Mathematics Of 2023 Presidential Election

Mathematics Of 2023 Presidential Election

I listened to the entire judgement of the contest between APC, PDP and LP. There were key issues that I was interested in hearing how they would be resolved. The 25% question was very important to me because it is embedded in logic and mathematics, although lawyers see it as a constitutional matter while linguistics experts see it as a coordinating conjunction. Unfortunately, when the judges got there, it was not addressed mathematically. Rather, it appeared that the lead judge childed PDP and LP for not understanding the simple statement. For me it was not resolved or at least, the mathematical implication was downplayed.

Honestly, I understand the difficulty the judges were facing and that was the reason the question was an interesting one. HE Peter Obi that met 25% and won Abuja came third. HE Bola Ahmed Tinubu that won the highest number of votes did not met 25% of Abuja. I have read the mathematical exploration of the S. 134(2)(b) by Professor Mike Ozhokome published in The Cable. He also gave some legal explanations and cited some authorities and precedents. I am not a Lawyer but I hold PhD in Engineering. Engineering is the application of mathematics and science to solve problems. So, I have a level of knowledge to analyse the mathematical logic of that part of the constitution. Nonetheless, the court has the power to interpret the constitution and I can only express a layman opinion. I wish to support the claim of PDP and LP that FCT, Abuja is required to win the presidency of Nigeria.

The Mathematical translation of the contentious portion of the constitution is as follows:

Winner = >=(1/4) or 25% in 2/3 of 36 + FCT.

= 24 + FCT (win 24 states and FCT).

An alternative mathematical expression is:

Winner = >=(1/4) or 25% in 2/3 of (36 + 1).

= 24.6667 = 25 states (favoured by the Judges).

The algebraic addition of two fruits, say apples and oranges can be used to show that the “and” in the constitution has a mathematical implication.

To calculate total number of fruits when I have 5 apples and 6 oranges, the answer cannot be 11 fruits or 11 apples or 11 oranges. This will go against Set theory. Based on set theory, there are two sets being considered – 36 states in Set A and 1 FCT in set B. Both Sets make up the Federating units and FCT as the capital of the federation. The structure, composition and administration of Set A and B are not the same.

Consider this Set expression to determine a total.

5 apples + 6 oranges = 5 apples + 6 oranges (the same way 5a + 6o = 5a + 6o in algebra). The equation highlights that there is a difference between apples and oranges, hence the use of “and”. Even in Probability, the use of “and” or “or” has a mathematical implication.

Nonetheless, of you have 4 apples and another 5 apples, you can simply state that you have 9 apples. There is no difference as they are of the same set and there is no need for “and”.

I reckon that the the framers of the constitution did not sincerely envisage a situation where a winner will not get at least 25% in FCT. Before 2023 elections, it was mathematically unimaginable that a winner of the presidential election can not get at least 25% at FCT. In this article, I will throw up other scenarios that may occur in future. I will also raise questions.


  1. It is mathematically possible that a contestant can win in Abuja only and not in the 36 states. A case of Kwankwaso and Kano State supports this probability.
  2. It is mathematically possible to have a situation where the contestant with the highest number of votes did not win 25% in 2/3 of 37 states. Assuming that FCT is treated as if it was a state. This could happen where there are up to 6 strong candidates from each geopolitical regions. In the future, when this happens, the question of 25% will pop up again and probably trigger a rerun.
  3. If all Nigerians are equal as the judges asserted, and each vote has the same mathematical weight, should not the framers state that 25% is required in each state of the federation to accord all states equal status and relevance. There is a mathematical probability that there will not be a clear winner in Presidential Election in Nigeria if 25% is required in all the states. Currently, it appears that FCT is the conglomeration of all the people of Nigeria and winning at least 25% in Abuja should be the only statistical prove of national acceptance of a candidate since ethnic, religious and regional biases may influence votes at the geopolitival zones. The Supreme Court may need to rethink the position of the Tribunal on the 25% requirements for FCT.
  4. Is the use of 1/4 and 2/3 mathematical constraints? Yes of course. Is FCT also constrained to be won by the winner? I think so. Consider the following:

Winner = 25% ((in 2/3 of 36) + FCT)).

If you expand the bracket, it will be 25% in 36 states and 25% in FCT.

That is  x (y + z) = xy + xz. Mathematically, “of” is a multiplication which can be replaced with a bracket.

4. If the winner did not get 25% and the person that got the 25% cannot be declared winner, as it is in the current case, I agree with the judges that it will be more democratic to declare the person with the highest number of votes the winner. However, it cannot be so of it is constrained. Supposing that HE Atiku  Abubakar of the PDP met 25% at Abuja but still retained the second position, would it be persuasive to declare PDP winner based on the special status of Abuja? I don’t  think so.  PDP will still not meet the constitutional requirements of winning the highest valid votes and democracy requires a rule by the majority number of votes. Still, majority outcome may deviate from the 25% rule from time to time based on the above analyses.

I think that the SC Justices should adopt a more mathematical approach in addressing the 25% question . Nigeria may need to amend the constitution to be more explicit. Until such amendment is made,  it appears that the mathematical implication of Winner = >=(1/4) or 25% in 2/3 of 36  and FCT is  24 states plus FCT.

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