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  24 6. All-Russian Political Party "UNITED RUSSIA" 4278 39.77%
  24 6. All-Russian Political Party "UNITED RUSSIA" 4278 39.77%
  25 7. All-Russian Political Party "CASE RIGHT" 53 0.49%
  25 7. All-Russian Political Party "CASE RIGHT" 53 0.49%
===Hierarchial Bayesian model===
This model assesses the data from the election based on the following assumptions:
* The honest vote distribution is based on a multinomial distribution Y<sub>i,j</sub> ~ MULTINOM(nh, P) with parameters
** n<sub>h</sub> = number of honest votes given
** P = DIR(p<sub>i</sub>) = Dirichlet probability of the party i to receive a vote
** p<sub>i</sub> is the same for all election commissions. There is only random variation between the commissions.
* In addition, there may be fabricated votes that within one commission are given to only one political party.
** Thus, the total observed votes n<sub>t</sub> is the sum of the number of honest votes n<sub>h</sub> and the number of fabricated votes n<sub>f</sub>, where n<sub>f</sub> must be within the range (0, max(n<sub>t,i</sub>), i.e. at most as many votes as the largest party has received total votes.
** The number of fabricated votes in a commission is a random variable that is binomially distributed BINOM(max(n<sub>t,i</sub>), p<sub>j</sub>), where p<sub>j</sub> is a commission-specific probability of getting a fabricated vote when a random vote is picked from the pile of votes to the largest party.
*** Some notes are important. First, we do not claim that the most popular party is always the one that is fabricating votes. We use that estimate because if only one party fabricates votes, the number of fabricated votes cannot be larger than this, and it is therefore a plausible and practical upper limit for calculations; if the data shows that the fabricating party is another one or the number of fabricated votes is smaller, this will show up in the parameter estimates.
* The fraction F<sub>j</sub> of honest votes (n<sub>h</sub>) out of the total eligible voters n<sub>e</sub> in a commission is a random variable following beta distribution F<sub>j</sub> ~ Beta(alpha, beta). Therefore, if the fraction is much higher than expected in a commission, the probability that there are fabricated votes goes up.
This will result in a hierarchical Bayes model with the following structure:
<pre>
NOTE! This model is just a placeholder.
model
{
for (i in 1 : nChild) {
theta[i] ~ dnorm(0.0, 0.001)
for (j in 1 : nInd) {
# Cumulative probability of > grade k given theta
for (k in 1: ncat[j] - 1) {
logit(Q[i, j, k]) <- delta[j] * (theta[i] - gamma[j, k])
}
}
# Probability of observing grade k given theta
for (j in 1 : nInd) {
p[i, j, 1] <- 1 - Q[i, j, 1]
for (k in 2 : ncat[j] - 1) {
p[i, j, k] <- Q[i, j, k - 1] - Q[i, j, k]
}
p[i, j, ncat[j]] <- Q[i, j, ncat[j] - 1]
grade[i, j] ~ dcat(p[i, j, 1 : ncat[j]])
cumulative.grade[i, j] <- cumulative(grade[i, j], grade[i, j])
}
}
</pre>


==Aiheeseen liittyviä tiedostoja==
==Aiheeseen liittyviä tiedostoja==

Versio 17. joulukuuta 2011 kello 18.27




Venäjän vaalit 2011 käsittelee duuman vaaleja 4.11.2011.

