WORLD OF FIGURES: Tallying election results is like eating githeri!

Soon after the Independent Electoral and Boundaries Commission (IEBC) started streaming presidential election results on Tuesday night, several people questioned the validity of the data. Their concern was that the percentage difference between Uhuru Kenyatta and Raila Odinga remained relatively constant.

These people expected the percentage difference to swing in a pattern resembling the “normal distribution curve”. Since this was not the case, they concluded that the transmission had been doctored.

Well, they are wrong: on the contrary, if the percentage difference kept varying significantly, that would have been an indication that the result transmission was doctored! Indeed, at 8:40 pm on Tuesday night, with about 9,400 polling stations reported, I posted on Twitter that I did not expect any major change in the difference.

At that time, about three million votes had been counted and Uhuru Kenyatta had 55 per cent while Raila Odinga had 44 per cent. By Friday evening when we went to press, 15 million votes had been counted and Uhuru had 54.25 per cent against Raila’s 44.86%.

The reason why the percentage score remained fairly constant is that the results were streaming from different stations around the country and in a fairly random arrival pattern. The time at which a particular polling centre files its vote count depends on what time it opened, how many voters turned up, how faster the clerks were counting, how many ballots were disputed and for how long… and so on and so forth.

All these factors were different for each polling station and so the time that each transmits its results is quite random. Thus, the early tally was fairly representative of the final outcome since it is naturally randomised in both space (i.e., location) and time.

The randomness of the location from where results originate ensured that each candidate’s strongholds got an equal chance of arriving at the tallying centre.

This phenomenon is similar to what happens when one is eating githeri. Suppose you scoop spoonfuls from different parts of the plate. Each spoon will have a different ratio of maize to beans. As you swallow the food, the ratio of maize to beans in your stomach initially varies widely but it quickly settles to a fairly constant value – well; only that now it is chewed! The constant value is approximately equal to that of the seeds in the plate.

In this illustration, the plate is the people who voted, the spoonfuls are the results from the polling stations and you stomach is the tallying centre at Bomas of Kenya.

What about the normal distribution? First of all, it is not the appropriate curve for this situation; anyone expecting to see it here has obviously never studied statistics! The correct graph is known as the Poisson Distribution. It describes situations where the data arrives in discrete packets – for example, the number of votes per candidate coming from discrete polling stations.

www.figures.co.ke  Twitter: @mungaikihanya