A few months back, I took a critical look at some dodgy arguments about the need for expensive security measures for cities to be “resilient” against terrorism. The whole thing got me thinking: how should we value protection against low-probability events?
This is quite relevant to transport policy at the moment. I’ve seen a number of references to resilience in discussions of major transport projects:
Today’s official construction start on the Transmission Gully Motorway marks a major step towards a safer and more resilient transport link in and out of Wellington.
In 2013 the Government announced its support for a tunnel in preference to a bridge. “With increasing demands on Auckland’s transport network, the Government will continue to work closely with its local government partners to provide a resilient network and wider transport choices,” Mr Bridges says.
But while resilience seems like a good thing, it seems to be more of a slogan than a careful piece of analysis. The whole discussion sometimes reminds me of this commercial featuring my favourite B-movie star, Bruce Campbell:
“If you have it, you don’t need it. If you need it, you don’t have it. If you have it, you need more of it. If you have more of it, you don’t need less of it.”
But is more resilience always good? Do we need more of it? Or do we already have too much of it? And how would we know?
First, it’s worth defining “resilience”. According to Mirriam-Webster dictionary, resilience means
the ability to become strong, healthy, or successful again after something bad happens
In transport, resilience seems to be defined as the ability to respond flexibly to unlikely or low-probability events. For example, here’s a picture of Tamaki Drive during some floods back in April 2014.
Tamaki Drive isn’t built with a massive barrier against the sea, so when a tropical cyclone hit the North Island, things got wet. Drivers were able to get home using other roads further up the hill, but it took much longer than usual. But, as this gent on a paddleboard shows, individuals came up with a range of innovative solutions to the short-term outage:
So with that in mind, how should we value our ability to be resilient to low-probability, potentially high-impact events?
One approach would be to calculate the value of resilience using actuarial techniques. Now, I’m not an actuarial scientist, but I’ve worked with people whose job it is to assess financial risks and picked up a few concepts in the process. An actuarial assessment of risk is conceptually pretty simple. It involves:
- Calculating the impact (i.e. net cost) of a given adverse event,
- Calculating the likelihood (i.e. probability over a given time period) of that event, and
- Multiplying the two together to obtain the expected value of protecting yourself against that risk.
So how does this work in practice. Suppose we’re dealing with a hypothetical case – the Auckland Harbour Bridge example mentioned above. Let’s say that we’re interested in making Auckland “resilient” against volcanic activity knocking out the existing bridge. So let’s make up some figures, and assume that:
- If the bridge was destroyed, it would take 1 year to get another one in place
- There are around 140,000 working people who live north of the bridge. Let’s assume that those people earn an average of $60,000 annually, and, furthermore, that their income would be reduced by 50% if the bridge was out. (Either due to reduced employment or increased cost and inconvenience of longer commutes around the Western Ring Route.)
- The Auckland volcano field has erupted at least 53 times, and the first eruption occurred around 248,000 years ago. This implies that we can expect one eruption every ~4,000 years, on average. So there’s perhaps a 1% chance that an eruption happens within the next 40 years.
Let’s be generous and assume that the next volcano will definitely destroy the existing bridge while leaving an adjacent crossing untouched. Multiplying these figures together, we find that the actuarial value of a second, volcano-proof harbour crossing is: (1 year outage)*(140,000 workers)*($60,000/year)*(50% loss in income)*(1% probability of volcano) = $42 million.
Frankly, that’s not a lot of benefit compared with the cost of a new harbour crossing. This is obviously a rather crude hypothetical example, but so far it doesn’t look like we should place that much weight on resilience to low-probability events. Even if we made a higher estimate of the cost of a bridge-destroying natural disaster, it wouldn’t change the outcome very much as a disaster probably won’t happen within our evaluation period.
However, there are some other factors at work. The first is that people are risk-averse and as a result may be willing to pay “over the odds” to avoid low-probability events. (The existence of profits in the insurance industry is good evidence for this hypothesis – people usually pay more for insurance than insurance companies pay out in claims.)
Returning to the Auckland Harbour Bridge hypothetical, it might be the case that Aucklanders, especially those living on the North Shore, are happy to pay more than $42 million to avoid the unlikely outcome of a volcano cutting one link to the shore. But how much more?
It’s hard to say without data, but I suspect that while people might be willing to pay (say) 20% or 50% above the odds, they wouldn’t be willing to pay 1,000% more. This is probably a productive angle for research, possibly with surveys or psychological studies.
A second factor at work is that we might not be able to accurately predict the likelihood or impact of some events. Nassim Taleb popularised the concept of “black swan events“, which should really be called “white swan events” in Australia and New Zealand. He points out that we often lack a good understanding of the statistical distribution of risks. This can be due to the fact that some events are outside the range that we have previously observed, or due to the fact that there can be a bunch of hard-to-predict indirect impacts in complex systems.
I’m not going to deal with the probability distribution issue that Taleb raises – I’m not a risk expert! – but I’d like to come back to the point about indirect impacts in a later post. Essentially, as the paddle-boarder on Tamaki Drive shows, people have a lot of different ways to react to a transport outage, so the net cost may actually be lower than we might initially assume.
How do you think we should value resilience in our transport system?