c9469 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"58c9469\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-4ba6ccb\" data-id=\"4ba6ccb\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-9414075 elementor-widget elementor-widget-heading\" data-id=\"9414075\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-heading-title{padding:0;margin:0;line-height:1}.elementor-widget-heading .elementor-heading-title[class*=elementor-size-]>a{color:inherit;font-size:inherit;line-height:inherit}.elementor-widget-heading .elementor-heading-title.elementor-size-small{font-size:15px}.elementor-widget-heading .elementor-heading-title.elementor-size-medium{font-size:19px}.elementor-widget-heading .elementor-heading-title.elementor-size-large{font-size:29px}.elementor-widget-heading .elementor-heading-title.elementor-size-xl{font-size:39px}.elementor-widget-heading .elementor-heading-title.elementor-size-xxl{font-size:59px}<\/style><h2 class=\"elementor-heading-title elementor-size-default\">Le vote d\u00e9mocratique est une solution \u00e0 laquelle nous avons souvent recours pour prendre une d\u00e9cision en groupe et qui a \u00e9t\u00e9 commun\u00e9ment admise dans notre soci\u00e9t\u00e9. Son int\u00e9r\u00eat repose sur la loi des grands nombres, un principe math\u00e9matique qui permet d\u2019approcher la probabilit\u00e9 d\u2019un \u00e9v\u00e9nement par la fr\u00e9quence de sa r\u00e9alisation. Que ce soit pour choisir un film, un restaurant ou un lieu de vacances, le vote permet de maximiser le nombre de personnes satisfaites par la d\u00e9cision prise. Mais est-il r\u00e9ellement la meilleure option \u00e0 prendre lorsque l\u2019objectif est de choisir entre deux propositions : une vraie et une fausse.<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-c0504d0 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"c0504d0\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-5833e5c\" data-id=\"5833e5c\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-9ee8798 elementor-widget elementor-widget-text-editor\" data-id=\"9ee8798\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-widget-text-editor.elementor-drop-cap-view-stacked .elementor-drop-cap{background-color:#69727d;color:#fff}.elementor-widget-text-editor.elementor-drop-cap-view-framed .elementor-drop-cap{color:#69727d;border:3px solid;background-color:transparent}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap{margin-top:8px}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap-letter{width:1em;height:1em}.elementor-widget-text-editor .elementor-drop-cap{float:left;text-align:center;line-height:1;font-size:50px}.elementor-widget-text-editor .elementor-drop-cap-letter{display:inline-block}<\/style>\t\t\t\t<p>Par exemple, pensez-vous qu\u2019un vote d\u00e9mocratique permettra de savoir si cette formule est vraie ou fausse ?<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-802f801 elementor-widget elementor-widget-image\" data-id=\"802f801\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-widget-image{text-align:center}.elementor-widget-image a{display:inline-block}.elementor-widget-image a img[src$=\".svg\"]{width:48px}.elementor-widget-image img{vertical-align:middle;display:inline-block}<\/style>\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"300\" height=\"84\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/03\/unnamed-4-300x84.png\" class=\"attachment-medium size-medium wp-image-57608\" alt=\"\" loading=\"lazy\" srcset=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/03\/unnamed-4-300x84.png 300w, https:\/\/datascientest.com\/wp-content\/uploads\/2021\/03\/unnamed-4.png 512w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-8e5bd50 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"8e5bd50\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-2653951\" data-id=\"2653951\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-97c7ff4 elementor-widget elementor-widget-text-editor\" data-id=\"97c7ff4\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><span style=\"font-weight: 400; color: #000000;\">Et celle l\u00e0 :<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-4edd1ab elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"4edd1ab\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-18d6647\" data-id=\"18d6647\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-eea6873 elementor-widget elementor-widget-image\" data-id=\"eea6873\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"300\" height=\"79\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/03\/unnamed-1-1-300x79.png\" class=\"attachment-medium size-medium wp-image-57609\" alt=\"\" loading=\"lazy\" srcset=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/03\/unnamed-1-1-300x79.png 300w, https:\/\/datascientest.com\/wp-content\/uploads\/2021\/03\/unnamed-1-1.png 512w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-74b2250 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"74b2250\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-f5d3590\" data-id=\"f5d3590\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-56b2e18 elementor-widget elementor-widget-text-editor\" data-id=\"56b2e18\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><span style=\"font-weight: 400; color: #000000;\">La r\u00e9ponse \u00e0 cette question repose sur la loi des grands nombre. Nous allons faire un peu de maths, mais pas de panique, nous verrons dans un second temps une interpr\u00e9tation intuitive des concepts qui suivent.