Tulos

{{#opasnet_base_link:Op_fi2768}}


Perustelut


The election results
Elections to the State Duma of the Federal Assembly of the Sixth Convocation
Date of vote: 12/04/2011
Name of the Election Commission 	Babayevskaya
Date and time of signing the protocol 5/12/2011 9:00:00
A 	Number of voters included in voters list 						18 947
2 	The number of ballots received by the precinct election commission 			17 294
3 	The number of ballots issued to voters who voted early 					0
4 	The number of ballots issued to voters at the polling 					9001
5 	The number of ballots issued to voters outside the polling station 			1761
6 	The number of canceled ballots 								6532
7 	The number of ballots in mobile ballot boxes 						1761
8 	The number of ballots in the stationary ballot boxes 					8995
9 	Number of invalid ballots 								201
10 	Number of valid ballots 								10 555
11 	The number of absentee ballots received by the precinct election commission 		795
12 	The number of absentee ballots issued to voters at a polling station 			549
13 	The number of voters who voted with absentee ballots at a polling station 		346
14 	The number of the unused absentee ballots 						246
15 	The number of absentee ballots issued to voters of the territorial election commission 	94
16 	Number of lost absentee ballots 							0
17 	The number of lost ballots 								0
18 	The number of ballots not recorded in obtaining 					0 
19 	1. Political party JUST RUSSIA 								2769 	25.74%
20 	2. Political Party "Liberal Democratic Party of Russia" 				1617 	15.3%
21 	3. Political Party "PATRIOTS OF RUSSIA" 						107 	0.99%
22 	4. Political party "Communist Party of the Russian Federation" 				1570 	14.60%
23 	5. A political party "Russian United Democratic Party" Yabloko " 			161 	1.50%
24 	6. All-Russian Political Party "UNITED RUSSIA" 						4278 	39.77%
25 	7. All-Russian Political Party "CASE RIGHT" 						53 	0.49%

Hierarchial Bayesian model

This model assesses the data from the election based on the following assumptions:

  • The honest vote distribution is based on a multinomial distribution Yi,j ~ MULTINOM(nh, P) with parameters
    • nh = number of honest votes given
    • P = DIR(pi) = Dirichlet probability of the party i to receive a vote
    • pi is the same for all election commissions. There is only random variation between the commissions.
  • In addition, there may be fabricated votes that within one commission are given to only one political party.
    • Thus, the total observed votes nt is the sum of the number of honest votes nh and the number of fabricated votes nf, where nf must be within the range (0, max(nt,i), i.e. at most as many votes as the largest party has received total votes.
    • The number of fabricated votes in a commission is a random variable that is binomially distributed BINOM(max(nt,i), pj), where pj is a commission-specific probability of getting a fabricated vote when a random vote is picked from the pile of votes to the largest party.
      • Some notes are important. First, we do not claim that the most popular party is always the one that is fabricating votes. We use that estimate because if only one party fabricates votes, the number of fabricated votes cannot be larger than this, and it is therefore a plausible and practical upper limit for calculations; if the data shows that the fabricating party is another one or the number of fabricated votes is smaller, this will show up in the parameter estimates.
  • The fraction Fj of honest votes (nh) out of the total eligible voters ne in a commission is a random variable following beta distribution Fj ~ Beta(alpha, beta). Therefore, if the fraction is much higher than expected in a commission, the probability that there are fabricated votes goes up.

This will result in a hierarchical Bayes model with the following structure:

NOTE! This model is just a placeholder.

model
	{
		for (i in 1 : nChild) {
			theta[i] ~ dnorm(0.0, 0.001)
			for (j in 1 : nInd) { 
	# Cumulative probability of > grade k given theta
				for (k in 1: ncat[j] - 1) {
					logit(Q[i, j, k]) <- delta[j] * (theta[i] - gamma[j, k])
				}
			}

	# Probability of observing grade k given theta
			for (j in 1 : nInd) {
				p[i, j, 1] <- 1 - Q[i, j, 1]
				for (k in 2 : ncat[j] - 1) {
					p[i, j, k] <- Q[i, j, k - 1] - Q[i, j, k]
				}
				p[i, j, ncat[j]] <- Q[i, j, ncat[j] - 1]
				grade[i, j] ~ dcat(p[i, j, 1 : ncat[j]])
				cumulative.grade[i, j] <- cumulative(grade[i, j], grade[i, j])
			}
		}
	}   

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