What is luck? [book review]

I was sent—by Columbia University Press—this book for a potential review in CHANCE: What are the chances? (Why we believe in luck?) was written by Barbara Blatchley, professor of Psychology and Neuroscience at Agnes Scott College in Decatur, Georgia. I have read rather quickly its 193 pages over the recent trips I made to Marseille and Warwick. The topic is truly about luck and the psychology of the feeling of being luck or unlucky. There is thus rather little to relate to as a statistician, as this is not a book about chance! (I always need to pay attention when using both words, since, in French chance primarily means luck, while malchance means bad luck. And the French term for chance and randomness is hasard…) The book is pleasant to read, even though the accumulation of reports about psychological studies may prove tiresome in the long run and, for a statistician, worrisome as to which percentage of such studies were properly validated by statistical arguments…

“…the famous quote by Louis Pasteur: “Dans les champs de l’observation, le hasard ne favorise que les esprits préparés”s (…) Pasteur never saw a challenge he couldn’t overcome with patience and preparation.” (p.19)

Even the part about randomness is a-statistical and mostly a-probabilist, rather focusing on our subjective and biased (un)ability to judge randomness. The author introduces us to the concepts of apophenia, which is “the unmotivated seeing of connections accompanied with a specific feeling of abnormal meaningfulness”, and of patternicity for the “tendency to find meaningful patterns in meaningless noise”. She also states that (Neyman-Pearson) Type I error is about seeing a pattern in random noise while Type II errors are for conclusion of meaningless when the data is meaningful (p.15). Which is reductive to say the least, but lead her to recall the four types of luck proposed by James Austin (which I first misread as Jane Austin).

“There is a long-standing and deeply intimate connection between luck, religion, and belief in the supernatural.” (p.28)

I enjoyed very much the sections on these connections between a belief in luck and religions, even though the anthropological references to ancient religions are not strongly connected to luck, but rather to the belief that gods and goddesses could modify one’s fate (and avoiding the most established religions). Still, I appreciate her stressing the fact that if one believes in luck (as opposed to sheer randomness), this expresses at the very least a form of irrational belief in higher powers that can bend randomness in one’s favour (or disfavour). Which is the seed for more elaborate if irrational beliefs. (For illustrations, Borgès’ stories come to mind.)

“B.F. Skinner believed that superstitious behaviour was a consequence of learning and reinforcement.” (p.85)

There are also parts where (a belief in) luck and (human) learning are connected, but, unfortunately, no mention is made of the (vaguely) Bayesian nature of the (plastic, p. 188) brain modus operandi. The large section on the brain found in the book is instead physiological, since concerned with finding regions where the belief in luck could be located. In relation with attention-deficit disorders. (Revealing the interesting existence (for me) of mirror neurons, dedicated to predicting what could happen! Described as “predictive coding”, p.153). The last chapter “How to get lucky” contains a rather lengthy account of “Clever Hans”, the 1990 German counting horse (!). Who, as well-known, reacted to subtle and possibly unconscious signals from his trainer rather than to an equine feeling for arithmetic…

One of the clearest conclusions of the book is (imho) that a belief in luck may improve the life of the believers, while a belief in being unlucky may deteriorate it. The Taoist tale finishing the book is a pure gem. But I am still in the dark as to whether or not my exceptional number of bike punctures in the past year qualifies as bad luck!

“Luck is the way you face the randomness of the world.” (p.191)

As an irrelevant aside, one anecdote at the beginning of the book brought back memories of the Wabash River flowing through Lafayette, IN, as it tells of the luck of two Purdue female rowers who attempted a transatlantic race and survived capsizing in the middle of the Atlantic. It also made me regret I had not realised at the time there was a rowing opportunity there!

Georgia on my mind

The riddle of this week was inspired by the latest presidential elections when one State after another flipped the winner from Trump to Biden. Incl. Georgia.

On election night, the results of the 80 percent who voted on Election Day are reported out. Over the next several days, the remaining 20 percent of the votes are then tallied. What is the probability that the candidate who had fewer votes tallied on election night ultimately wins the race?

Assuming many votes, perfect balance between both candidates (p=½), and homogeneity between early and late ballots, the question boils down to the probability of a sum of two normals, X+Y, ending up being of the opposite sign from X, when the variances of X and Y are α and 1-α. Which writes as the expectation

equal to

which returns a probability of about 0.14 when α=0.8. When looking at the actual data for Georgia, out of 5 million voters, at some point 235,000 ballots remained to be counted with Trump on the lead. This means an α about 0.05 and implies a probability of 7% (not accounting for the fact that the remaining mail-in-ballots were more favourable to Biden.)

it was the best of times, it was the worst of times