Trying to think when logarithmic thinking makes sense and why humans might often think like that:
If I am in control of all (or almost all) of my risks then a pandemic where I am only taking a 0 person risk is very different from a pandemic where I am taking a 99 person risk. So moving from 0 to 1 in the presumably-very-deadly-pandemic where I am being super-cautious is a very bad thing. Moving from 99 to 100 in the probably-not-too-bad-pandemic where I’m already meeting up with 99 people is probably not too bad.
So thinking logarithmically makes sense if my base level of risk is strongly correlated to the deadliness of the pandemic. The more sensible route is to skip the step of looking at what risk I’m taking to give me evidence of how bad things are and just look directly at how bad things are.
In the 2 examples you give there are external reasons for additional base risk and these are not (strongly) correlated with the deadliness of the pandemic.
Another explanation for logarithmic thinking is Laplace’s rule of succession.
If you have N exposures and have not yet had a bad outcome, the Laplacian estimate of a bad outcome from the next exposure goes as 1/N (the marginal cost under a logarithmic rule).
Applying this to “number of contacts” rather than “number of exposures” is admittedly more strained but I could still see it playing a part.
This is interesting.
Trying to think when logarithmic thinking makes sense and why humans might often think like that:
If I am in control of all (or almost all) of my risks then a pandemic where I am only taking a 0 person risk is very different from a pandemic where I am taking a 99 person risk. So moving from 0 to 1 in the presumably-very-deadly-pandemic where I am being super-cautious is a very bad thing. Moving from 99 to 100 in the probably-not-too-bad-pandemic where I’m already meeting up with 99 people is probably not too bad.
So thinking logarithmically makes sense if my base level of risk is strongly correlated to the deadliness of the pandemic. The more sensible route is to skip the step of looking at what risk I’m taking to give me evidence of how bad things are and just look directly at how bad things are.
In the 2 examples you give there are external reasons for additional base risk and these are not (strongly) correlated with the deadliness of the pandemic.
Another explanation for logarithmic thinking is Laplace’s rule of succession.
If you have N exposures and have not yet had a bad outcome, the Laplacian estimate of a bad outcome from the next exposure goes as 1/N (the marginal cost under a logarithmic rule).
Applying this to “number of contacts” rather than “number of exposures” is admittedly more strained but I could still see it playing a part.