{"id":19994,"date":"2015-12-15T14:03:06","date_gmt":"2015-12-15T10:03:06","guid":{"rendered":"https:\/\/uic.am\/19994"},"modified":"2015-12-15T14:03:06","modified_gmt":"2015-12-15T10:03:06","slug":"statistical-analysis-of-the-ra-constitutional-amendments-referendum","status":"publish","type":"post","link":"https:\/\/uic.am\/en\/19994","title":{"rendered":"Statistical Analysis of the RA Constitutional Amendments Referendum"},"content":{"rendered":"<p>&nbsp;<\/p>\n<h1>Linear Regression<\/h1>\n<p>The graph shows the dependency of the percentage of people who voted \u201cyes\u201d on the percentage of voter turnout. The dots correspond to the preliminary results from all the 1997 polling stations. The percentage of \u201cyes\u201d votes&#8221; is high in those polling stations where high turnout was recorded. Regression line coefficient k=0,938: Ideally, we should have k=0, that is, the result should not depend on voter turnout. If ballot stuffing does not occur, on average we should have the same result in all the polling stations irrespective of voter turnout. In case of k&gt;0, we deal with ballot stuffing. In our case, on average the percentage of \u201cyes\u201d votes is in explicit proportion to the percentage of voter turnout. That is also substantiated by the fact that in case of double voting, ballot stuffing and falsification of results protocols, not only \u201cyes\u201d votes increase, but also the voter turnout becomes higher.<\/p>\n<p><a href=\"https:\/\/uic.am\/wp-content\/uploads\/2015\/12\/stateng01.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-1276\" src=\"https:\/\/uic.am\/wp-content\/uploads\/2015\/12\/stateng01-300x275.jpg\" alt=\"stateng01\" width=\"300\" height=\"275\" srcset=\"https:\/\/uic.am\/wp-content\/uploads\/2015\/12\/stateng01-300x275.jpg 300w, https:\/\/uic.am\/wp-content\/uploads\/2015\/12\/stateng01-600x550.jpg 600w, https:\/\/uic.am\/wp-content\/uploads\/2015\/12\/stateng01.jpg 700w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<p>Some opponents of this methodology claim that the active participation is related to the fact that the \u201cyes\u201d proponents were more eager to go to the polling stations and vote. However, we do not observe such tendencies in Switzerland, where referendums are held most frequently.\u00a0 Below you can find respective <a href=\"http:\/\/www.pnas.org\/content\/109\/41\/16469.fullv\">graphs<\/a> of elections in different countries. They are aimed at statistical revelation of election fraud. Our graph is similar to those of Uganda and Russia.<\/p>\n<p><a href=\"https:\/\/uic.am\/wp-content\/uploads\/2015\/12\/stateng02.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-1277\" src=\"https:\/\/uic.am\/wp-content\/uploads\/2015\/12\/stateng02-300x226.jpg\" alt=\"stateng02\" width=\"300\" height=\"226\" srcset=\"https:\/\/uic.am\/wp-content\/uploads\/2015\/12\/stateng02-300x226.jpg 300w, https:\/\/uic.am\/wp-content\/uploads\/2015\/12\/stateng02-600x453.jpg 600w, https:\/\/uic.am\/wp-content\/uploads\/2015\/12\/stateng02-174x131.jpg 174w, https:\/\/uic.am\/wp-content\/uploads\/2015\/12\/stateng02-70x53.jpg 70w, https:\/\/uic.am\/wp-content\/uploads\/2015\/12\/stateng02.jpg 700w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<p>There is one more interesting observation: as the percentage of \u201cno\u201d votes decreases along with increase of voter turnout, the percentage of invalid\/spoilt ballots also decreases. That is, the lower the voter turnout, the lower the percentage of invalid ballots. This allows us to assume that in the polling stations where low voter turnout was registered, and where it was not possible to add \u201cyes\u201d votes, the method of making \u201cno\u201d ballots invalid has been applied.<\/p>\n<p><a href=\"https:\/\/uic.am\/wp-content\/uploads\/2015\/12\/stateng032.