How to estimate the results of presidential elections

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

14 August 2022

Kenyans become interested in statistics during the general elections. So, I was not surprised when some one asked me if it is possible to predict the outcomes from a random process. The answer is both yes and no.

Here is why: If you tossed a coin just once, you would not be able to predict whether it will turn out heads or tails. However, if you did it 100 times, you can confidently expect that approximately 50 tosses will produce heads and another 50 will be tales.

The behaviour of a large number of random events can be predicted fairly accurately while that of a single occurrence cannot. Indeed, if you tossed a coin 100 times and found that, say, 20 heads and 80 tales, you would conclude that the coin was biased and, therefore, the outcomes were not random.

This idea can be applied to election results. We can usually tell the winner of the presidential election very early in the vote tallying process. With just 10 percent of the polling stations, the trend is set and no movement of percentage scores is expected.

Unfortunately, in this year’s election, the Independent Electoral and Boundaries Commission (IEBC) did not stream the tallying live. Instead, they posted the completed Forms 34A on their website and anyone wishing to do a parallel tally was free to download the forms.

Media houses tried it but, by the middle of the first day after the election, it was clear that they had underestimated the volume of work. While IEBC had posted over 40,000 forms, the media had tallied around 15,000. The question is: is it necessary for the general public to tally all the 46,229 forms?

No.  Since what really matters is the percentage of votes garnered by each candidate, one can just pick a few of the forms at random. But they must be drawn evenly from across the country, say one or two from each of the 290 constituencies.

I randomly downloaded one form each of the 47 counties and did a tally. The total number of votes cast in the 47 stations sampled was 12,908. From this sample, I found that Raila Odinga got 47.6 per cent, William Ruto 51.8pc, David Waihiga 0.2pc and George Wajackoyah 0.5pc.

By the time you read this, the final results will probably be out so this is a good test to see how accurate such sampling can be.