President-elect Nana Akufo-Addo (right) meets with the incumbent, President John Mahama.

NTOABOMA—I’ve read, from my humble village, several media reports about the failed attempts in predicting Ghana’s “change-election.” Nana Akufo-Addo, 72, defeated President John Mahama, 58, by a margin of 10 percentage points to become the president-elect after a third attempt. (What a charm a third time makes!) Few, on my side of town, saw it coming. Even for those who had the knack to foresee it, the gap still stupefied many. And, although one may applaud the cautiousness of Charlotte Osei, the electoral commissioner, in announcing the result, which came on late Friday, December 9—two days after the election—the declaration of the steep gorge of votes that separated Nana and Mahama made for an incredible excuse for delaying an expected earlier broadcast.

The news sparked scenes of jubilation in parts of Ntoaboma. Depending on which side of the political divide you fell on, which determined what perceptions you held of the world and your candidate of choice, the news brought you either hope or fear.  But it is neither these excited masses nor the terrified crowds that stoked my interest. What fueled my fascination was the level to which many of my own friends stooped to declare, in one way or another, that they saw President-elect Nana Akufo-Addo defeat President John Mahama through astute polling.

By ‘astute polling’ my friend Ozodiah Godwilling meant that by the standards of his own polling methods he had made the correct prediction. Although, like many of my friends, he challenged official polling in Ghana prior to December 7, his alternative methods were woefully wanting of any required rigor—that is if the rigor of survey statistical mathematics was anything to swear by. The depth of Ozodiah’s polling showed ‘partisan political belief’ more so than a sticking to real calculations grounded in first principles.

On the whole only two polls by Goodman AMC—one in April and another in June 2016—predicted an Akuffo-Addo win. One poll by the same company, in August 2016, with the biggest sample size back then of 2,184 respondents, predicted a Mahama win. In tandem, two other polls by Ben Ephson (although he refused to publish his methods and samples), and another by Restart International in early December with about 2,000 respondents, all predicted a Mahama win.  Three of these polls predicted a one-touch victory for the incumbent—only the August poll predicted a second runoff since Ghana uses a two-round system for the selection of its president.

Nana’s win defied these odds. At least that’s how some pollsters today hope to wish away the contradiction. But suffice it to say that it wasn’t an Earth-shattering event that Nana Akufo-Addo beat John Mahama in a one-touch victory, beating the polling odds to dust.  Few unofficial polls—forgiving the sententious standards of what is official and what is not—“saw” the Nana victory coming. Like the ground-breaking U.S. elections in which Donald Trump forced Hillary Clinton to snatch defeat right from the jaws of victory, the question in the past presidential election in Ghana is also about the usefulness of polls: “Where did the pollsters get it wrong?”

By “wrong,” those who believed in the polls, and swore by it, were peeved to have failed some kind of a “rationality” test. While those who railed against the polls and predicted something different, if only to massage their concealed egos, feel relieved to have passed some kind of a “rationality” assessment. If you feel either way then I bring you news. There’s no such thing as a “rationality” check. Or is there a “rationality” test in predicting an election! Those who got it “right” by predicting a Nana-win were just as irrational if not as rational as those who did not.

Here’s why.

My friends have a point when they insist that although their calculations may have lacked real mathematical grounding that by their own polling assumptions and, in fact, by the standards of “politics itself, which is one percent inference and ninety-nine percent sheer knack,” they had at least got something spot-on. By “knack” they refer predominantly to their miracle mathematics—that of predicting a Nana-win. Albeit to be fair Ozodiah in particular seems to have been heavily involved in many grassroots political movements in Ghana prior to the elections. If this experience informed his “knack” for the Nana prediction then it cannot be said to be purely “mathematical.” Knack has always had something to do with confidence, and with it, predicting an event based on inductive inference. What then is a prediction: is it “knack” or is it rooted in “mathematical rigor” or is it a combination of both?

Predicting who will win an election is not any more difficult, or less complicated, than predicting whether or not the Sun will rise tomorrow morning or whether or not an Atomic Bomb will fall from the sky and quench your entire village. This is because the concept of the “probability,” or of the “chance,” of winning say an election is philosophically puzzling. Part of the puzzle is in ascertaining the meaning of the word “chance” or “probability” itself. Take for instance, prior to December 7, if you read a Grandmother Africa Poll that said that Nana Akuffo-Addo had a 54 percent chance of winning the elections, you would understand this as saying that 54 out of every 100 people who were registered voters would vote for Nana. This is known as the frequency interpretation of probability, which equates probabilities with proportions or frequencies.