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-1289\" src=\"https:\/\/uic.am\/wp-content\/uploads\/2015\/12\/stateng032-300x235.jpg\" alt=\"stateng03\" width=\"300\" height=\"235\" srcset=\"https:\/\/uic.am\/wp-content\/uploads\/2015\/12\/stateng032-300x235.jpg 300w, https:\/\/uic.am\/wp-content\/uploads\/2015\/12\/stateng032-600x471.jpg 600w, https:\/\/uic.am\/wp-content\/uploads\/2015\/12\/stateng032.jpg 622w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<p><strong>The distribution of percentage of \u201cYes\u201d votes does not represent normal distribution. <\/strong><\/p>\n<p><strong>The concept of normal distribution in statistics<\/strong><strong>. <\/strong>Normal or Gaussian distribution represents such a distribution of values in case of which those values are probable (among different values) which are close to the mean of all the values. Moreover, the larger the deviation of the value is from the mean, the smaller the possibility of encountering it. In case of such distribution, we can say that all the values are subject to a common law. Roughly speaking, in our case the distribution will be normal, if 63% \u201cyes\u201d is registered in the largest number of polling stations. In other words, the most probable result should coincide with the average index. The polling stations that registered larger or smaller number of \u201cyes\u201d votes compared to the mean (63%) should be smaller in number. Moreover, the larger the difference from the mean, the smaller the probability should be. If distribution is not normal, it is assumed that the principle of randomness has been violated. In our particular case, the latter means that voting irregularities (election fraud) have occurred. There are tests that allow us to check the normality of distribution. Those are Kolmogorov-Smirnov, D\u2019Agostino-Pierson and Shapiro-Wilkie tests. In our case, all the test results indicate that the distribution is not normal. It is worth mentioning that there are numerous precedents of checking the presence of election fraud in this specific way. Particularly, normal distribution is observed in elections in Switzerland and Canada. However, we cannot say the same about elections in Russia.<\/p>\n<p>Thus, the histogram shown in the picture below clearly shows that 80% is the most recurrent one, which can be found in 186 polling stations.<\/p>\n<p><a href=\"https:\/\/uic.am\/wp-content\/uploads\/2015\/12\/stateng04.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-1279\" src=\"https:\/\/uic.am\/wp-content\/uploads\/2015\/12\/stateng04-300x246.jpg\" alt=\"stateng04\" width=\"300\" height=\"246\" srcset=\"https:\/\/uic.am\/wp-content\/uploads\/2015\/12\/stateng04-300x246.jpg 300w, https:\/\/uic.am\/wp-content\/uploads\/2015\/12\/stateng04-600x493.jpg 600w, https:\/\/uic.am\/wp-content\/uploads\/2015\/12\/stateng04.jpg 700w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<p>A second peak can also be observed in the histogram \u2013 35%, which has been found in 109 polling stations. Hence, we can assume that we have two peaks, and, consequently, two distributions and two patterns. If we give a very rough assessment, we can speculate that the first pattern -35% expressed the true picture, and the second pattern corresponds to rigged polling stations, where up to 80% was rigged. As a result, the mean value in the republic has resulted to be 63%.<\/p>\n<p><a href=\"https:\/\/uic.am\/wp-content\/uploads\/2015\/12\/stateng05.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-1280\" src=\"https:\/\/uic.am\/wp-content\/uploads\/2015\/12\/stateng05-300x245.jpg\" alt=\"stateng05\" width=\"300\" height=\"245\" srcset=\"https:\/\/uic.am\/wp-content\/uploads\/2015\/12\/stateng05-300x245.jpg 300w, https:\/\/uic.am\/wp-content\/uploads\/2015\/12\/stateng05-600x490.jpg 600w, https:\/\/uic.am\/wp-content\/uploads\/2015\/12\/stateng05.jpg 700w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<p>The same two peaks can also be observed in the histogram of \u201cno\u201d votes. The first peak is observed on 15% (200 polling stations), the second peak \u2013 on 60% (120 polling stations).