Why 2013 elections were rigged – a statistical analysis


The ECP should make sure nobody steals a voter’s right



Were the 2013 elections rigged? There is blood on the constitution avenue and thousands of people protesting against rigged elections. By some media reports there were at least 49 polling stations in the 2013 elections, registering a voter turnout of more than 100 per cent and some of the Election Commission of Pakistan (ECP) officials (including an ex-additional secretary) have come out supporting claims of vote rigging. Given this, it is time to look at the data from the ECP and put it to the test. What follows is to the best of my knowledge the first and most detailed comparison of election results of 2008 and 2013.

When we compare data from the 2008 and 2013 elections we can see that there are clear signs of suspicious activity and rigging in the 2013 elections. Using data from the ECP and using measures like skewness, extra votes cast and confidence intervals we can not only see how many suspicious votes were cast, but also in which seats rigging may have taken place. There are several reasons why comparing 2008 and 2013 elections make sense. For one, they are consecutive elections. Secondly, the incumbents in 2008 lost, which is a sign that the elections were not rigged, whereas, in 2013 by and large incumbents won. For instance, PML-N won in Punjab, where it controlled the provincial government and PPP won in Sindh where it controlled the provincial government. Lastly, both the government of the time and opposition parties accepted the results of the 2008 elections, in contrast to the aftermath of the 2013 election. Given these reasons, using the 2008 elections as a base to make comparison with the 2013 elections seems natural.

A statistical analysis of 2008 and 2013 elections can give us significant information and more importantly, it can give us a road map of which seats to verify first – if the ECP goes down that route.

A statistical analysis of 2008 and 2013 elections can give us significant information and more importantly, it can give us a road map of which seats to verify first – if the ECP goes down that route. For completeness, let me give a qualification, we can only know for sure which seats were rigged by physically verifying the ballots. However, this statistical analysis can become an important map for future verification processes and it can become an important tool to press for such verifications.

Let’s start with some basic comparison between the 2008 and 2013 elections. In 2013 there were about 46.6 million votes cast, compared to 34.8 million votes in 2008. This means that in 2013 there were about 11.8 million extra votes cast (figure 1). The percentage of votes polled to registered voters increased by 9.8 percentage points to 54.0 per cent in the 2013 elections.

Figure 1

Figure 1

*Source of data: Election Commission of Pakistan

Probably the most significant sign of rigging will show up in the increased skewness of vote distribution. In a non-rigged election we would expect some seats to have low voter turnout and some seats to have high voter turnout, with most seats falling in the middle. This type of distribution is called a normal distribution. However, if there was rigging in an election then we would see a proportionally higher number of seats with high voter turnout (because of bogus votes and ballot stuffing), skewing the distribution to the right. Moreover, the magnitude of skewness will be proportional to the rigging undertaken. Figure 2 shows the distribution of 2008 and 2013 election votes by National Assembly (NA) seats. The 2008 elections look fairly normally distributed, which as discussed before, is a sign that the 2008 elections were relatively rigging free. However, the 2013 election results are significantly skewed to the right. Furthermore, Kurtosis (a statistical measure of skewness) for a 2013 was 4.5 compared to 2.6 in 2008, which is a significant increase in skewness. This puts a question mark on the whole increase of 11.8 million votes in 2013. This skewness of vote distribution is a clear sign of vote rigging in 2013. Based on this measure alone, the people of Pakistan can and should demand impartial vote verification.

Figure 2

Figure 2

*Source of data: Election Commission of Pakistan

The second measure we look at is to see if the increase in votes cast in each seat were outside the norm. If a seat witnessed unusually high voter turnout in 2013 compared to 2008, then this may be an indication of vote rigging. To look at unusually high voter turnout (votes polled as a percentage of registered voters), we can look at seats where the increase in voter turnout in 2013 was outside the 90 per cent confidence interval. A confidence interval is a range of values that describes the uncertainty surrounding an estimate. The “90 per cent” in the confidence interval represents a level of certainty about our estimate. So very loosely speaking and in lay man’s terms, confidence intervals are a statistical tool to look at the likelihood of an event. If an event is likely it will be within the confidence interval, whereas unusually or unlikely events will be outside of the confidence interval. Being outside confidence in itself is probably not a sign of rigging. However, being outside of confidence interval and the increased skewness of the data, probably points towards suspicious activity.

