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Impact of developer uncertainty on estimating probabilities
For over 50 years, it has been known that people tend to overestimate the likelihood of uncommon events/items occurring, and underestimate the likelihood of common events/items. This behavior has replicated in many experiments and is sometimes listed as a so-called cognitive bias.
Cognitive bias has become the term used to describe the situation where the human response to a problem (in an experiment) fails to match the response produced by the mathematical model that researchers believe produces the best output for this kind of problem. The possibility that the mathematical models do not reflect the reality of the contexts in which people have to solve the problems (outside of psychology experiments), goes against the grain of the idealised world in which many researchers work.
When models take into account the messiness of the real world, the responses are a closer match to the patterns seen in human responses, without requiring any biases.
The 2014 paper Surprisingly Rational: Probability theory plus noise explains biases in judgment by F. Costello and P. Watts (shorter paper), showed that including noise in a probability estimation model produces behavior that follows the human behavior patterns seen in practice.
If a developer is asked to estimate the probability that a particular event, 
, occurs, they may not have all the information needed to make an accurate estimate. They may fail to take into account some s, and incorrectly include other kinds of events as being s. This noise, 
, introduces a pattern into the developer estimate:
where: 
is the developer’s estimated probability of event occurring, 
is the actual probability of the event, and is the probability that noise produces an incorrect classification of an event as 
or (for simplicity, the impact of noise is assumed to be the same for both cases).
The plot below shows actual event probability against developer estimated probability for various values of , with a red line showing that at 
, the developer estimate matches reality (code):
The effect of noise is to increase probability estimates for events whose actually probability is less than 0.5, and to decrease the probability when the actual is greater than 0.5. All estimates move towards 0.5.
What other estimation behaviors does this noise model predict?
If there are two events, say 
and 
, then the noise model (and probability theory) specifies that the following relationship holds:
where: 
denotes the probability of its argument.
The experimental results show that this relationship does hold, i.e., the noise model is consistent with the experiment results.
This noise model can be used to explain the conjunction fallacy, i.e., Tversky & Kahneman’s famous 1970s “Lindy is a bank teller” experiment.
What predictions does the noise model make about the estimated probability of experiencing 
(
) occurrences of the event in a sequence of 
assorted events (the previous analysis deals with the case 
)?
An estimation model that takes account of noise gives the equation:
where: 
is the developer’s estimated probability of experiencing s in a sequence of length , and 
is the actual probability of there being .
The plot below shows actual event probability against developer estimated probability for various values of , with a red line showing that at , the developer estimate matches reality (code):
This predicted behavior, which is the opposite of the case where , follows the same pattern seen in experiments, i.e., actual probabilities less than 0.5 are decreased (towards zero), while actual probabilities greater than 0.5 are increased (towards one).
There have been replications and further analysis of the predictions made by this model, along with alternative models that incorporate noise.
To summarise:
When estimating the probability of a single event/item occurring, noise/uncertainty will cause the estimated probability to be closer to 50/50 than the actual probability.
When estimating the probability of multiple events/items occurring, noise/uncertainty will cause the estimated probability to move towards the extremes, i.e., zero and one.
Telepathic communication with a Supreme Being
Every year the Christmas cards I receive are a reminder of how seriously a surprisingly large percentage of software developers I know take their beliefs in a Supreme Being.
Surely anybody possessing the skills needed to do well in software engineering would have little trouble uncovering for themselves the significant inconsistencies in any system of beliefs intended to support the existence of a Supreme Being? The evidence from my Christmas card collection shows that some very bright would disagree with me.
This Christmas I have finally been able to come up with some plausible sounding hand waving that leaves me feeling as if I at least have a handle on this previously incomprehensible (to me) behavior.
The insight is to stop considering the Supreme Being question as a problem in logic (i.e., is there a model consistent with belief in a Supreme Being that is also consistent with the known laws of Physics) and start thinking of it was a problem in explaining structure. Love of structure is a key requirement for anybody wanting to get seriously involved with software development (a basic ability to ‘do logic’ is also required, but logic is just another tool and outside of introductory courses and TV shows is vastly overrated).
On the handful of occasions I have spoken to developers about religion (in general I try to avoid this subject, it is just too contentious) things have always boiled down to one of having core belief, a feeling that random is just not a good enough explanation for things being the way they are, while the existence of a Supreme Being slots rather well into their world view.
The human agency detection system has been proposed as one of the reasons for religion; see Scott Atran’s book “In Gods We Trust: The evolutionary landscape of religion” for a fascinating analysis of various cognitive, social and economic factors that create a landscape favoring the existence of some form of religion.
Of course anybody choosing to go with a Supreme Being model has to make significant adjustments to other components of their world view and some of these changes will generate internal inconsistencies. Any developer who has ever been involved in building a large system will have experienced the strange sensation of seeing a system they know to be internally inconsistent function in a fashion that appears perfectly acceptable to everybody involved; listening to users’ views of the system brings more revelations (how could anybody think that was how it worked?) Having had these experiences with insignificantly small systems (compared to the Universe) I can see why some developers might be willing to let slide inconsistencies generated by inserting a Supreme Being into their world view.
I think the reason I don’t have a Supreme Being in my world view is that I am too in love with the experimental method, show me some repeatable experiments and I would be willing to take a Supreme Being more seriously. Perhaps at the end of the day it does all boil down to personal taste.
At the personal level I can see why people are not keen to discuss their telepathic communication sessions (or pray to use one of the nontechnical terms) with their Supreme Being. Having to use a channel having a signal/noise ratio that low must be very frustrating.
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