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:

Paddleboarding on Tamaki Drive

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?

Share this


  1. Resilience used as big argument for NZTA for the Western Ring Route. However thats assumes new WRR will be rather empty, which is very hard to believe. I suspect that while the WRR may function has useful diversionary route for a couple of years if their is incident on CMJ/Harbour Bridge. However the WRR itself will soon become congested, so incident on central motorways, will just lead to WRR quickly jamming up, and we will be no better off.
    Resilence is quite a different matter for provincial state highways, often where the diversionary route can be hours longer, and closures for days, weeks or even months are not unheard of, rather than hours in Auckland’s case.
    NZTA talk as if resilience is the same in these two cases, when it clearly is not.

  2. We could make our communities a lot more resilient by making them denser and more walkable. Walking is the pinnacle of resilient transport (provided you haven’t designed your city around some crazy walking bottle neck – like a single bridge) because there’s very little that can remove a large number of people’s ability to walk, whereas all motor transport methods are going to be at least semi vulnerable because they typically rely on dedicated corridors (motorways, rail lines, etc).

    1. Good point, I was in Wellington for the Seddon earthquakes 2 years ago and was amazed at how fragile the transport system is. Roads were closed, traffic was gridlocked and with trains cancelled many people were stranded in the CBD. However my bike ride home took the same amount of time as always.

  3. There’s lies, damned lies and statistics.

    But I can confidently predict, with 100% certainty, that if a second harbour crossing is built, it and the existing Bridge will be tolled.

    And as a result the North Shore residents will collectively pay more than $42m *a year* in tolls to have this second crossing in place.

    Therefore the expected benefits massively outweighs the cost, by at least a factor of 40 to 1.

    And if a volcanic event can take out the harbour bridge, its just as likely to take out or damage the tunnels nearby.
    Either through direct eruption/explosion through the tunnel or via the seismic activity of said eruption shaking the sh*t out of the existing tunnel causing leaks and floods galore.

    1. “But I can confidently predict, with 100% certainty, that if a second harbour crossing is built, it and the existing Bridge will be tolled.”

      I am equally confident that any tolls collected will not repay the full cost of the crossing. Tolls on duplicate roads simply don’t collect enough money.

  4. Resilience is a buzzword along with sustainability, neither one being carefully defined but are understood in a very general way. We’re at a place, though, where it would be difficult to *not* build something that isn’t resilient and sustainable, by some definition or other.

    As for the “people” being inconvenienced, they don’t give a fig about a $42 million dispersed impact. All they care about is their personal $30,000 impact and to save that they will pay a fair amount of money. (People never think of themselves as a small part of a risk pool.)

    I wouldn’t look to paddle-boarding and dog sleds to solve much of the problem, though.

    1. “All they care about is their personal $30,000 impact and to save that they will pay a fair amount of money.”

      Two corrections: First, the expected value of the impact on the average Shore-ite (under these assumptions) is $300 ($30,000*1% likelihood), not $30,000. And second, the option available to them to mitigate this risk is to advocate for other people to pay a lot of money.

      1. And also, if I’ve understood the made-up numbers, that would be $300 spread over a 40 year period (the time frame of assumed 1% chance of eruption).

      2. You said “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.)”

        So their income *would be* reduced by $30,000 if the bridge was out. In this case, both conditions are met – the person *does* lose $30,000, and the bridge *is* out, not maybe out – so the reduction for that person is $30,000.

        If you add a probability factor, which that statement does not, everyone is possibly affected and no one is doing a CBA to find out what the expected value of his income loss will be. Theoretically it’s $300 (which won’t be acceptable anyway), but no one pays theoretical money to the bank on their mortgage.

        I understand the method for policy analysis purposes, but it’s not not useful for mitigation of actual costs.

        1. I’m not sure if I understand your point. People regularly make rational decisions about how much to spend to insure themselves against low-probability events. For example, home insurance. A catastrophic house fire would definitely be a high-impact event – it would put you out of pocket for hundreds of thousands of dollars. But people don’t pay hundreds of thousands for home insurance, because the likelihood of a house fire is very small.

