The Theory Of Symmetrical Error

Apologies, faithful readers. This is one of my most common rants being recast into yet another guise. However, I felt the need to do it because I think the idea is sound, but I have no convenient label for it. That means I have to explain the idea every time I want to discuss it. Forgive me, but if I write the idea down, and give it a name, at least I can use the name in future and point to this blog as an explanation of what the idea is. So what is the idea? Well, for want of a better name, let us call it the theory of symmetrical error…

My experience suggests that the likelihood of errors in complicated systems, be they human error, system error, errors in data or however you want to categorize errors, is not well correlated to the consequences of those errors. Errors that are easy to commit may have significant consequences. Errors that are highly unorthodox and unlikely to be repeated may have negligible consequences, though be errors all the same. If leakage is the product of a mistake, and not caused deliberately – so I will exclude the impact of fraudulent activity from this analysis – then I believe those mistakes are no more likely to reduce profits than they are to increase them. This symmetry of consequences, and the equal likelihood of consequences on either side, is what I mean by symmetrical error.

Of course, an external party may be vigilantly looking for errors that negatively impact them, in order to protect their own interests. However, the likelihood of discovering the error is not related to the likelihood of committing the error, so this is irrelevant to the point. All the theory concerns is the likelihood of committing an error, not the likelihood of it being found or how hard people look. The probability of committing an error in one direction, and the distribution of the magnitudes of the errors in that direction, is approximately equal to the probability and distribution of magnitudes for errors in the opposite direction. It is approximate because I concede there must be some limits to the symmetry. For example, if a bill should really be stated to be for $x, it is easier to imagine an error where it is instead stated as 2x, 3x, 4x and so forth, and hence x, 2x, 3x over the correct amount, than it is to imagine it is stated as 0, -x, and -2x and hence x, 2x and 3x under the correct amount. Similarly, data may be “lost” at many stages, but may be wrongly created or added to (duplication aside) less often, so there may be some kind of one-sided errors that skew the overall results.

If the theory of symmetrical error is approximately correct, then it has some important conclusions for revenue assurance. First and foremost, if error is symmetrical then revenue assurance, if conducted in an unbiased way, is not an activity that can promise to regularly generate a positive return for the business. It is as likely to reduce business profits as to increase them. The only way to consistently increase profits would be to selectively detect, investigate or resolve errors in one direction, and ignore errors in the other direction. One could assume that external parties will protect their own interests, but in this era where corporate governance is on the lips of so many executives, it might be considered foolish to protect your own interests and play fast and loose with everyone else’s. Secondly, promising skewed results leads to skewed expectations, skewed collection of data, skewed interpretation of that data, and skewed remedial action. In other words, the prophesy of generating financial benefits from revenue assurance is self-fulfilling. If you want to generate positive results, only acknowledge errors that will generate a positive return when resolved; ignore all other errors. This is unhealthy if the interests of customers and partners deserve to be given more than lip service. Third, protecting the interests of the company and protecting the interests of external parties is not fundamentally different. They are both addressed by the same kinds of controls, monitoring and preventative activities, because the errors themselves are essentially alike. The only reason for separating responsibility for executing controls to protect the business from controls to protect external parties is the difficulty, or undesirability, of motivating staff to do both at the same time. Finally, estimates of error fall between two extremes postulated by revenue assurance practitioners. At one extreme, when estimating errors that reduce profits, the average level of error is grossly exaggerated. At the other extreme, when estimating errors that increase profits, because they wrongly overcharge customers, the average level of error is understated by the numbers in the public domain.

I will make two observations to support the theory of symmetrical error.

  1. When settling charges between telcos, whether interconnect, roaming or whatever, any errors in the final settlement must be symmetrical. Whoever “loses”, the other party “wins” by the same amount. It is worth noting that many commentaries on revenue assurance discuss the risk of leakage from inter-telco transactions and treat it as comparable to other kinds of risk of revenue leakage, but fail to highlight the unequivocal zero-sum nature of any errors in these transactions.
  2. Estimates of errors for retail transactions show the greatest divergence depending on the direction. Estimates of revenue loss due to failure to charge customers for transactions, or undercharging of transactions, are high, whilst estimates of the overcharging of customers are low. This result suggests that errors are highly asymmetrical. However, examination of the specific basis used to calculate errors in each direction highlights severe inconsistencies in approach, each selective of what data is used and how it is interpreted. Skewed mechanisms to calculate error in each direction suggests underlying error rates are more similar than the unreconciled headline error rates.

The symmetry of error is not a trivial problem for revenue assurance. If the conclusions are correct, and the revenue assurance profession needs to put its house into order, and admit that it has an equal job to do in both protecting the business and its customers. If the business is at risk, then customers are at risk. If the customers are not at risk, then the business is not at risk. If the conclusions are incorrect, then there is still a job of work to do, in explaining why error is so asymmetrical. Asymmetry should not be assumed, it needs to be shown using consistent data and consistent interpretations and calculations based upon that data. And if asymmetry can be shown, there is still a responsibility to explain why risk is so significantly skewed in one direction. The need for an explanation is made all the more pertinent by the fact that asymmetric error rates would be remarkably convenient for practitioners of revenue assurance. Asymmetric errors reduce the burden for protecting customers and guarantee overall financial returns for the business. Any good scientist should be wary of theories that give results that also coincide perfectly with their own interests. Because asymmetry would be so very convenient, revenue assurance needs to apply a higher standard if it is to conclude that errors tend to be asymmetric.

This is the theory of symmetrical error, if you will. I know it is not a very scientific exposition, but then revenue assurance is not a very scientific discipline. Sciences need to start somewhere. This would be a good place if revenue assurance is going move on from making promises to explaining how they are kept.

Eric Priezkalns
Eric Priezkalns
Eric is the Editor of Commsrisk. Look here for more about the history of Commsrisk and the role played by Eric.

Eric is also the Chief Executive of the Risk & Assurance Group (RAG), a global association of professionals working in risk management and business assurance for communications providers.

Previously Eric was Director of Risk Management for Qatar Telecom and he has worked with Cable & Wireless, T‑Mobile, Sky, Worldcom and other telcos. He was lead author of Revenue Assurance: Expert Opinions for Communications Providers, published by CRC Press. He is a qualified chartered accountant, with degrees in information systems, and in mathematics and philosophy.