<\/p>\n<p>Such \u201cdouble hump\u201d histograms can be observed in countries where different regions have serious differences. For instance, in Belgium, French-speaking and Flemish-speaking regions are largely different and, hence, such an election outcome is possible. Another example is Spain, where two regions want to secede and, hence, display different tendencies during elections. Nevertheless, all the marzes (regions) of Armenia have the same national, religious, linguistic and social structure. Armenia itself is a unitary state. In other words, there is no border in our country beyond which there are people who have radically different views. Consequently, we can exclude the generation of such \u201cdouble-peaked\u201d histograms of elections without falsifications.<\/p>\n<h1>Results for Polling Stations with Low Voter Turnout<\/h1>\n<p>It is known that the number of adult population in the republic is less than the number included in the electoral list by as much as 20-25%. Consequently, the polling stations that have registered more than 60-70% voter turnout should arouse doubt. For that reason, a widespread method of checking is the comparison of results by polling stations with low turnout and those with high turnout. If the elections have been fair, the same result should be registered in polling stations with low voter turnout as well.<\/p>\n<p>However, we have the following picture: in 600 polling stations with the lowest voter turnout, \u201cyes\u201d has got 43%, and \u201cno\u201d has got 52%. In 800 polling stations with the lowest voter turnout, \u201cyes\u201d has got 46% and \u201cno\u201d has got \u201c48%\u201d. In 1000 polling stations with the lowest voter turnout, \u201cyes\u201d has got 49% and \u201cno\u201d has got 45%. And in the 998 polling stations with the highest voter turnout, \u201cyes\u201d has got 75% and \u201cno\u201d has got 22%.<\/p>\n<p><a href=\"https:\/\/uic.am\/wp-content\/uploads\/2015\/12\/stateng061.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-1290\" src=\"https:\/\/uic.am\/wp-content\/uploads\/2015\/12\/stateng061-300x114.jpg\" alt=\"stateng06\" width=\"300\" height=\"114\" srcset=\"https:\/\/uic.am\/wp-content\/uploads\/2015\/12\/stateng061-300x114.jpg 300w, https:\/\/uic.am\/wp-content\/uploads\/2015\/12\/stateng061-600x228.jpg 600w, https:\/\/uic.am\/wp-content\/uploads\/2015\/12\/stateng061-620x237.jpg 620w, https:\/\/uic.am\/wp-content\/uploads\/2015\/12\/stateng061.jpg 624w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<p><a href=\"https:\/\/uic.am\/wp-content\/uploads\/2015\/12\/stateng071.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-1291\" src=\"https:\/\/uic.am\/wp-content\/uploads\/2015\/12\/stateng071-300x114.jpg\" alt=\"stateng07\" width=\"300\" height=\"114\" srcset=\"https:\/\/uic.am\/wp-content\/uploads\/2015\/12\/stateng071-300x114.jpg 300w, https:\/\/uic.am\/wp-content\/uploads\/2015\/12\/stateng071-600x228.jpg 600w, https:\/\/uic.am\/wp-content\/uploads\/2015\/12\/stateng071-620x237.jpg 620w, https:\/\/uic.am\/wp-content\/uploads\/2015\/12\/stateng071.jpg 625w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<p><a href=\"https:\/\/uic.am\/wp-content\/uploads\/2015\/12\/stateng081.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-1292\" src=\"https:\/\/uic.am\/wp-content\/uploads\/2015\/12\/stateng081-300x114.jpg\" alt=\"stateng08\" width=\"300\" height=\"114\" srcset=\"https:\/\/uic.am\/wp-content\/uploads\/2015\/12\/stateng081-300x114.jpg 300w, https:\/\/uic.am\/wp-content\/uploads\/2015\/12\/stateng081-600x228.jpg 600w, https:\/\/uic.am\/wp-content\/uploads\/2015\/12\/stateng081-620x237.jpg 620w, https:\/\/uic.am\/wp-content\/uploads\/2015\/12\/stateng081.jpg 625w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<p><a href=\"https:\/\/uic.am\/wp-content\/uploads\/2015\/12\/stateng091.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-1293\" src=\"https:\/\/uic.am\/wp-content\/uploads\/2015\/12\/stateng091-300x114.jpg\" alt=\"stateng09\" width=\"300\" height=\"114\" srcset=\"https:\/\/uic.am\/wp-content\/uploads\/2015\/12\/stateng091-300x114.jpg 300w, https:\/\/uic.am\/wp-content\/uploads\/2015\/12\/stateng091-600x228.jpg 600w, https:\/\/uic.am\/wp-content\/uploads\/2015\/12\/stateng091-620x237.jpg 620w, https:\/\/uic.am\/wp-content\/uploads\/2015\/12\/stateng091.jpg 625w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<p>Such a picture can have only one explanation: in the polling stations where the \u201cyes\u201d proponents have had an opportunity to make an evidently false results protocol (that is, de facto there was no representative of \u201cno\u201d in these polling stations), a few techniques have been used \u2013 not only have \u201cno\u201d votes been moved to \u201cyes\u201d votes, but also the ballots of citizens who did not vote were attributed to the \u201cyes\u201d votes.