We have seen how the Prior Indifference Fallacy underlies three well-documented cognitive biases: Representativeness, Anchoring and Availability. A fourth one that can be similarly interpreted is the Hindsight Bias: the tendency to regard events as predictable after they have occurred (see Chapter 19 of Thinking, Fast and Slow).
How could US intelligence fail to prevent 9/11? How could the Federal Reserve fail to detect the US housing bubble? How could the SEC fail to spot Bernard Madoff?
As events happen, they require explanations. We want to know why they happened. Explanations make sense of events, linking them to preceding events in a causal chain that gives us a satisfactory account of what turned out to be the case. But causes can only be seen after the events. Before events happen, all we can see are other events – evidence whose links to what happened was only probable. 9/11 was the result of a countless number of preceding events, none of which was bound to happen for certain. High house prices were not destined to cause the 2008 recession. As hard as it is to believe after the fact, Madoff did not look like an obvious fraud.
Nothing that happens is bound to do so. Everything is the result of a long chain of more or less probable events. As common sense as this is, it runs counter to the Principle of Sufficient Reason, according to which there is no such thing as chance: everything is destined to occur in the only possible way, according to its causes. The Hindsight Bias is a corollary of the Principle of Sufficient Reason.
Let’s take Madoff. A few years before the scandal broke out, I was having dinner with a friend who, until a few months earlier, had been the Italian private banking head of a large American firm. He told me he had quit his job and was now working for one of the largest feeder funds of Madoff Investment Securities. Who?, I said, as he embarked in an enthusing description of the split-strike conversion strategy that had allowed Madoff to earn 15% returns year after year, with little volatility and no management fee. “I know what you’re thinking” – he concluded, as I stared at him with a are-you-out-of-your-mind look – “it can’t be true. But it is. It is one of the largest broker-dealer firms on Wall Street and Madoff is one of the best respected hedge fund managers”.
So let’s go back a few years and test the hypothesis ‘Madoff is a crook’. As we know, PO=LR∙BO: the Posterior Odds of the hypothesis equal the Likelihood Ratio of the evidence times the Prior Odds of the hypothesis. In this case, our evidence is the split-strike conversion strategy. Let’s take a very sceptical view of it and say TPR=100%: the probability that Madoff would use that strategy, given that he is a crook, is 100%; and FPR=5%: the probability that he would use the strategy, given that he is not a crook, is only 5%. Hence LR=20: the evidence is highly confirmative of the hypothesis that Madoff is a crook. But in order to measure the probability that Madoff is a crook, given that he uses the strategy, we need to multiply LR by BO: the prior probability that Madoff is a crook. In my perfect ignorance – I didn’t know who he was – I had BO=1, which gave me PO=20 and therefore PP=95%: Madoff was almost certainly a crook – hence my bewilderment. But for my friend – along with thousands of wealthy investors and sophisticated advisors – the prior probability that Madoff was a crook was very small: let’s say one in a thousand. We know these numbers: they are the same as in our child footballer story. According to my friend, then, the probability that Madoff was a crook, in the light of his investment strategy, was only 2%. In fact, it was probably much less than that, given that my friend would have chosen a much higher FPR. With FPR=20%, for example, LR=5 and PP=0.5%. In that case, even after increasing BR to a more circumspect 1%, PP would still have been less than 5%.
This is not to justify my friend’s or anybody else’s gullibility. But to conclude that they were all utter dunces or, worse, that the feeders ‘could not have possibly ignored’ who Madoff was, and were therefore in cahoots with him, is wrong. The mistake is caused by a Hindsight Bias: once events happen – Madoff’s fraud is discovered – we tend to ignore the state of knowledge on which prior beliefs were formed. Once we find out that Madoff was a crook, we forget that he was a highly respected professional, and mistakenly conclude that his dishonesty was highly predictable. This is a backward Prior Indifference Fallacy: blinded by the evidence of our discovery, we inadvertently shift our and everybody else’s past priors to 50%. In Madoff’s case, these would have been much better priors. But we can only say so with the benefit of hindsight.
