Should precise percentage of odds (of whether something will happen) be treated as nonsense?

June 29th, 2010

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Recently, we saw an article that reported,

There is a 10 percent to 20 percent chance of BP being taken over,? said Gudmund Halle Isfeldt, an Oslo-based analyst at DnB NOR ASA, in an e-mailed note this week.

Whenever we read about analysts stating precise odds about whether certain event will happen (e.g. takeover, interest rates movement), we get very suspicious. How do they come up with such precise percentage? More importantly, are these kinds of precise numbers valid in the first place? If not, why?

To answer this question, let?s go back to the very basics.

Consider the odds of a dice showing up a ?1? on a throw. Obviously, the odds are 1/6. What if you do not know that the dice has 6 sides and instead, incorrectly think that there are only 5 sides on it? In that case, your computation of the odds (1/5) will be wrong. What if, you correctly understand that the dice has 6 sides but instead, do not know that the dice is loaded? In this case, your computation of the odds (1/6) is wrong because the dice is biased.

In both cases, there is a gap between how much you think you know and how much you actually know. The wider the gap, the more wrong your computation of the odds will be. As we quoted Nassim Nicholas Taleb in Failure to understand Black Swan leads to fallacious thinking,

Epistemic arrogance bears a double effect: we overestimate what we know, and underestimate uncertainty, by compressing the range of possible uncertain states (i.e. by reduce the space of the unknown).


I remind the reader that I am not testing how much people know, but assessing the difference between what people actually know and how much they think they know.

Whenever an analyst give such precise percentage for the odds of whether something will happen, he is implying that the gap between how much he actually know and how much he thinks he knows is very small. Perhaps it is true that he is really that knowledgeable. But it is very common for humans to underestimate the size of that gap when it comes to assessing themselves.

In the case of assessing the odds of a corporate takeover that has implications on national interests, perhaps something is happening secretly within the inner recesses of corporate and political machinery? Chances are, if the analyst is privy to the secret happenings, he will have to drastically change his assessment of the odds. If not, his assessment is like assessing the odds of a dice while not knowing it is loaded. When analysts show their confidence by giving such precise percentages, we can?t help but wonder whether he is falling into Ludic Fallacy (see How To Foolproof Yourself Against Salesmen & Media Bias).

For investors, they are at a disadvantage. You see, when assessing the odds of a dice throw, you can easily verify whether your assessment is correct or not (e.g. whether the dice is loaded) by repeating the throw many times and then use statistical analysis to check the results. But what about assessing whether BP will be taken over? Unfortunately, this event, if it happens, will only happen once. That means there?s no way you can verify the analyst?s number. For example, if the analyst said that there?s a 91.32 percent change that BP would be taken over and if that event did not happen, there?s no way you could prove that the analyst got the number very wrong. He could argue that it is due to sheer bad luck that it did not happen.

Thus, whenever analysts give such precise percentage of odds, ponder how big the gap is.

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