The problem is that some folks like Ozodiah would immediately exude confidence from a sample of about two thousand eligible voters that Nana was set to win. But is this rational? Is this the test of “rationality?” Bear with the world of statistics and appease yourself that this idea itself is based on the assumption that one can “reasonably” sample some two thousand “random” respondents from a pool of sixteen million voters. Again, is this really that “reasonable?” Does calling some two thousand voters prior to an election imply that the pollster will obtain the same manner of responses in the next 15.7 million calls for all registered Ghanaian voters?

But what if you read Ozodiah’s statement before December 7 that the probability that Ivor Greenstreet of the Convention People’s Party (CPP) wins the election in one in a million chances?  Does this mean that only about 16 people out of the 16 million registered Ghanaian voters will vote for Ivor Greenstreet? Clearly it does not follow. For one thing the CPP has more officials and parliamentary candidates in the 275 constituencies across the country. Unless of course you begin a cynical proposition that a candidate might vote against himself! Barring that, a different notion of probability is at work here. This is the subjective interpretation of probability. Evidently, Ozodiah’s idea of “knack” rests carefully on this interpretation.

But you might still insist that we can usually tell the difference between opinion (knack) and statistics (polls). That is correct, but only to an extent. So you are wrong! The mathematical study of probability does not by itself tell us what “probability” means, which is the main issue. Most pollsters, mathematicians and statisticians would favor the frequency interpretation of probability but the problem of how to interpret any given probability is mathematically intractable. The formulae for working out who wins an election remains the same whichever interpretation we adopt.

Why is this important, you might ask? Well, for one, you can’t know for sure—certainly not from a sample—who will win the next election in Ghana. Which is the point—there’s no test of “rationality” henceforth!  You can boost your confidence levels about who you “think” might win the next election by asking more and more people who are going to vote (polling), but you cannot know for sure. Unless, you have asked everyone! Certainly, no one in his right mind would do this.  This problem, although a straightforward and simple looking one is also referred to as Hume’s Problem (named after a Scottish philosopher who lived in the 1700s and who Western scholars insist is the only one who probably first came up with this dilemma in the world’s over 12,000 years civilizational history): that the premises of an inductive inference do not guarantee the truth of its conclusion. It is tempting to say that the premises of an inductive reasoning, such as in polling, do make the polls highly predictive of elections. But we must be careful about what interpretation this statement assumes in the face of “Hume’s Problem.”

On the frequency definition, to say that it is highly probable that Ghanaians will vote for Nana is to say that a very high proportion of Ghanaians will vote for Nana. But we have no way of knowing that except through inductive inference (we cannot poll all 16 million Ghanaian registered voters so we poll a couple thousand and assume that they were randomly selected and that this random sample is closely representative of the whole!). On the contrary, suppose that Ozodiah believes that Nana will win the election based on his grassroots experience with voters and Jebrudiah Godasks believes that Nana will lose. Both accept the evidence prior, of asking a few thousand Ghanaians polling 54 percent in Nana’s favor. Intuitively we want to say that Ozodiah is rational and Jebrudiah isn’t, because the evidence makes Ozodiah’s belief more probable.

But if probability is simply a matter of subjective opinion, we cannot say this. All we can say is that Ozodiah assigns a higher probability for Nana while Jebrudiah does not. If there are no objective facts about probability, then we cannot say that the conclusions of inductive inferences are objectively probable. So we have no explanation of why someone like Jebrudiah, who declines to use induction, is “irrational.” Or that another person, much like Jebrudiah, who declines to use induction to insist that the Sun will rise tomorrow, is irrational. Like most philosophical questions this essay probably does not admit to final answers, but in grappling with the meaning of “probability” and the power of prediction we might be more lenient in our castigation of friends who we deem to be more “irrational” than ourselves. Nana’s win was certainly a case, if not of sheer will, then of a third charm. However you like it, take it, but stop bothering others with your ideas about “rationality.” There’s no such thing!



  1. The Probability of Winning an Election in Ghana.

    Due to difficulties on Grandmother Africa’s website (we get hacked all the time, which is testament of the great essays our Scribes provide for free to the world), we bring you the full version of the latest of Narmer Amenuti’s essays. This brilliant piece is driven by the mathematical and philosophically interpretations of “probability” and with that a conversation centered on the meaning of polling and the power of predicting elections. Narmer throws out any suggestion of “rationality” in inductive inference and supports his thesis with a copious outpouring of prose and the sheer force of a deep understanding of statistics and probability.

    By all means enjoy this essay and engage in a lively debate!