          I would argue that it is logical to treat duplicating infrastructure for “resilience” purposes the exact same way. Under the assumptions I’ve made above, there is a 99% probability that people who normally commute over the bridge suffer zero income loss. The 99% probability of no impact whatsoever far outweighs the 1% chance of a large impact, no matter how you slice it.

  5. There’s this current NZTA research tender too (titled ‘Research to establish a consistent approach to transport’ which is maybe missing the R-word):

    “This research seeks to improve the quantification of benefits from changing transport system resilience (with potential application to other infrastructure or community sectors). This seeks to improve consistency on prioritising resilience both across the transport sector and across transport outcomes.

    Resilience can be defined as the availability and restoration of an acceptable social and economic level of service when there is an unplanned disruptive event. Resilience may include providing a reduced level of service through alternative routes or informing users of other transport choices. Disruptive events range from congestion arising from transport incidents to a complete loss of access. For roads, the One Network Road Classification defines resilience according to road function using customer levels of service, technical performance measures and targets.”

    1. Yeah, I’d noticed that tender! Hopefully something interesting comes out of it.

      One thing I’d definitely recommend to anyone researching the value of resilience is to do some surveying to establish how risk-averse people are – i.e. to what extent they are willing to pay “above the odds” to avoid a small chance of a negative outcome. The cost-benefit analysis literature is generally lacking on good studies of personal risk-aversion.

  6. Also, you need to discount the future cost. There is a 1/4000 chance in year one + a 1/4000 chance in year 2 etc. The costs in later years will be discounted to get your NPV.

    But yes your example illustrates what I have always thought – the NPV of low probability events disrupting transport networks is generally going to be fairly small. So, I think we can all agree it is a way of justifying uneconomic projects.

    Earlier this year Wellington was cut off, and proponents of TG pointed to this event as being evidence for the need for TG. Except that sky didnt fall in, which is what would need to happen to justify the cost.

    1. And as I recall TG, had it been open, would have about as badly affected as all the other routes by the Wellington floods at the Wellington end (if not the other end as well).
      So the “resilience” argument simply doesn’t hold water for TG or AWHC.

      As for building resilience – GNS has reviewed the likely damage from the next Main Alpine Fault earthquake, they now say its has at least a 30% likelihood in the next 50 years.
      [the more research they do on the Alpine fault, the bigger that percentage gets].

      And when it does hit most roads to/from and some up and down the West coast will have extended closures due to slips and rail and road bridge damage. Including all the 3 passes (Haast, Arthurs and Lewis). The one route they predict that will remain least damaged and could be opened again quickly is the route down to Westport/Reefton from Nelson. So GNS recommend that local councils and NZTA on the West Coast collectively put time and effort into making that route more resilient and to pre-stage repair equipment along the route to aid recovery.

      Of course, NZTA would rather fritter its money and resources on studies of road tunnels under the Waitemata harbour or PPPs in Wellington than deal with these sorts of real issues.

      Yes, the West Coast and SI in general is less populated than those other places, but has a big economic contribution in dairy and tourism related “exports” and also to the rest of NZ via the main electricity grids that run up the eastern side of the main divide.

      Any disruption to the 3 east/west pass roads will have a severe impact, including on the main electricity grids, and lack of roads will hamper speedy restoration of power supplies.
      So yes even the folks in the NI will be impacted by that.

      And this isn’t some future fantasy prediction, its gonna happen, and it will be sooner than later, and will be bigger than all the Christchurch quakes combined both physically and economically. And when it does, that’s when true resiliency of the transport and other networks will be tested.

      1. “GNS recommend that local councils and NZTA on the West Coast collectively put time and effort into making that route more resilient and to pre-stage repair equipment along the route to aid recovery.”

        Thanks for pointing this out. One thing that this recommendation suggests, to me at least, is that investing in disaster preparedness can be a good way of improving resilience. Resilience isn’t necessarily about bits of concrete and steel – it’s about the ability of society and the economy to work around events.

        Look at the Christchurch earthquakes. Building more roads prior to the quakes wouldn’t have helped the city’s resilience – they would have been munted, same as the rest. But investments in civil defense, emergency food distribution networks, and temporary accommodation would have been really useful.