<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e0f906e elementor-widget elementor-widget-heading\" data-id=\"e0f906e\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Loi faible des grands nombres<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-bec923c elementor-widget elementor-widget-text-editor\" data-id=\"bec923c\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Consid\u00e9rons une<b>&nbsp;variable al\u00e9atoire X<\/b>.<\/p>\n<p>Consid\u00e9rons aussi&nbsp;<b>N autres variables al\u00e9atoires ind\u00e9pendantes&nbsp;<\/b>qui suivent la m\u00eame loi de probabilit\u00e9 que X. On les note<b>&nbsp;X1, &#8230; , XN<\/b>.<\/p>\n<p>Alors la loi faible des grands nombres nous stipule que :<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-20ead43 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"20ead43\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-09c2d91\" data-id=\"09c2d91\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-4e8cffa elementor-widget elementor-widget-image\" data-id=\"4e8cffa\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"514\" height=\"92\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/03\/pasted-image-0.png\" class=\"attachment-large size-large wp-image-57610\" alt=\"\" loading=\"lazy\" srcset=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/03\/pasted-image-0.png 514w, https:\/\/datascientest.com\/wp-content\/uploads\/2021\/03\/pasted-image-0-300x54.png 300w\" sizes=\"(max-width: 514px) 100vw, 514px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-00a4aac elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"00a4aac\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-154bc63\" data-id=\"154bc63\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-b7a7741 elementor-widget elementor-widget-text-editor\" data-id=\"b7a7741\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><span style=\"color: #000000;\"><span style=\"font-weight: 400;\">Pour tout <\/span><span style=\"font-weight: 400;\">&gt;0<\/span><\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-2370089 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2370089\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-3925b0c\" data-id=\"3925b0c\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-339570a elementor-widget elementor-widget-image\" data-id=\"339570a\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"300\" height=\"57\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/03\/unnamed-2-2-300x57.png\" class=\"attachment-medium size-medium wp-image-57614\" alt=\"\" loading=\"lazy\" srcset=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/03\/unnamed-2-2-300x57.png 300w, https:\/\/datascientest.com\/wp-content\/uploads\/2021\/03\/unnamed-2-2.png 512w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-96bdc1a elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"96bdc1a\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-f3cc9e2\" data-id=\"f3cc9e2\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-a0f12e0 elementor-widget elementor-widget-text-editor\" data-id=\"a0f12e0\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<blockquote><p><span style=\"font-weight: 400; color: #000000;\">En fran\u00e7ais, cette formule signifie que plus on prend un nombre de variables al\u00e9atoires ind\u00e9pendantes N \u00e9lev\u00e9, plus la probabilit\u00e9 que la moyenne des r\u00e9sultats de toutes ces variables X1, \u2026, XN soient proches de la moyenne de la variable X.<\/span><\/p><\/blockquote>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-771e4fc elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"771e4fc\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-1e7024e\" data-id=\"1e7024e\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-89d5fbc elementor-widget elementor-widget-image\" data-id=\"89d5fbc\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"300\" height=\"84\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/03\/pasted-image-0-1-300x84.png\" class=\"attachment-medium size-medium wp-image-57620\" alt=\"\" loading=\"lazy\" srcset=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/03\/pasted-image-0-1-300x84.png 300w, https:\/\/datascientest.com\/wp-content\/uploads\/2021\/03\/pasted-image-0-1.png 675w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-28e5080 