Quantifying Uncertainty

Author: Ron Dembo

Do you know if it will rain tomorrow? Take a guess, yes or no. How certain are you? Would you bet your umbrella on it?

It’s tricky to picture the type of uncertainty we face in life, especially when it’s just one person making a prediction. How can we know whether we’re about to take a big risk or make a fairly safe bet? We could ask 100 forecasters (or their models) to choose among 5 options for a possible tomorrow:

No rain, A few drops, Brief light rain, Rain for a while, Rain all day

And here are their answers tabulated:

To make it easy for people, we tell them: There is a 78% chance of rain tomorrow.

Rather than asking a single forecaster, the above graph gives us a more subtle picture of what could happen: it shows what the majority believe and indicates possible extremes.

Some of us (the risk takers) will risk getting wet. Risk thinkers will hedge their bets and take an umbrella just in case. It is possible they will not need it. On the other hand, it is possible that they will. And that is what uncertainty is all about.

Why We Should Think About Uncertainty as a Distribution

Some forecasters will simply say it will rain, and others will say it won’t. A forecast is simply a single choice of one of these 5 options. It can hide important information behind a single prediction.

That is why our weather channel prefers the statement “a 78% chance of rain” (indicating something about the level of uncertainty) and leaves the decision of what to do about it up to you.

From the above graph, we can clearly see how it is possible to present the uncertainty surrounding a particular risk factor (rain) in a frequency distribution (a spread of future estimates).

Radical Uncertainty

Radical uncertainty is a very wide range of uncertainty, even wider than we have ever seen before. But this speaks to why, when describing uncertainty, we first need to identify what the risk factors are (rain in this case) and then estimate what this distribution will look like at some future point in time, e.g. tomorrow.

Forecasting is simply throwing a dart at this distribution and picking out a single point. Clearly, if the distribution is wide (radical uncertainty), this is a crazy bet and tells us nothing about how to manage the future.

If the distribution varies only slightly from one extreme to another, however, then a forecast could be useful. So therein lies the answer to when forecasting works well: when dealing with tame uncertainty, not radical uncertainty.

But real life gets far trickier when there are multiple risk factors at play in concert with one another. That is when we need to learn how to generate scenarios based on combinations of multiple factors and start learning to strategize as risk thinkers.

Ron Dembo,


Toronto, December 2020.



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