Refuting Hon. William Ruto's statistical fallacies

Following the just concluded referendum, it is evident that Kenyans have overwhelmingly accepted the Proposed Constitution. The proponents of the ‘No’ side, on the other hand, have also ‘conceded defeat’. However, their concession has come forth with some statistical fallacies that should not be left unchallenged.

Hon. Ruto was quoted in most media outlets, in the country, inferring that close to 60% of Kenyans either out rightly rejected the Proposed Constitution or abstained from voting. However, one key issue that all Kenyans need to note is that the referendum, just like all the preceding opinion polls, showed that a significant majority of the people of Kenya are in favour of the new Constitution. Of all the polls that were conducted, the most valid and accurate should ideally be the referendum itself, which has a much larger ‘sample’, read voters.

Earlier, it was reported in the media that the registered voters for the referendum were over 12.5 million. And the results showed that 70% of those who participated in the plebiscite voted for the new Constitution with 30% voting ‘no’. However, the 70% and 30% respectively represents the universe of those who voted only. Those who abstained from the referendum were about 30%, according to the IIEC. A distinction, therefore, needs to be made as regards these two similar but separate 30 percents.

In combining both the proportion that abstained and the ones that voted ‘red’, the ideal thing is to recalculate using the absolute numbers, rather than incorrectly adding the two percentage figures. If we add the percentages, the ‘60% that either abstained or rejected’ the Proposed Constitution’ and the 70% that voted ‘green’, then you end up with an accumulated 130%. You do not need to be a statistician to know that this is impossible. If we recalculate using the total registered voters, we find that 48% voted ‘yes’ and 22% voted ‘no’ and a 30% that abstained. These correctly add up to 100%.

Since we know that the referendum was the most valid and accurate poll; then, using the same 70 and 30 percents, we can correctly come to the conclusion that, of those who abstained, 21% would have voted ‘yes’ and only 9% voting ‘no’. These last two figures are respectively, 70% and 30% of the 30% that abstained. Therefore, using these recalculated percentages, we end up with about 69% ‘green’ and 31% ‘red’. In absolute figures, these would mean; 6 million who actually voted for ‘yes’ and another 2.6 million hypothetically voting ‘green’. On the flip side, it means 2.8 million Kenyans who actually voted ‘no’ and another 1.1 million hypothetically voting ‘red’. The total, both for the absolute figures and the percentages, add up to the number of registered voters (12.5 million) and 100% respectively.

I need to also caution the propagators of these misconceptions from attempting to use the 48% figure written above as below the ‘internationally recommended 50% threshold’. This figure only comes up when you try to cater for the abstained votes, among the universe of the registered voters. Therefore, the correct thing would be to use the same (48%) while acknowledging the proven breakdown of ‘yes’ and ‘no’ voters among the abstainers – which, as stated, is 70% and 30 % respectively. Thus, you either accept the 48% with the additional hypothetical votes or else leave it as it is currently – 70% actually voting ‘yes’.

Also, we can, with statistical certainty, predict that the so named hypothetical voters above, given a chance, would have voted exactly in the manner as envisaged above. This is informed by the fact that, as written above, the validity and accuracy of the plebiscite is above reproach. Therefore, if we had other Kenyans who being eligible to vote but did not register; then they too would most likely have voted 70% for ‘yes’ and 30% ‘no’.

Using the same distorted logic circulated - that of 60% either rejecting or abstaining from the referendum - we can as well come to the conclusion that 70% of the registered voters turned out for the referendum and 70% of them voted ‘yes’ adding up to a total of 140%. However, it would be inappropriate for me to refute one statistical fallacy with yet another one.

Therefore, the only valid conclusion is that the majority of Kenyans are in favour of the Proposed Constitution, regardless of whether they registered for the referendum, voted on August 4th, or whichever side they voted for or would have voted for. In other words, if your get a fairly representative number of Kenyans anywhere, they would have voted 70% for ‘green’ and 30% for ‘red’. We have no reason, at this point in time, to believe that those who abstained were a homogenous group; from the same region, with similar ethnic and religious background etc.