## Analysis of Venezuela's referendum counts## By Jonathan TaylorI was asked by Dr. Jennifer McCoy of the Carter Center, to look at the machine by machine counts of the recall election in Venezuela, specifically to see if there was any evidence of the opposition's claim of election fraud. The main issue I was asked to look at was the number of ties both for SI and NO at each mesa and determine if there were an excessive number of ties for SI.
- A model based on the empirical SI votes across all machines. R code
- A Poisson model with one parameter shared by all machines. R code
- A Poisson model with a parameter varying by mesa. R code
- A multinomial model where the SI votes are redistributed across all machines within a mesa (p=(1/3,1/3,1/3) if there were three machines, p=(1/2,1/2) if there were two machines). R code
- A parametric bootstrap model for the counts in each machine within each mesa, having conditionally independent Binomial counts within each machine with probability of success the observed proportion of SI votes within the mesa. R code
- Another parametric bootstrap model, where the residuals were resampled assuming they were (conditionally) independent (given the counts). This was a mistake (see below). R code
## Correction to the results in The EconomistThere was an error in the figures quoted by the Economist in an article written by Dr. McCoy. The figures were based on the above parametric bootstrap model, and the error was based on a mistake on my part. Specifically, I fit a multivariate normal to the scaled residuals between the number of votes in a
given machine and the total number of votes in the
mesa (scaled by the square root of the total number of votes in each
mesa). Unfortunately, in my first models, I made the significant error
by ignoring the multivariate
aspect of the residuals and generated ## Results for SI
Standard errors above are based on a Poisson approximation, as the number of ties is (under all of these models) the sum of many independent, rare counts. It is likely a slight underestimate of the true standard error. ## Results for NO
Standard errors above are based on a Poisson approximation, as the number of ties is (under all of these models) the sum of many independent, rare counts. It is likely a slight underestimate of the true standard error. ## SummaryIt seems that an expected number of ties between 345 and 350 is reasonable, as it came out from many different models. Using the Poisson assumption to estimate the standard error, it seems then that the probability of observing 402 or more ties for SI is between 1 and 3 in 1000. While this probability is small, I do not feel that it should be interpreted as overwhelming evidence of fraud.
## © by Vcrisis.com & the author |