  2. Gee, the forces of Khazaria are busy at work. Those keyboard worriers better find something else to do with their sorry lives or I am going to engage with them soon, real soon. What a shame!

    But I enjoyed this essay. I learned quite a bit from this straightforward and easy to understand treatment of the philosophy of the science of probability. Bravo!

  3. Yes probability samples give results ; thê only difference is that they remain probable until proved otherwise. Sometimes speculations also give insight to quotas and other types of sampling which my brothers and sisters of thê inky fraternity apply a lot in thê media and other allied jobs. Once again my fellow ghanaians havê proved that they r peace loving during thê recent polls generally speaking despite thê fact that a few incidents occurred at least expected places. Even thê so called flashpoints became cool points; thanks to both security personnel and Moslem leaders plus all who helped in maintaining peace. As for thê less busy ones who havê turned into political fanatics and fighters i suggest they better find sth profitable to do and refrain from being stoogy. Thê incumbent and incoming presidents r men of sterling qualities. They both havê experiences me and u dont havê. So lets keep calm and pray that thê president elect will deliver according to his manifesto. Am proud to be ghanaian with reference to all that has happened in other parts of developing world, Rwanda Liberia etc. Yahayah example in Gambia. Lets continue lighting thê peace flame.

    • Emma Ama Gladzah when you say that: “probability samples give results; thê only difference is that they remain probable until proved otherwise,” that is a contradiction. What “results?” And I suppose here, you mean the more “probable” result? When an event is “probable” it means that there’s a chance that it might not “occur.” Either the frequency interpretation or the subjective interpretations will arrive you at the same conclusion. Since we cannot know for sure what will happen. This means only two things in the end: the event can happen or it will not. We are back to the original idea. The more we probe it we start circling our own tails. This is the problem.

  4. So if thê two giants can shake hands, why shd we fight one another? Tell me. No condition is permanent.

  5. First, I love this topic! Second, I like the way you have swung the “Hume Problem.” At some point, we can stop calling it thus: there’s absolutely no proof that he was the first to have framed the problem. We cannot know unless we observe “the world’s 12,000 years of civilizational history.” Since we cannot do this, we cannot ascribe all credit to a “probable” man. Your implication, Narmer, not mine! Lol.

    That said, thanks for clarifying a difficult topic. Probability Theory is a subject of much mathematical headache but much philosophical interest. However, the challenge by those who insist that the “truth” or the “fact” or whatever we want to call it cannot be established through induction are clutching at straws.

    Much of life and the values of living are very much established through induction. As you wrote this essay, your computer did not explode. Or did it? As you typed, your keyboard worked every time you pressed a key, or did it not? Now, suppose that induction wasn’t so full-proof, as truthers like yourself, Narmer, constantly espouse, and consider drinking arsenic (arsenic is toxic juice and you will die by engulfing any of it). Do you think that you “might” die or you “will” die? Which one?

    • Gee… Narmer, you are a difficult nut to crack! So the “think” is your subjective assessment? So you will refuse to admonish your son not to try drinking arsenic if he thought that he might fly as a result?

    • If my son “thinks that he might fly” by drinking arsenic, then he doesn’t know for sure. The competing argument is that he might die. Weighing the two will serve him well, depending on his circumstance. If he was a Gbeto Spy in the land of Barbarians, he might weigh both competing arguments equally: fly out of enemy territory or die trying. In another situation he might consider living and not necessarily flying!

    • Lol. Ok, well then, if this way is the correct way to thing about issues then there’s no need waiting for the Sun to rise in the morning!

  6. Well i think i agree; we havê come to thê same point if i say an idea is probable until proved right so peruse my argument once again.

    • An event is probable. This means it’s not certain the event will happen. Certainty is key in establishing truth! Suppose I asked you if whatever event you deemed probable would actually happen (for sure)? You cannot give a definitive answer. So you cannot know, for sure, what will happen. Which invariable turns every bit of your calculation, if in fact there was a statistical grounding, into a subjective interpretation of “probable.”

  7. So what do you say about rubrics or rules of thumb? Are they needless because they are derived from inductive inference.

  8. Let’s start with a thought experiment. You’ve been taught a rule that all Moyhicans are intellectually inferior to you (you are Anglo-Saxon). You come across the first Moyhican, you both agree you are smarter. You come across the second Moyhican, he is smarter. Now, does that make the rule or refute it? What if again assuming; you first came across 100 Moyhicans and you all agree you are smarter. And you come across the 101 Moyhican and you both agree he is smarter! Does that make the rule or break it?


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