Another problem with probability is that it always involves fractions, often very small ones. Due to familiarity with decimal coinage, most people understand decimal fractions down to 2 decimal places, but smaller fractions are much harder to understand.
A problem with creating a scale of risk is that many risks are very small; risks of the order of one in a million or less being very common. But few risks are very high, such as one in two. We therefore need a scale that will amplify small risks, so that we can compare small risks in a meaningful way, but still allow us to compare small and large risks. That is why we invented decirisk.
The only way to include all these values is to use a logarithmic scale. The best known logarithmic scale is the decibel scale, but logarithmic scales are also used in photography and elsewhere. The trouble with logarithmic scales is that people tend to interpret them linearly. I will return to this issue later.
One way to achieve these requirements is to use the formula LOG10(P)+10 where P is the probability whose risk we are trying to assess. LOG10 means the logarithm to base 10. This scale goes from maximum 10 downward, without limit. 10 is complete certainty. Every step down is a tenfold decrease in risk, so 9 is a risk of 1 in 10.
If this scale is to be recognised it needs a name. I will call it the decirisk scale. It is named after the decibel scale, but decirisk also implies 'decision about risk'. It will be used to help the public and others assess and take decisions based on risk. The deci part of the name helps us to remember that the maximum value is 10 and that every step is a tenfold change.
Problems with DeciriskThe main problem with decirisk is that people are not used to logarithmic scales.
It is natural to assume that scales are linear, and that steps are equal. In the decirisk scale, going up by 1 means a tenfold increase in risk. The name decirisk should help to remind people of this odd behaviour.
Another possible cause of confusion is that a decirisk of 0 might suggest a probability of 0, whereas it is a small but finite probability of 1 in ten billion. For most practical purposes this is close enough to zero to make no significant difference. However one benefit of the scale is that it can represent any risk, no matter how small. A decirisk of -1 represents a risk of 1 in 100 billion. It turns out the booklet COMMUNICATING ABOUT RISKS TO PUBLIC HEALTH: Pointers to Good Practice, EOR Division, Dept of Health. uses the same idea of a logarithmic scale up to 10, calling it Risk Magnitude. The booklet does not recommend its use by NHS staff, considering it might confuse people. Nor does it use the word decirisk.
I consider that having no quantitative measure of risk is much worse that any possible danger from using decirisk. Without decirisk we have no way of measuring or comparing risk. I recommend decirisk is used widely, so the public becomes used to it and begins to understand the scale of risk.
Other Decirisk pages on the web siteIntroduction to Decirisk