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"28e5080\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-98315d8\" data-id=\"98315d8\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-128da74e elementor-align-center button-principale elementor-widget elementor-widget-button\" data-id=\"128da74e\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm elementor-animation-grow\" href=\"https:\/\/datascientest.com\/formation-data-scientist\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">En savoir plus sur notre formation Data Scientist<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-fb2f182 elementor-widget elementor-widget-text-editor\" data-id=\"fb2f182\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><span style=\"font-weight: 400; color: #000000;\">Un autre exemple, si vous montrer la phrase suivante \u00e0 X, il vous dira qu\u2019elle est vraie aussi :<\/span><\/p><p><span style=\"font-weight: 400; color: #000000;\">\u201cDatascientest est la meilleure plateforme d\u2019apprentissage aux m\u00e9tiers de la data\u201d\u00a0<\/span><\/p><p><span style=\"font-weight: 400; color: #000000;\">Et X ne se trompe jamais.<\/span><\/p><p><span style=\"font-weight: 400; color: #000000;\">Maintenant, imaginez que nos X1, X2, \u2026 XN correspondent aux choix de Pierre, Paul et Jacques. Par exemple, si vous montrez l\u2019\u00e9quation pr\u00e9c\u00e9dente \u00e0 Pierre (X1), il pourra se tromper et vous r\u00e9pondre qu\u2019elle est fausse. Si vous la montrer \u00e0 Paul (X2), il pourra quant \u00e0 lui r\u00e9pondre qu\u2019elle est vraie. Et ainsi de suite N fois.<\/span><\/p><p><span style=\"font-weight: 400; color: #000000;\">Et bien dans l\u2019hypoth\u00e8se o\u00f9 ces Xi sont ind\u00e9pendantes (c\u2019est-\u00e0-dire que le vote de Pierre n&rsquo;influence pas ceux de Paul et Jacques), al\u00e9atoires (c\u2019est-\u00e0-dire que c\u2019est bien des personnes diff\u00e9rentes avec des points de vue vari\u00e9s qui votent et pas Pierre qui vote N fois) et suivent la m\u00eame loi que X (c\u2019est-\u00e0-dire qu\u2019en moyenne, Pierre, Paul et Jacques se rapprochent de la v\u00e9rit\u00e9 de X au moins 50% du temps), alors nous pouvons dire que le choix du vote des N personnes sera le m\u00eame que le choix de X si le nombre de personnes N qui votent est assez grand.<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-93e682e elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"93e682e\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-67b1ec1\" data-id=\"67b1ec1\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-fd95ef6 elementor-widget elementor-widget-heading\" data-id=\"fd95ef6\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Mod\u00e9lisation algorithmique<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-934b7b5 elementor-widget elementor-widget-text-editor\" data-id=\"934b7b5\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><span style=\"color: #000000; font-size: 15px; font-weight: 400;\">Pour illustrer cela, nous allons simuler une exp\u00e9rience \u00e0 l\u2019aide d\u2019un algorithme. Nous allons soumettre un questionnaire de 20 questions \u00e0 plusieurs personnes. Chaque question sera r\u00e9pondue par vrai ou faux. Nous consid\u00e9rons ensuite pour chacune des 20 questions la r\u00e9ponse donn\u00e9e en majorit\u00e9 (donc issue d\u2019un vote).<\/span><\/p><p><span style=\"font-weight: 400; color: #000000;\">Dans la vid\u00e9o suivante, vous pouvez voir \u00e9voluer le pourcentage de bonnes r\u00e9ponses issues du vote, en fonction du nombre de participants. Nous avons pris comme hypoth\u00e8se que les participants sond\u00e9s avaient un taux de r\u00e9ussite de 55%.<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-ca7da87 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ca7da87\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-66bb053\" data-id=\"66bb053\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-615e6ad elementor-widget elementor-widget-video\" data-id=\"615e6ad\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/youtu.be\\\/n6km-WEMBts&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-widget-video .elementor-widget-container{overflow:hidden;transform:translateZ(0)}.elementor-widget-video .elementor-wrapper{aspect-ratio:var(--video-aspect-ratio)}.elementor-widget-video .elementor-wrapper iframe,.elementor-widget-video .elementor-wrapper video{height:100%;width:100%;display:flex;border:none;background-color:#000}@supports not (aspect-ratio:1\/1){.elementor-widget-video .elementor-wrapper{position:relative;overflow:hidden;height:0;padding-bottom:calc(100% \/ var(--video-aspect-ratio))}.elementor-widget-video .elementor-wrapper iframe,.elementor-widget-video .elementor-wrapper video{position:absolute;top:0;right:0;bottom:0;left:0}}.elementor-widget-video .elementor-open-inline .elementor-custom-embed-image-overlay{position:absolute;top:0;right:0;bottom:0;left:0;background-size:cover;background-position:50%}.elementor-widget-video .elementor-custom-embed-image-overlay{cursor:pointer;text-align:center}.elementor-widget-video .elementor-custom-embed-image-overlay:hover .elementor-custom-embed-play i{opacity:1}.elementor-widget-video .elementor-custom-embed-image-overlay img{display:block;width:100%;aspect-ratio:var(--video-aspect-ratio);-o-object-fit:cover;object-fit:cover;-o-object-position:center center;object-position:center center}@supports not (aspect-ratio:1\/1){.elementor-widget-video .elementor-custom-embed-image-overlay{position:relative;overflow:hidden;height:0;padding-bottom:calc(100% \/ var(--video-aspect-ratio))}.elementor-widget-video .elementor-custom-embed-image-overlay img{position:absolute;top:0;right:0;bottom:0;left:0}}.elementor-widget-video .e-hosted-video .elementor-video{-o-object-fit:cover;object-fit:cover}.e-con-inner>.elementor-widget-video,.e-con>.elementor-widget-video{width:var(--container-widget-width);--flex-grow:var(--container-widget-flex-grow)}<\/style>\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-98703be elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"98703be\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-6fe0b54\" data-id=\"6fe0b54\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-2a9bf2a elementor-widget elementor-widget-text-editor\" data-id=\"2a9bf2a\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><span style=\"font-size: 15px; font-weight: 400; color: #000000;\">On remarque que lorsqu&rsquo;on a que quelques participants (&lt;20), le taux de r\u00e9ussite du vote ne d\u00e9passe pas les 65%. Il est alors plus judicieux dans ce cas de faire confiance \u00e0 un seul expert dans le domaine (par exemple un \u00e9tudiant en pr\u00e9pa pour savoir si la formule pr\u00e9c\u00e9dente \u00e9tait vraie ou fausse) qui aurait un taux de r\u00e9ussite de 85% par exemple.<\/span><\/p><p><span style=\"font-size: 15px; font-weight: 400; color: #000000;\">En revanche, d\u00e8s que le nombre de participants est suffisamment grand (&gt;200), le taux de r\u00e9ussite du vote d\u00e9passe les 90%, il est donc meilleur que celui d\u2019un expert. Et rappelez-vous, chaque personne de cette foule ne pr\u00e9dit un r\u00e9sultat qu\u2019avec 55% de pr\u00e9cision et est donc \u00e0 peine meilleure que si elle r\u00e9pondait au hasard.\u00a0<\/span><\/p><p><span style=\"font-size: 15px; color: #000000;\"><span style=\"font-size: 15px; font-weight: 400;\">La puissance de ce ph\u00e9nom\u00e8ne, que l\u2019on appelle aussi la sagesse de la foule, repose dans le fait que m\u00eame si les votants r\u00e9pondent avec tr\u00e8s l\u00e9g\u00e8rement plus de justesse que s&rsquo;ils r\u00e9pondaient au hasard, alors le r\u00e9sultat de leur vote sera plus pr\u00e9cis que celui d\u2019un expert en la mati\u00e8re.<\/span><span style=\"font-size: 15px; font-weight: bold;\">\u00a0Il faut toutefois veiller \u00e0 avoir une foule de participants assez grande, diversifi\u00e9e et un minimum comp\u00e9tente.\u00a0<\/span><\/span><\/p><p><span style=\"font-size: 15px; font-weight: 400; color: #000000;\">\u00c0 l\u2019inverse, si nos participants sont \u00e0 peine moins bons que s\u2019ils r\u00e9pondaient au hasard, c\u2019est le ph\u00e9nom\u00e8ne contraire qui se produit et le r\u00e9sultat du vote n\u2019est alors jamais juste. Voici la m\u00eame simulation que pr\u00e9c\u00e9demment, mais cette fois-ci avec un taux de r\u00e9ussite de chaque participant de 45%.<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-717e7797 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"717e7797\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-12a6bb8b\" data-id=\"12a6bb8b\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-3ba672e3 elementor-align-center button-principale elementor-widget elementor-widget-button\" data-id=\"3ba672e3\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm elementor-animation-grow\" href=\"https:\/\/datascientest.com\/formation-data-scientist\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Apprendre \u00e0 d\u00e9velopper des algorithmes<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-b068f4e elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b068f4e\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-7b9e89e\" data-id=\"7b9e89e\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-9e38b67 elementor-widget elementor-widget-video\" data-id=\"9e38b67\" data-element_type=\"widget\" data-settings=\"{&quot;youtube_url&quot;:&quot;https:\\\/\\\/youtu.be\\\/mIdWUM_XXRc&quot;,&quot;video_type&quot;:&quot;youtube&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-wrapper elementor-open-inline\">\n\t\t\t<div class=\"elementor-video\"><\/div>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-232fc6e elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"232fc6e\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-2d0b417\" data-id=\"2d0b417\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-53ff4db elementor-widget elementor-widget-text-editor\" data-id=\"53ff4db\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\tLa probabilit\u00e9 de v\u00e9racit\u00e9 du r\u00e9sultat du vote tend alors vers 0.