Shorrock’s Law of Limits

David Manheim
May 25, 2018 · 3 min read

I recently saw an interesting new insight into the dynamics of over-optimization failures stated by Steven Shorrock; “When you put a limit on a measure, if that measure relates to efficiency, the limit will be used as a target.” This seems to be a combination of several dynamics that can co-occur in at least a couple ways, and despite my extensive earlier discussion of related issues, I think it’s worth laying out these dynamics along with a few examples to illustrate them.

When limits become targets

First, there is a general fact about constrained optimization that, in simple terms, says that for certain types of systems the best solution to a problem is going to involve hitting one of the limits. This was formally shown in a lemma by Dantzig about the simplex method, where for any convex function the maximum must lie at an extreme point in the space. (Convexity is important, but we’ll get back to it later.)

When a regulator imposes a limit on a system, it’s usually because they see a problem with exceeding that limit. If the limit is a binding constraint — that is, if you limit something critical to the process, and require a lower level of the metric than is currently being produced, the best response is to hug the limit as closely as possible. If we limit how many hours a pilot can fly (the initial prompt for Shorrock’s law,) or that a trucker can drive, the best way to comply with the limit is to get as close ot the limit as possible, which minimizes how much it impacts overall efficiency.

There are often good reasons not to track a given metric, when it is unclear how to measure it, or when it is expensive to measure. A large part of the reason that companies don’t optimize for certain factors is because they aren’t tracked. What isn’t measured isn’t managed — but once there is a legal requirement to measure it, it’s much cheaper to start using that data to manage it. The companies now have something they must track, and once they are tracking hours, it would be wasteful not to also optimize for them.

Even when the limit is only sometimes reached in practice before the regulation is put in place, formalizing the metric and the limitation means that it becomes more explicit — leading to reificiation of the metric. This isn’t only because of the newly required cost of tracking the metric, it’s also because what used to be a difficult to conceptualize factor like “tiredness” now has a newly available albeit imperfect metric.

Lastly, there is the motivation to cheat. Before fuel efficiency standards, there was no incentive for companies to explicitly target the metric. Once the limit was put into place, companies needed to pay attention — and paying attention to a specific feature means that decisions are made with this new factor in mind. The newly reified metric gets gamed, and suddenly there is a ton of money at stake. And sometimes the easiest way to perform better is to cheat.

So there are a lot of reasons that regulators should worry about creating targets, and ignoring second-order effects caused by these rules is naive at best. If we expect the benefits to just exceed the costs, we should adjust those expectations sharply downward, and if we haven’t given fairly concrete and explicit consideration to how the rule will be gamed, we should expect to be unpleasantly surprised. That doesn’t imply that metrics can’t improve things, and it doesn’t even imply that regulations aren’t often justifiable. But it does mean that the burden of proof for justifying new regulation needs to be higher that we might previously have assumed.

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