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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
Tämä sivu on tutkimus.
Sivutunniste: Op_fi2768 |
|---|
| Moderaattori:Ei ole (katso kaikki) Kuinka ryhtyä moderaattoriksi? Sivun edistymistä ei ole arvioitu. Arvostuksen määrää ei ole arvioitu (ks. peer review). |
| Lisää dataa
|
Venäjän vaalit 2011 käsittelee duuman vaaleja 4.11.2011.
Tulos
{{#opasnet_base_link:Op_fi2768}}
Perustelut
- An election commission
- Äänestysdata Opasnet Basessa
- Data löytyy täältä: http://peregrins.com/elect/results.csv.gz
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])
}
}
}
Aiheeseen liittyviä tiedostoja
Vaalien tulokset äänestysalueittain.
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