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Steve Hoy

Coin Tossing

Understanding the difference between risk and uncertainty should lead to more careful thought about the consequences of our decisions, including that outcomes will be unknowable most of the time. This can be hard to accept, especially in Business.

Often in business we are asked for our opinion on the odds of something happening, and we may be tempted to say “I’m 90% sure x will happen” or some-such. But what does this mean? Have we carefully determined all possible outcomes and after detailed analysis assigned probabilities to each? More likely this is just an opinion where we really mean “I’m nearly certain x will happen”. But putting a number on a possible outcome obscures more information than is revealed. Without the underlying analysis this sort of number is very likely to mislead.

"Probabilities disguise uncertainty in a way that obscures more useful information" Barack Obama

Risk & Uncertainty

In a 1921 paper, Risk, Uncertainty, and Profit, Frank Knight defined uncertainty as a lack of knowledge which is immeasurable and impossible to calculate. This is called (in economics) Knightian Uncertainty, the kind of distinction economists love to make; taxonomies of uncertainty to assign probabilities and probability density functions to try to measure it. This is par for the course with economists in general, who tend to believe everything in their social ‘science’ can be expressed as a number; economics has a very bad case of Physics Envy. Frank Knight had a different view, which I think is useful.

When the probabilities of all possible outcomes are known (such as when tossing a coin or throwing a dice), we call it Risk. Where the randomness of outcomes cannot be expressed in terms of specific probabilities we call it uncertainty.

Tossing a coin is less random than we think

When we toss a coin we’re trying to fairly and randomly choose something. But tossing a coin does not create a random outcome; in fact, a coin toss is governed by the laws of mechanics and is fully deterministic. For example it is possible to build a machine to consistently toss a coin so that the outcome is certain every time.

Where we get fooled is by the abstraction of probability. In a probabilistic sense a fair, two-sided coin of zero thickness will come up heads or tails with 0.5 probability. However, when we toss a coin, we use an analogue of the theoretical and perfectly fair random process in which uncertainty is introduced by the human factor. Chaos is added by the variations between coin tosses by humans. These are known unknowns (we know what the factors are but we cannot yet measure them or decide how much weight to give to each). We know the mechanical process can be manipulated, so we have rituals to guard against the skilled coin-tosser:

  • One to toss, the other to call.
  • The toss before the call: The tosser flips the coin and slaps their other hand on top of the coin so that the caller can observe the toss before choosing (and maybe dispute a dubious flip).
  • The toss after the call: the caller calls and then the coin is tossed and allowed to fall to the ground and bounce around. (Sporting events may get a child to do this on the basis that children have less guile and skill, and presumably little invested in the outcome of the toss. Also good publicity, possibly).

So in this Laws of Physics view, the coin toss is not random, but there are so many variables it might as well be in practice. It is the introduction of uncertainty which makes a deterministic, mechanical process become sufficiently random. Risk is the 50/50 bit, uncertainty is the chaos.

Understand what is actually going on

Tossing a coin is suitably unpredictable for decisions where the outcomes are equivalent, such as how to have your eggs for breakfast, or which player gets to serve first. On the other hand, where the outcome is material we want a bit more thought than just flipping a coin. A careful study of random phenomena is truly difficult, and Decision Theory has many heuristics to assist, but in business there are so many variables and uncertain factors that assigning probabilities is mostly futile.

Many disputes between people boil down to the meaning of words, so for this blog I thought I'd set out what I mean when I use "Risk" and "Uncertainty".

Things we take for granted can be more involved than they seem. Next I’ll talk a little about Physics Envy; vain attempts to quantify the unknowable.