    2. Yes, you’re correct. I avoided doing that in the interests of simplicity – talking about expected value is hard enough without mixing in discounting the future!

      Some quick calcs indicate that the discounted present value would be around 40% of the value I’ve calculated here. So more like $17 million.

    1. Ahh, but NZTA will say “we won’t paying to have it reopened – as we only pay when TG its open and usable” [well in theory anyway]!

      And no doubt the PPP provider has a “Force Majeure” clause in their contract meaning when it is knocked out by an “act of God” e.g. the big quake or flood, well its not their fault either to fix it, so NZTA should pay them while they fix it.

      So it will all end up in the courts in due course. More wasted money down the drain.

      1. True, following the quake that knocks tmg out it could remain closed for ages while they haggle over who pays for it.

      2. Full details of the contract are not available, but the available documents indicate that payments to the private financiers will be linked to the “availability” of the road. I.E. if the road’s not open, they’re not getting paid.

        Here’s what the NZTA’s Q&A document had to say on the matter:

        “The NZTA will use an availability and performance-based contract, which means the PPP consortium will be paid for making the road available to traffic when they have achieved specified performance levels. Payments are not linked to the volume of traffic using the road. An availability PPP contract is more attractive to potential consortium partners as it removes demand risk. As a result, availability contracts offer greater potential of delivering value for money for the government.”

  7. The term Resilience has risen to prominence for 2 reasons:
    1. The current government effectively banned the use of the term Sustainability, believing it to represent things they consider dangerously radical rather than simply meaning the more conservative ‘able to be sustained’. Resilient is sort of synonymous to Sustainable but without the fearful Green tinge.
    2. As the justification for the otherwise unjustifiable by traditional economic evaluation processes; projects like Transmission Gully and AWHC. Things they passionately want to spend our money on for reasons obscure, or at least not very convincing; like gut feel.

  8. “people are risk-averse and as a result may be willing to pay “over the odds” to avoid low-probability events”

    And yet, people throw their risk-aversion to the wind each time they take to the roads in cars. Statistically, road accidents represent the biggest risk of harm that most people will face throughout their prime years, but do we see this factor influencing their decisions on travel? No.
    Yet one can imagine these same people running a mile from a building deemed to be an earthquake risk”, despite the probability of a severe earthquake any time soon being extremely low. Or panicking about the presence of a little asbestos, even though the risk of minor exposure is low. Or becoming regular smokers or drug-users even though the risk to long-term health is high.

    Risk-aversion is a selective thing, a perceived thing, often bearing little relation to the actual or statistical risk, It is easily talked up or talked down by the mass media, and readily seized on by crowds climbing onto bandwagons. It is driven more by panic/hysteria or apathy/denial than by dispassionate and rational thinking.

  9. Hi all. New to this – but thought I’d add my 2 cents.
    With the degree of ‘unknowability’ around most hazards, IMO a far better spend is to invest in early discovery (if possible) and fast recovery from a failure / emergency… and also look to design for ‘safe-failure’ within systems. To try and make a cost-benefit analysis stack up for a massive capital outlay to mitigate a potential rare event is simply too fraught.
    What ‘safe-failure’ actually means in practice would be an interesting thought experiment…. This guy Dave Snowden delves into the differences between risk-based approaches and ‘resilience’ and touches on these other ideas too. Its worth a watch if you’re into the academic side of things: https://www.youtube.com/watch?v=2Hhu0ihG3kY

  10. I’m willing to bet $100 of my own money the expected value of a volcano in Auckland exceeds Mr Nunn’s projections (probably by an order of magnitude…)

    PS you do realise that $42m is an annualised figure (just like an insurance premium). So multiply 42m by the lifetime of the bridge (50 years?) to get the amount you’d be willing to spend.

    1. Yes, the total impact of an eruption could obviously be higher, as I haven’t accounted for damage to anything _but_ the bridge. But that’s irrelevant for an analysis of resilience benefits, as an additional harbour crossing wouldn’t do anything to protect homes and businesses from volcanic activity.