\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-64dd17a elementor-widget elementor-widget-heading\" data-id=\"64dd17a\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Conclusion<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-54e7921 elementor-widget elementor-widget-text-editor\" data-id=\"54e7921\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><span style=\"font-weight: 400; color: #000000;\">Gr\u00e2ce \u00e0 la loi des grands nombres, il sera toujours pr\u00e9f\u00e9rable de suivre le choix d\u2019une foule d\u2019individus plut\u00f4t que celui d\u2019un expert, du moment qu\u2019ils sont assez nombreux, al\u00e9atoires, ind\u00e9pendants entre eux et qu\u2019ils savent faire un choix qui est en moyenne meilleure que le hasard (m\u00eame tr\u00e8s l\u00e9g\u00e8rement).<\/span><\/p><p><span style=\"font-weight: 400;\"><span style=\"color: #000000;\">Si un jour vous vous retrouvez devant Jean-Pierre Foucault et qu\u2019il vous reste le vote du public et l\u2019appel \u00e0 un ami, \u00e0 qui ferez-vous confiance ?<\/span> <\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-00995e5 elementor-align-center button-principale elementor-widget elementor-widget-button\" data-id=\"00995e5\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm elementor-animation-grow\" href=\"https:\/\/datascientest.com\/formations-data\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">D\u00e9couvrir nos formations<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Le vote d\u00e9mocratique est une solution \u00e0 laquelle nous avons souvent recours pour prendre une d\u00e9cision en groupe et qui a \u00e9t\u00e9 commun\u00e9ment admise dans notre soci\u00e9t\u00e9. Son int\u00e9r\u00eat repose sur la loi des grands nombres, un principe math\u00e9matique qui permet d\u2019approcher la probabilit\u00e9 d\u2019un \u00e9v\u00e9nement par la fr\u00e9quence de sa r\u00e9alisation. Que ce soit [&hellip;]<\/p>\n","protected":false},"author":77,"featured_media":65856,"comment_status":"open","ping_status":"open","sticky":false,"template":"elementor_theme","format":"standard","meta":{"content-type":"","inline_featured_image":false},"categories":[2497],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v21.7 (Yoast SEO v21.7) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Loi des grands nombres et vote d\u00e9mocratique<\/title>\n<meta name=\"description\" content=\"Le vote d\u00e9mocratique est une solution \u00e0 laquelle nous avons souvent recours pour prendre une d\u00e9cision en groupe et qui a \u00e9t\u00e9 commun\u00e9ment admise dans notre soci\u00e9t\u00e9. Son int\u00e9r\u00eat repose sur la loi des grands nombres, un principe math\u00e9matique qui permet d\u2019approcher la probabilit\u00e9 d\u2019un \u00e9v\u00e9nement par la fr\u00e9quence de sa r\u00e9alisation\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/datascientest.com\/loi-des-grands-nombres-et-vote-democratique\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Loi des grands nombres et vote d\u00e9mocratique\" \/>\n<meta property=\"og:url\" content=\"https:\/\/datascientest.com\/loi-des-grands-nombres-et-vote-democratique\" \/>\n<meta property=\"og:site_name\" content=\"Formation Data Science | DataScientest.com\" \/>\n<meta property=\"article:published_time\" content=\"2021-05-03T07:34:20+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2023-11-09T14:07:27+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/datascientest.com\/wp-content\/uploads\/2021\/03\/illu_loigrandnombre-147.png\" \/>\n\t<meta property=\"og:image:width\" content=\"1024\" \/>\n\t<meta property=\"og:image:height\" content=\"562\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"author\" content=\"Raphael Kassel\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u00c9crit par\" \/>\n\t<meta name=\"twitter:data1\" content=\"Raphael Kassel\" \/>\n\t<meta name=\"twitter:label2\" content=\"Dur\u00e9e de lecture estim\u00e9e\" \/>\n\t<meta name=\"twitter:data2\" content=\"5 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/datascientest.com\/loi-des-grands-nombres-et-vote-democratique\",\"url\":\"https:\/\/datascientest.com\/loi-des-grands-nombres-et-vote-democratique\",\"name\":\"Loi des grands nombres et vote d\u00e9mocratique\",\"isPartOf\":{\"@id\":\"https:\/\/datascientest.com\/#website\"},\"datePublished\":\"2021-05-03T07:34:20+00:00\",\"dateModified\":\"2023-11-09T14:07:27+00:00\",\"author\":{\"@id\":\"https:\/\/datascientest.com\/#\/schema\/person\/6eca16f63daaafcbc96e15549b9d4ee1\"},\"description\":\"Le vote d\u00e9mocratique est une solution \u00e0 laquelle nous avons souvent recours pour prendre une d\u00e9cision en groupe et qui a \u00e9t\u00e9 commun\u00e9ment admise dans notre soci\u00e9t\u00e9. 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