In addition, hindsight makes evidence appear more accurate than it was before the event. As we have seen, starting from a low prior of dishonesty, even a very sceptical view of the split-strike conversion strategy was not enough to conclude that Madoff was a crook. After the event, however, we tend to regard the same evidence as conclusive, and retrospectively drop FPR all the way to zero: there was no way that Madoff would have used that strategy if he were not a crook. It can indeed be argued that a closer look at Madoff’s strategy should have convinced anyone that its FPR was virtually 0%: there was near-perfect evidence that Madoff was dishonest, irrespective of his outstanding reputation. And there is no denying that the prospect of hefty returns and advisory fees made some people’s scrutiny not as diligent as it should have been. But for most people this became clear only with the benefit of hindsight.
The Hindsight Bias follows from the Principle of Sufficient Reason: everything that happens was bound to do so, according to its causes. So, as causes become clear after the event, we erroneously infer that they were as clear before the event, i.e. that there was conclusive evidence that the event was certainly going to happen. Hence the question: Why didn’t we see it? Or rather: Why didn’t they see it – those who were supposed to know: the controllers, the experts, the advisors? The hindsight answer is: because they were negligent, incompetent, irresponsible. Or worse: they knew it all along – how could they possibly ignore it? – and did nothing.
Backward prior indifference, combined with the spurious accuracy of retrospective evidence, make hindsight a particularly powerful bias. This is bad news for decision makers. No matter how well designed their decision process might be, the occurrence of a bad outcome – always a possibility in risky conditions – may be taken as a proof that the process was not well designed.
This might be true: a bad outcome may reveal a flaw in the process – Madoff’s case is a perfect example. But it is wrong to conclude that a process is badly designed because a bad outcome occurred. A good process needs to balance risk reduction with its associated costs. A process aimed at entirely eliminating risk irrespective of costs is not a well-designed one.
Bad processes are easy to design. You want to eliminate road accidents? Impose a 30kph speed limit. You want to eliminate airport threats? Give each passenger a one-hour check. You want to avoid plane crashes? Ban air travel! Just like in hypothesis testing, a well-balanced decision process requires a proper evaluation of the trade-off between False Negatives and False Positives. The higher the cost of a Miss, the higher is our willingness to bear the cost of a False Alarm. But since the latter must have a limit, in most cases the risk of a Miss cannot be eliminated. Planes will crash.
The Hindsight Bias promotes the design of excessively risk averse decision processes. Left to their own devices, decision makers have an incentive to impose a high cost of a False Alarm on others, in order to avoid the cost of a Miss on themselves – including the cost of self-blame and regret. As Baruch Fischhoff, who pioneered the study of the Hindsight Bias, put it:
Consider decision makers who have been caught unprepared by some turn of events and who try to see where they went wrong by re-creating their pre-outcome knowledge state of mind. If, in retrospect, the event appears to have seemed relatively likely, they can do little more than berate themselves for not taking the action that their knowledge seems to have dictated. They might be said to add the insult of regret to the injury inflicted by the event itself. When second-guessed by the hindsightful observer, their misfortune appears as incompetence, folly, or worse. (p. 84)
By skewing the error trade-off towards private risk aversion, the Hindsight Bias can transform risk management into CYA, promoting bureaucracy and inertia against initiative and accountability.
Interestingly, on the other hand, in the same way that a bad outcome does not prove that a decision process was badly designed, a good outcome does not prove that the process was well designed. Again, this might be true: a good outcome may indicate a good process. But it is wrong to conclude that a process is well designed because a good outcome occurred. Just as good decision makers may be wrongly blamed for a bad outcome, bad decision makers may be wrongly praised for a good one. As causes become clear after the event, the question becomes: Why did they see it? And the hindsight answer is: because they were brilliant, talented, prescient. Or better: they knew it all along – sheer genius.
Ultimately, this is also bad news for decision makers. The more they enjoy the praise after a good outcome, the more they will suffer and regret the blame after a bad one. A good decision process cannot be defined by its outcomes. It depends on a clear definition and a balanced attribution of the reward of Hits and the costs of Misses and False Alarms.