<\/p>\n<p>The point is that by the current legislation, persons who have not been present in the polling station, cannot demand recounting of votes. Hence, if all those who are present in the polling station\u00a0 are accomplices of the falsification, there is no possibility for recounting to take place. \u00a0As a result of that circumstance, a possibility arsies to add all the possible ballots to the \u201cyes\u201d votes in the polling stations where no proper control was ensured. As a result, very high turnout and an extremely high number of \u201cyes\u201d votes is \u201cregistered\u201d in these polling stations (which, naturally, has nothing to do with the expression of will of the citizens).<\/p>\n<p><em>Union of Informed Citizens<\/em><\/p>\n<p><a href=\"https:\/\/uic.am\/wp-content\/uploads\/2016\/01\/Stat-english.pdf\">Download full version (PDF)<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>&nbsp; Linear Regression The graph shows the dependency of the percentage of people who voted \u201cyes\u201d on the percentage of voter turnout. The dots correspond to the preliminary results from all the 1997 polling stations. The percentage of \u201cyes\u201d votes&#8221; is high in those polling stations where high turnout was recorded. Regression line coefficient k=0,938:<\/p>\n","protected":false},"author":2,"featured_media":23599,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2164],"tags":[],"class_list":["post-19994","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-elections"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 5.0.5 - aioseo.com -->\n\t<meta name=\"description\" content=\"Linear Regression The graph shows the dependency of the percentage of people who voted \u201cyes\u201d on the percentage of voter turnout. The dots correspond to the preliminary results from all the 1997 polling stations. The percentage of \u201cyes\u201d votes&quot; is high in those polling stations where high turnout was recorded. Regression line coefficient k=0,938:\" \/>\n\t<meta name=\"robots\" content=\"max-image-preview:large\" \/>\n\t<meta name=\"author\" content=\"uicadmin\"\/>\n\t<link rel=\"canonical\" href=\"https:\/\/uic.am\/en\/19994\" \/>\n\t\t<meta name=\"generator\" content=\"All in One SEO (AIOSEO) 5.0.5\" \/>\n\t\t<meta property=\"og:locale\" content=\"en_US\" \/>\n\t\t<meta property=\"og:site_name\" content=\"Union of Informed Citizens -\" \/>\n\t\t<meta property=\"og:type\" content=\"article\" \/>\n\t\t<meta property=\"og:title\" content=\"Statistical Analysis of the RA Constitutional Amendments Referendum - Union of Informed Citizens\" \/>\n\t\t<meta property=\"og:description\" content=\"Linear Regression The graph shows the dependency of the percentage of people who voted \u201cyes\u201d on the percentage of voter turnout. The dots correspond to the preliminary results from all the 1997 polling stations. The percentage of \u201cyes\u201d votes&quot; is high in those polling stations where high turnout was recorded. Regression line coefficient k=0,938:\" \/>\n\t\t<meta property=\"og:url\" content=\"https:\/\/uic.am\/en\/19994\" \/>\n\t\t<meta property=\"article:published_time\" content=\"2015-12-15T10:03:06+00:00\" \/>\n\t\t<meta property=\"article:modified_time\" content=\"2015-12-15T10:03:06+00:00\" \/>\n\t\t<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n\t\t<meta name=\"twitter:title\" content=\"Statistical Analysis of the RA Constitutional Amendments Referendum - Union of Informed Citizens\" \/>\n\t\t<meta name=\"twitter:description\" content=\"Linear Regression The graph shows the dependency of the percentage of people who voted \u201cyes\u201d on the percentage of voter turnout. The dots correspond to the preliminary results from all the 1997 polling stations. The