May 19 2022

The Linear Bias

Having a working understanding of the biases and heuristics that our brains use to make sense of the world is critical to neuropsychological humility and metacognition. They also help use make better sense of the world, and therefore make better decisions. Here’s a fun example. Let’s say you increase your driving speed from 40 mph to 60 mph over a 100 mile journey. How much would you need to increase your speed from a starting point of 80 mph in order to save the same amount of time on the journey? Is it 100 mph or 120 mph?

Many people follow the linear bias, the false assumption that most systems follow a linear path. It is an interesting question as to why this bias is so deeply rooted in human psychology, but research shows that it is. Others may follow the ratio heuristic, and consider that 60 mph is 50% more than 40 mph so you would have to increase your speed to 120 mph to get the same 50% increase. But this too is wrong. The real answer is 240 mph. Do the math for yourself. While the ratio heuristic seems more reasonable, in this context it fails because you are not considering the fact that at higher speeds the overall trip time is less and therefore the potential time saving is also less.

When the linear and ratio biases are applied to time, in fact, psychologists refer to this as the time-saving bias. We tend to underestimate how much time we can save when starting at a slow speed and vastly overestimate time saving when starting at a relatively high speed. This bias applies to more than just driving, but also to any task. We feel that if we push our speed or efficiency higher, there will be substantial gains, but there usually isn’t. At the same time, we need to realize that bottlenecks where speed is very low present an opportunity for significant increases in efficiency. We know this, but we still tend to underestimate its effects, especially relative to increasing already high speeds.

So in any operation, whether driving on a journey, completing a task at work, or maximizing the efficiency of a factory, it is best to focus on the slowest components. There is significantly diminishing returns when improving already fast processes, and they are probably not worth it.

While driving, for example, speeding does not make sense from a risk-benefit consideration. Speeding means you are going over the speed limit, which is already reasonably fast, so that time saving is actually negligible. Going from 60 to 80 mph on a 10 mile commute would save you 2.5 minutes, and increasing further to 90 mph saves you a further 54 seconds. For that you are risking a costly and time-consuming ticket, burning more gas, and risking an accident.

Similarly, squeezing more work out of already fast-working employees may have diminishing returns not worth the effort and increased stress that would be necessary.

The linear bias creeps up in many other ways as well. When thinking about the course of future technology or society there is a tendency to extrapolate linearly into the future. But trends are rarely linear. Technically this must be true because “linear” is mathematically a special case in which change is exactly equal over equal increments of time. But even if allow for some mathematical wiggle room, trends are rarely even roughly linear. A dramatic example of this is Moore’s law regarding the number of transistors per area on a microchip, translating into an approximate doubling of computer capabilities every 18 months to 2 years. This is a geometric progression. Not all technologies follow this extreme trend, but overall it may be a better first approximation than a linear assumption.

On the other side, the problems we are attempting to solve are often not linear either, they become increasingly difficult as we try to push advances further and further. We ran into this with speech recognition technology, and are having the same experience with self-driving cars. Any attempt to increase efficiency will also experience diminishing returns, both in the benefits and the efforts necessary to make progress. Going from 80-90% efficiency may be orders of magnitude easier than going from 90-95% efficiency, which also has less benefit. In the last two decades commercial solar panels improved roughly from 10 to 20% efficiency. Now we are trying to push further, to a theoretical maximum for silicon of about 30%. This is proving more difficult, but also would have less relative benefit.

Practically speaking we need to be aware of the linear bias, and how that translates in different contexts, including the time-saving bias. When we decide where to put our efforts, and make risk/expense vs benefit calculation, this can have a huge impact. It always makes sense to focus on the low-hanging fruit – tackle the easiest problems first, and the ones that will have the biggest effect. For example, while I favor the eventual phasing out of all fossil fuels for various reasons I have explored in detail previously, I also have to acknowledge that going from coal burning to natural gas has more benefit than going from natural gas to renewables. Coal is the low-hanging fruit, with the greatest harm from pollution. Phasing out coal would have more benefit than any other change we can make to the energy infrastructure, and should therefore have the highest priority. (Yes, I know methane is a powerful GHG and has to go as well, I am not underestimating how bad natural gas is, just don’t underestimate how much worse coal is.)

Metacognition is critical to thinking accurately and making good decisions – and the linear bias is just one of many.

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