Based on 90 per cent confidence interval measure, there are about 76 NA seats, in the 2013 elections, where voter turnout increase was outside the confidence interval. This means that there is a significantly high chance of vote rigging in these NA seats. As this is based on probability, so not all of these 76 seats may be rigged, and indeed there may be many rigged seats that have not been captured in this 90 per cent confidence interval. Having said that, these 76 NA seats are an indication of potential vote rigging in the 2013 elections and may be just the tip of the iceberg.

Rigging involves support of the ECP officials, police and state machinery. Given this, incumbents have greater means to rig election. Using this logic, we can look at incumbents who have won seats where voter turnout was unusually high, i.e., outside the 90 per cent confidence interval. Based on this, there are 31 seats with strong potential signs of vote rigging. Table 1 lists these seats. As these seats in table 1 saw an unusually high voter turnout compared to 2008, this table can be used as a starting point for vote verification.

Table 1

Table 1


Some people can argue that maybe the increased votes were based on a higher proportion of young voters, and/or the entrance of a politician who inspired higher voter turnout, i.e., Imran Khan effect. It is important to address these concerns. Let’s look at the Imran Khan effect first. If we look at the seats where Pakistan Tehreek-e-Insaf (PTI) won, voter participation increased by 9.02 percentage points between 2008 and 2013, far less than the difference of 15.66 percentage points used in the 90 per cent confidence interval employed above.

Now let’s look at the youth effect. If the increase in voter turnout in 2013 was due to higher youth participation then we would expect to see this effect in all constituencies and not just some. However, looking in Figure 1, we can see that votes do not rise proportionally in all constituencies. In fact, as discussed before, the distribution of 2013 votes are skewed to the right. So we can rule out the theory that this unusually high voter turnout in some NA seats for the 2013 elections is based on higher youth participation. Lastly, the standard deviation of the confidence intervals used above is based on increased votes between 2008 and 2013. Given this, the confidence intervals used already take variables like youth and/or entrance of a dynamic politician into account. More simply put, even after taking these concerns into account, there are clear signs of potential vote rigging in the 2013 elections.

Rigging involves support of the ECP officials, police and state machinery. Given this, incumbents have greater means to rig election. Using this logic, we can look at incumbents who have won seats where voter turnout was unusually high.

Moreover, it is interesting to see who won the above seats and where are they located. Most of these seats were won by either Pakistan People’s Party Parliamentarians (PPPP) or Pakistan Muslim League ‑ Nawaz (PML-N) (figure 3). So it is not a surprise when we see these parties as being the biggest obstacle to vote verification. Moreover, most of these seats were either located in interior Sindh or Punjab – bastions of PPPP and PML-N.

Figure 3.

Figure 3

*Where suspicious seats are as based on Table 1.

If true, then these 76 NA seats, or even the more conservative estimate of 31 NA seats (using the incumbent measure), are a clear indication of voter fraud. Moreover, these numbers are far higher than the four seats where PTI wants ballot verification.

Given the measure of skewness and the unusually high number of votes cast in some seats, the ECP should use table 1 as a starting point for vote verification. Votes cast by the people are probably the most important tool and right of democracy. Moreover, democracy is a process of choosing your government, but if someone overrules the choice of the people by vote rigging, then can it still be called a democracy? The answer for me is a resounding no. Given this, it is the duty of the ECP to make sure that no one steals this valuable right and that a proper, impartial and systematic vote verification is launched to look at the anomalies of 2013 elections.


  1. You have taken 2008 election as a benchmark however it would have made more sense if you have also compared it with 1997 elections. 2008 elections cannot be used as a benchmark for various reasons. First they were held under Musharraf regime which overtly favored PML-Q; second NS was barred from contesting thus the supporters interest vanned affecting the outcome severely.

  2. Congratulations Omer Majeed Sahib for producing a brilliant piece of analysis. All evidence even before this examination clearly pointing towards huge rigging taking place. PMLN refusal to allow even a token examination demanded by Imran Khan is enough evidence a significant indication who is the guilty

  3. Ineffective and inconclusive analysis, in addition, to being politically biased. Poor level of scholarship for a doctoral candidate! You may want to revise it with the help of a political scientist!

  4. @ Sam.. Can't these ignorant N supporters keep their level of illiteracy to themselves? poor level of argument for a educated person. You may want to revise it with the help of mental doctor ! :p

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