      I’d like to propose a variation to your bet. Rather than speculating about events that probably won’t happen within our lifetime, let’s ask about the last natural disaster to strike NZ. So: How much of an impact do you think the Canterbury Earthquakes had on New Zealand’s GDP? They were pretty major – do you think they reduced GDP by $1 billion? $5 billion? $500 million? What’s your estimate?

      1. If I play the GDP game and ignore all utility loss through non-monetary activities (as an economist you realise money is only one small proxy for utility 😉 )

        Canterbury GDP (RNA) grew from 13.13bn in 2000 to 22.59bn in 2008, an increase of 72% in 8 years or an average year-on-year increase of about 7% compounding.

        Canterbury GDP (RNA) then grew from 22.59bn in 2008 to 23.83bn in 2010 or 5.5% in 2 years… 2.7% growth.

        If we assume without the earthquake that Canty GDP RNA would have grown at the same speed…it would have been 25.86bn in 2010 so roughly a 2bn loss 🙂

        1. Wrong. The correct answer is “no measurable effect on the national economy”.

          A new paper (working paper version available here) has estimated the macroeconomic effects of the Canterbury earthquakes using vector autoregression modelling.

          The author’s conclusion is as follows: “In short, we conclude that the Christchurch earthquake had no real observable macroeconomic impact at the national level, even with a horizon of several quarters (to Q1 2013).” They comment further: “Another important factor that may explain why the Canterbury earthquakes had a mild economic impact at the national level is the degree to which the direct damages were insured. The Canterbury disaster is unusual, from an international perspective, as about 80% of damages were insured. For most other disasters in high-income countries, the insurance coverage is around 20%-50%.”

          I’d draw three conclusions. First, any negative regional impacts were cancelled out by increases elsewhere, or adjustments within the region. Second, the true cost of the earthquakes isn’t monetary, but related to deaths and suffering for affected people. Third, insurance policies or centralised disaster relief funds work as a solution to low-probability, high-impact events.

        2. I have no doubt that the analysis you quote is absolutely correct, but a useful analogy to remember might be that the German economy *grew* during 2+ years of strategic bombing in WW2.

          That is, if an action that would be otherwise harmful stimulates a growth response (the “Dragon in the Shire Effect”) the overall effect of the harmful action may not APPEAR to be harmful. Thus the Canterbury rebuild.

          Peter, from an “economic impact analysis” perspective, would dropping $1m in dollar bills from a helicopter hovering over Aotea Square be beneficial?

        3. And PS I only looked at the Canterbury GDP. Not national. Displacement effects obviously occur.

        4. Also, your analysis period (a) pre-dates the earthquake and (b) coincides with the impact of the GFC. So I think what you are actually saying is that “if the GFC didn’t happen the NZ economy would be larger”, which is a statement I fully agree with.

    2. If Auckland gets a large to very large eruption it would be a write off. The city could be buried in a layer of ejecta five or ten metres deep. We don’t have the industrial capacity to remove that amount of anything… we’d all better just move 100km down the road.

  11. If we kill 1 person a day on the roads what do we need to spend to get that to nil per day?
    Are we prepared to do that?
    How likely is ti to be me that is killed?

  12. Ability to deal with unexpected events is resilience!
    We used to have Bailey Bridging stored at various points around NZ for ease of deployment. My understanding is that was all disposed of in the mid 1080’s, did that reduce our ability to be resilient?
    We used to have MWD who were usually first responders to most road disruption with depots spread around the regions they have gone and I wonder what has taken their place?

  13. Well that’s interesting – I didn’t realise that the Bailey Bridges were disposed of as part of the possum control programme !

    Here’s a question: would the resurrection of some vehicular ferry services be a more effective and economic resilience solution than a second harbour crossing ? How about Mechanics Bay to Devonport near the Naval Base entrance (using the redundant RORO ramps), or Island Bay to Te Atatu?

  14. The NZTA current obsession with (re)roading has nothing to do with “resilience” or “safety” -that is just a lie the NZTA told you that you are believing.
    The govt/NZTA use the inception word “disasters” so you let foreign owned corporations build more unnecessary & expensive roading why they tell you about austerity . To pull off this brain washing they use peoples fear of disasters (fear which then shuts off the critical thinking process).

Leave a Reply

Your email address will not be published. Required fields are marked *