This week’s post continues the review of Thinking in Bets by Annie Duke. As I indicated last week, the book is fun and informative, and I gave it 4 out of 5 stars. Consider for instance the following footnote (p. 90):

 
 
 
 
 
 

“I lifted these [absurd reasons people give for their car accidents – EJ] from an article by Robert MacCoun (described in the following paragraph) and repeat them without guilt. First, they are incredibly amusing and informative; the greater crime would be not sharing them. Second, MacCoun acknowledged that he got them from the book Anguished English, written by my father, Richard Lederer.”

Last week I also outlined three traps that the book presents for the unaware reader. To this list I want to add only a single trap, and it relates to the author’s conceptualization of hindsight bias.

From the very beginning, the author argues that the quality of a decision should not be assessed by the outcome. Indeed, the book starts by recounting of how Seahawks coach Pete Carroll made an unexpected call in the closing seconds of the 2015 Superbowl: instead of calling for a handoff, he called for the quarterback to pass. The pass was intercepted and the Seahawks lost the game. Did Carroll make a bad call? If you believe that he did, for the sole reason that the play did not work out, you have fallen prey to what poker players call “resulting”. As is evident in poker, you can make an entirely reasonable decision but still lose the hand, as the game involves luck, that is, a random unknown element that is beyond the players capacity to know.

One of the causes of “resulting” is hindsight bias. To understand the origin of hindsight bias, the final section of Thinking in Bets presents an analogy in terms of trees and chainsaws. The analogy is enticing but I believe it is mostly wrong. Here is the first relevant fragment:

“(…) think about time as a tree. The tree has a trunk, branches at the top, and the place where the trunk meets the branches. The trunk is the past. A tree has only one, growing trunk, just as we have only one, accumulating past. The branches are the potential futures. Thicker branches are the equivalent of more probable futures, thinner branches are less probable ones. The place where the top of the trunk meets the branches is the present. There are many futures, many branches of the tree, but only one past, the trunk.”

The author argues for “potential futures”. But what process governs which potential future will come to be? For instance, consider the 2015 Superbowl just after Pete Carroll has called his play to pass the ball. I am assuming that, from the author’s perspective, a potential alternative future is the outcome “pass is complete, Seahawks win the Superbowl”. But how exactly could this potential future have been realized in this universe? Let’s do a Gedankenexperiment: suppose we are able to reconstruct the entire stadium, atom-by-atom, including the players, coaches, referees, audience, the wind, the sun rays, the entire thing. Practically this is of course infeasible, but that’s why it is a Gedankenexperiment. We would then view the same play, and –my goodness– the pass is intercepted again, by the same player, in exactly the same fashion. And as long as we copy the situation sufficiently accurately, this will always be the case, like a movie scene on repeat.

The situation is complicated (but not much) by the fact that the Copenhagen interpretation of quantum theory posits that on the microscopic level, chance is inherent to nature. However, these quantum effects are fragile and do not appear to operate on a macroscopic level; therefore, they are exceedingly unlikely to change the fate of Carroll’s play (for a detailed treatise on determinism see Earman, 1986). And even if they somehow would exert a macroscopic effect, these effects would be absolutely dwarfed by the dominant source of uncertainty on the macro-level: our limited knowledge of the situation at hand.

The author continues:

“As the future becomes the past, what happens to all those branches? The ever-advancing present acts like a chainsaw. When one of those many branches happens to be the way things turn out, when that branch transitions into the past, present-us cuts off all of those other branches that didn’t materialize and obliterates them. When we look into the past and see only the thing that happened, it seems to have been inevitable. (…) That’s hindsight bias, an enemy of probabilistic thinking.”

According to a determinist, whatever happened was indeed inevitable. But that does not mean a determinist necessary suffers from hindsight bias, or is unable to think probabilistically. Probability, Jevons argued, belongs wholly to the mind. What this means is that the probabilistic element refers to a lack of knowledge — in advance of a football play, we do not know how fast a particular defender will be able to move, we do not know when the quarterback will throw the ball…the depth of our ignorance, even mere seconds before the play of a football game, is staggering. A few seconds later, after the play is over, our knowledge has vastly increased: in particular, we know whether the play was a success or a failure. Hindsight bias occurs because we underestimate how little we knew just moments earlier. In other words, hindsight bias is a failure to properly appreciate our previous state of ignorance. This is why hindsight bias is also known as the “knew-it-all-along” bias. Potential futures do not have to enter into it.

For a determinist, the correct metaphor is a movie rather than a tree. As the movie progresses, we learn more and more about the characters and the plot; at any point during the movie, we have a pretty clear idea about what has happened, but we can only guess how the movie will unfold. It will unfold, however, in only a single way. And if you execute our earlier Gedankenexperiment and return to an earlier scene, the characters will play out that scene exactly as before.

Previous blog posts on determinism are The Merovingian, or Why Probability Belongs Wholly to the Mind and Laplace’s Demon.

References

Duke, A. (2018). Thinking in bets: Making smarter decisions when you don’t have all the facts. New York: Portfolio/Penguin.

Earman, J. (1986). A primer on determinism. Dordrecht: Reidel.

Lederer, R. (2006). Anguished English. Layton, UT: Wyrick & Co.

About The Authors

Eric-Jan Wagenmakers

Eric-Jan (EJ) Wagenmakers is professor at the Psychological Methods Group at the University of Amsterdam.