percentage of \u201cyes\u201d votes&quot; is high in those polling stations where high turnout was recorded. Regression line coefficient k=0,938:\" \/>\n\t\t<script type=\"application\/ld+json\" class=\"aioseo-schema\">\n\t\t\t{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"BlogPosting\",\"@id\":\"https:\\\/\\\/uic.am\\\/en\\\/19994#blogposting\",\"name\":\"Statistical Analysis of the RA Constitutional Amendments Referendum - Union of Informed Citizens\",\"headline\":\"Statistical Analysis of the RA Constitutional Amendments Referendum\",\"author\":{\"@id\":\"https:\\\/\\\/uic.am\\\/en\\\/author\\\/uicadmin#author\"},\"publisher\":{\"@id\":\"https:\\\/\\\/uic.am\\\/en\\\/#organization\"},\"image\":{\"@type\":\"ImageObject\",\"url\":\"https:\\\/\\\/uic.am\\\/wp-content\\\/uploads\\\/2015\\\/12\\\/statarm06.jpg\",\"width\":640,\"height\":252},\"datePublished\":\"2015-12-15T14:03:06+04:00\",\"dateModified\":\"2015-12-15T14:03:06+04:00\",\"inLanguage\":\"en-US\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/uic.am\\\/en\\\/19994#webpage\"},\"isPartOf\":{\"@id\":\"https:\\\/\\\/uic.am\\\/en\\\/19994#webpage\"},\"articleSection\":\"Elections, Optional\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/uic.am\\\/en\\\/19994#breadcrumblist\",\"itemListElement\":[{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/uic.am\\\/en\\\/#listItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\\\/\\\/uic.am\\\/en\\\/\",\"nextItem\":{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/uic.am\\\/en\\\/category\\\/elections#listItem\",\"name\":\"Elections\"}},{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/uic.am\\\/en\\\/category\\\/elections#listItem\",\"position\":2,\"name\":\"Elections\",\"item\":\"https:\\\/\\\/uic.am\\\/en\\\/category\\\/elections\",\"nextItem\":{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/uic.am\\\/en\\\/19994#listItem\",\"name\":\"Statistical Analysis of the RA Constitutional Amendments Referendum\"},\"previousItem\":{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/uic.am\\\/en\\\/#listItem\",\"name\":\"Home\"}},{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/uic.am\\\/en\\\/19994#listItem\",\"position\":3,\"name\":\"Statistical Analysis of the RA Constitutional Amendments Referendum\",\"previousItem\":{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/uic.am\\\/en\\\/category\\\/elections#listItem\",\"name\":\"Elections\"}}]},{\"@type\":\"Organization\",\"@id\":\"https:\\\/\\\/uic.am\\\/en\\\/#organization\",\"name\":\"[:hy]\\u053b\\u0580\\u0561\\u0566\\u0565\\u056f \\u0584\\u0561\\u0572\\u0561\\u0584\\u0561\\u0581\\u056b\\u0576\\u0565\\u0580\\u056b \\u0574\\u056b\\u0561\\u057e\\u0578\\u0580\\u0578\\u0582\\u0574[:en]Union of Informed Citizens[:ru]\\u0421\\u043e\\u044e\\u0437 \\u0438\\u043d\\u0444\\u043e\\u0440\\u043c\\u0438\\u0440\\u043e\\u0432\\u0430\\u043d\\u043d\\u044b\\u0445 \\u0433\\u0440\\u0430\\u0436\\u0434\\u0430\\u043d\",\"url\":\"https:\\\/\\\/uic.am\\\/en\\\/\"},{\"@type\":\"Person\",\"@id\":\"https:\\\/\\\/uic.am\\\/en\\\/author\\\/uicadmin#author\",\"url\":\"https:\\\/\\\/uic.am\\\/en\\\/author\\\/uicadmin\",\"name\":\"uicadmin\",\"image\":{\"@type\":\"ImageObject\",\"@id\":\"https:\\\/\\\/uic.am\\\/en\\\/19994#authorImage\",\"url\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/04e572d0723517f2413aa7ca9fd8231515a7d6248f02ff9837b4af90abc626ee?s=96&d=blank&r=g\",\"width\":96,\"height\":96,\"caption\":\"uicadmin\"}},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/uic.am\\\/en\\\/19994#webpage\",\"url\":\"https:\\\/\\\/uic.am\\\/en\\\/19994\",\"name\":\"Statistical Analysis of the RA Constitutional Amendments Referendum - Union of Informed Citizens\",\"description\":\"Linear Regression The graph shows the dependency of the percentage of people who voted \\u201cyes\\u201d on the percentage of voter turnout. 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The dots correspond to the preliminary results from all the 1997 polling stations. The percentage of \u201cyes\u201d votes\" is high in those polling stations where high turnout was recorded. 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