Pascal’s Wager

Pascal’s argument (written in the 1600’s) went like this: Suppose you concede that you don’t know whether or not God exists and therefore assign a 50 percent chance to either proposition How should you weight these odds when decided whether to lead a pious life? If you act piously and God exists, Pascal argued, your gain – eternal happiness - is infinite. If, on the other hand, God does not exist, your loss, or negative return, is small – the sacrifices of piety. To weigh these possible gains and losses, Pascal proposed, you multiply the probability of each possible outcomes by its payoff and add them all up, forming a kind of average or expected payoff. 

In other words, the mathematical expectation of your return on piety is one-half infinity (your gain if God exists) minus one-half a small number (your loss if he does not exist). Pascal knew enough about infinity to know that the answer to this calculation is infinite, and thus the expected return on piety is infinitely positive. Every reasonable person, Pascal concluded, should therefore follow the laws of God. Today this argument is know as Pascal’s wager. 

Pascal’s wager is often considered the founding of the mathematical discipline of game theory, the quantitative study of optimal decision strategies in games.

Leonard Mlodinow, The Drunkard's Walk: How Randomness Rules Our Lives

Assume They’re Wrong

From military predictions to technological predictions to sports predictions, when experts foretell the future, it’s always safest to assume they’re wrong. 

Because they are deeply knowledgeable in a particular field, experts are more prone than others to view the world through a too-narrow lens, assuming that the current trends they understand so well are indicators of what is to come. Their expertise reinforces their confidence in their own analysis, blinding them to contrary data or disconfirming evidence. 

As you listen to their smart, persuasive, credible prophecies, just remember: Most of them, most of the time, will be wrong. (You can take my word for it. After all, I’m an expert.)

Jeff Jacoby is a columnist for The Boston Globe 

Who is best at predicting the future

(In a contest involving hundreds of geopolitical questions) a small number of forecasters began to pull clear of the pack: the titular “superforecasters”. Their performance was consistently impressive. With nothing more than an internet connection and their own brains, they consistently beat everything from financial markets to trained intelligence analysts with access to top-secret information.

They were an eclectic bunch: housewives, unemployed factory workers and professors of mathematics. But Philip Tetlock (who teaches at the Wharton School of Business) and his collaborators were able to extract some common personality traits. Superforecasters are clever, on average, but by no means geniuses. More important than sheer intelligence was mental attitude. Borrowing from Sir Isaiah Berlin, a Latvian-born British philosopher, Mr Tetlock divides people into two categories: hedgehogs, whose understanding of the world depends on one or two big ideas, and foxes, who think the world is too complicated to boil down into a single slogan. Superforecasters are drawn exclusively from the ranks of the foxes.

Humility in the face of a complex world makes superforecasters subtle thinkers. They tend to be comfortable with numbers and statistical concepts such as “regression to the mean” (which essentially says that most of the time things are pretty normal, so any large deviation is likely to be followed by a shift back towards normality). But they are not statisticians: unlike celebrity pollsters such as Nate Silver, they tend not to build explicit mathematical models.

But superforecasters do have a healthy appetite for information, a willingness to revisit their predictions in light of new data, and the ability to synthesise material from sources with very different outlooks on the world. They think in fine gradations. 

Most important is what Mr Tetlock calls a “growth mindset”: a mix of determination, self-reflection and willingness to learn from one’s mistakes. The best forecasters were less interested in whether they were right or wrong than in why they were right or wrong. They were always looking for ways to improve their performance. In other words, prediction is not only possible, it is teachable.

Prediction, like medicine in the early 20th century, is still mostly based on eminence rather than evidence. The most famous forecasters in the world are newspaper columnists and television pundits. Superforecasters make for bad media stars. Caution, nuance and healthy scepticism are less telegenic than big hair, a dazzling smile and simplistic, confident pronouncements.

From a review in The Economist of the book Superforecasting: The Art and Science of Prediction by Philip Tetlock and Dan Gardner